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1 #
2 # This file is the units database for use with GNU units, a units conversion
3 # program by Adrian Mariano adrianm@gnu.org
4 #
5 # September 2020 Version 3.09
6 #
7 # Copyright (C) 1996-2002, 2004-2020
8 # Free Software Foundation, Inc
9 #
10 # This program is free software; you can redistribute it and/or modify
11 # it under the terms of the GNU General Public License as published by
12 # the Free Software Foundation; either version 3 of the License, or
13 # (at your option) any later version.
14 #
15 # This program is distributed in the hope that it will be useful,
16 # but WITHOUT ANY WARRANTY; without even the implied warranty of
17 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 # GNU General Public License for more details.
19 #
20 # You should have received a copy of the GNU General Public License
21 # along with this program; if not, write to the Free Software
22 # Foundation, Inc., 51 Franklin Street, Fifth Floor,
23 # Boston, MA 02110-1301 USA
24 #
25 ############################################################################
26 #
27 # Improvements and corrections are welcome.
28 #
29 # Fundamental constants in this file are the 2018 CODATA recommended values.
30 #
31 # Most units data was drawn from
32 # 1. NIST Special Publication 811, Guide for the
33 # Use of the International System of Units (SI).
34 # Barry N. Taylor. 2008
35 # https://www.nist.gov/pml/special-publication-811
36 # 2. CRC Handbook of Chemistry and Physics 70th edition
37 # 3. Oxford English Dictionary
38 # 4. Webster's New Universal Unabridged Dictionary
39 # 5. Units of Measure by Stephen Dresner
40 # 6. A Dictionary of English Weights and Measures by Ronald Zupko
41 # 7. British Weights and Measures by Ronald Zupko
42 # 8. Realm of Measure by Isaac Asimov
43 # 9. United States standards of weights and measures, their
44 # creation and creators by Arthur H. Frazier.
45 # 10. French weights and measures before the Revolution: a
46 # dictionary of provincial and local units by Ronald Zupko
47 # 11. Weights and Measures: their ancient origins and their
48 # development in Great Britain up to AD 1855 by FG Skinner
49 # 12. The World of Measurements by H. Arthur Klein
50 # 13. For Good Measure by William Johnstone
51 # 14. NTC's Encyclopedia of International Weights and Measures
52 # by William Johnstone
53 # 15. Sizes by John Lord
54 # 16. Sizesaurus by Stephen Strauss
55 # 17. CODATA Recommended Values of Physical Constants available at
56 # http://physics.nist.gov/cuu/Constants/index.html
57 # 18. How Many? A Dictionary of Units of Measurement. Available at
58 # http://www.ibiblio.org/units/
59 # 19. Numericana. http://www.numericana.com
60 # 20. UK history of measurement
61 # http://www.ukmetrication.com/history.htm
62 # 21. NIST Handbook 44, Specifications, Tolerances, and
63 # Other Technical Requirements for Weighing and Measuring
64 # Devices. 2011
65 # 22. NIST Special Publication 447, Weights and Measures Standards
66 # of the the United States: a brief history. Lewis V. Judson.
67 # 1963; rev. 1976
68 # 23. CRC Handbook of Chemistry and Physics, 96th edition
69 # 24. Dictionary of Scientific Units, 6th ed. H.G. Jerrard and D.B.
70 # McNeill. 1992
71 # 25. NIST Special Publication 330, The International System of
72 # Units (SI). ed. Barry N. Taylor and Ambler Thompson. 2008
73 # https://www.nist.gov/pml/special-publication-330
74 # 26. BIPM Brochure, The International System of Units (SI).
75 # 9th ed., 2019
76 # https://www.bipm.org/en/publications/si-brochure/
77 #
78 ###########################################################################
79 #
80 # If units you use are missing or defined incorrectly, please contact me.
81 # If your country's local units are missing and you are willing to supply
82 # them, please send me a list.
83 #
84 ###########################################################################
85
86 ###########################################################################
87 #
88 # Brief Philosophy of this file
89 #
90 # Most unit definitions are made in terms of integers or simple fractions of
91 # other definitions. The typical exceptions are when converting between two
92 # different unit systems, or the values of measured physical constants. In
93 # this file definitions are given in the most natural and revealing way in
94 # terms of integer factors.
95 #
96 # If you make changes be sure to run 'units --check' to check your work.
97 #
98 # The file is USA-centric, but there is some modest effort to support other
99 # countries. This file is now coded in UTF-8. To support environments where
100 # UTF-8 is not available, definitions that require this character set are
101 # wrapped in !utf8 directives.
102 #
103 # When a unit name is used in different countries with the different meanings
104 # the system should be as follows:
105 #
106 # Suppose countries ABC and XYZ both use the "foo". Then globally define
107 #
108 # ABCfoo <some value>
109 # XYZfoo <different value>
110 #
111 # Then, using the !locale directive, define the "foo" appropriately for each of
112 # the two countries with a definition like
113 #
114 # !locale ABC
115 # foo ABCfoo
116 # !endlocale
117 #
118 ###########################################################################
119
120 !locale en_US
121 ! set UNITS_ENGLISH US
122 !endlocale
123
124 !locale en_GB
125 ! set UNITS_ENGLISH GB
126 !endlocale
127
128 !set UNITS_ENGLISH US # Default setting for English units
129
130 !set UNITS_SYSTEM default # Set a default value
131
132 !varnot UNITS_SYSTEM si emu esu gaussian gauss hlu natural natural-gauss hartree planck planck-red default
133 !message Unknown unit system given with -u or UNITS_SYSTEM environment variable
134 !message Valid systems: si, emu, esu, gauss[ian], hlu, natural, natural-gauss
135 !message planck, planck-red, hartree
136 !message Using SI
137 !prompt (SI)
138 !endvar
139
140 !var UNITS_SYSTEM si
141 !message SI units selected
142 !prompt (SI)
143 !endvar
144
145 ###########################################################################
146 # #
147 # Primitive units. Any unit defined to contain a '!' character is a #
148 # primitive unit which will not be reduced any further. All units should #
149 # reduce to primitive units. #
150 # #
151 ###########################################################################
152
153 #
154 # SI units
155 #
156 # On 20 May 2019, the SI was revised to define the units by fixing the
157 # values of physical constants that depend on those units.
158 #
159 # https://www.nist.gov/si-redefinition/
160 #
161 # The BIPM--the International Bureau of Weights and Measures--provides a
162 # succinct description of the new SI in its Concise Summary:
163 #
164 # https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-concise-EN.pdf
165 #
166 # The SI is the system of units in which:
167 #
168 # * the unperturbed ground state hyperfine transition frequency of the
169 # caesium 133 atom is delta nu_Cs = 9 192 631 770 Hz,
170 # * the speed of light in vacuum, c, is 299 792 458 m/s,
171 # * the Planck constant, h, is 6.626 070 15 * 10^-34 J s,
172 # * the elementary charge, e, is 1.602 176 634 * 10^-19 C,
173 # * the Boltzmann constant, k, is 1.380 649 * 10^-23 J/K,
174 # * the Avogadro constant, N_A, is 6.022 140 76 * 10^23 mol^-1,
175 # * the luminous efficacy of monochromatic radiation of frequency
176 # 540 * 10^12 Hz, K_cd, is 683 lm/W,
177 #
178 # where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz,
179 # J, C, lm, and W, respectively, are related to the units second, metre,
180 # kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg,
181 # A, K, mol, and cd, respectively, according to Hz = s^–1, J = kg m^2 s^–2,
182 # C = A s, lm = cd m^2 m^–2 = cd sr, and W = kg m^2 s^–3.
183 #
184 # These definitions specify the exact numerical value of each constant when
185 # its value is expressed in the corresponding SI unit. By fixing the exact
186 # numerical value the unit becomes defined, since the product of the
187 # numerical value and the unit has to equal the value of the constant,
188 # which is invariant.
189 #
190 # The defining constants have been chosen such that, when taken together,
191 # their units cover all of the units of the SI. In general, there is no
192 # one-to-one correspondence between the defining constants and the SI base
193 # units. Any SI unit is a product of powers of these seven constants and a
194 # dimensionless factor.
195 #
196 # Until 2018, the SI was defined in terms of base units and derived units.
197 # These categories are no longer essential in the SI, but they are maintained
198 # in view of their convenience and widespread use. They are arguably more
199 # intuitive than the new definitions. (They are also essential to the
200 # operation of GNU units.) The definitions of the base units, which follow
201 # from the definition of the SI in terms of the seven defining constants, are
202 # given below.
203 #
204
205 s ! # The second, symbol s, is the SI unit of time. It is defined
206 second s # by taking the fixed numerical value of the unperturbed
207 # ground-state hyperfine transition frequency of the
208 # cesium-133 atom to be 9 192 1631 770 when expressed in the
209 # unit Hz, which is equal to 1/s.
210 #
211 # This definition is a restatement of the previous one, the
212 # duration of 9192631770 periods of the radiation corresponding
213 # to the cesium-133 transition.
214
215 c_SI 299792458
216 c 299792458 m/s # speed of light in vacuum (exact)
217
218 m ! # The metre, symbol m, is the SI unit of length. It is
219 meter m # defined by taking the fixed numerical value of the speed
220 metre m # of light in vacuum, c, to be 299 792 458 when expressed in
221 # units of m/s.
222 #
223 # This definition is a rewording of the previous one and is
224 # equivalent to defining the meter as the distance light
225 # travels in 1|299792458 seconds. The meter was originally
226 # intended to be 1e-7 of the length along a meridian from the
227 # equator to a pole.
228
229 h_SI 6.62607015e-34
230 h 6.62607015e-34 J s # Planck constant (exact)
231
232 kg ! # The kilogram, symbol kg, is the SI unit of mass. It is
233 kilogram kg # defined by taking the fixed numerical value of the Planck
234 # constant, h, to be 6.626 070 15 * 10^-34 when expressed in
235 # the unit J s which is equal to kg m^2 / s.
236 #
237 # One advantage of fixing h to define the kilogram is that this
238 # affects constants used to define the ampere. If the kg were
239 # defined by directly fixing the mass of something, then h
240 # would be subject to error.
241 #
242 # The previous definition of the kilogram was the mass of the
243 # international prototype kilogram. The kilogram was the last
244 # unit whose definition relied on reference to an artifact.
245 #
246 # It is not obvious what this new definition means, or
247 # intuitively how fixing Planck's constant defines the
248 # kilogram. To define the kilogram we need to give the mass
249 # of some reference in kilograms. Previously the prototype in
250 # France served as this reference, and it weighed exactly 1
251 # kg. But the reference can have any weight as long as you
252 # know the weight of the reference. The new definition uses
253 # the "mass" of a photon, or more accurately, the mass
254 # equivalent of the energy of a photon. The energy of a
255 # photon depends on its frequency. If you pick a frequency,
256 # f, then the energy of the photon is hf, and hence the mass
257 # equivalent is hf/c^2. If we reduce this expression using
258 # the constant defined values for h and c the result is a
259 # value in kilograms for the mass-equivalent of a photon of
260 # frequency f, which can therefore define the size of the
261 # kilogram.
262 #
263 # For more on the relationship between mass an Planck's
264 # constant:
265 #
266 # https://www.nist.gov/si-redefinition/kilogram-mass-and-plancks-constant
267 # This definition may still seem rather abstract: you can't
268 # place a "kilogram of radiation" on one side of a balance.
269 # Metrologists realize the kilogram using a Kibble Balance, a
270 # device which relates mechanical energy to electrical energy
271 # and can measure mass with extreme accuracy if h is known.
272 #
273 # For more on the Kibble Balance see
274 #
275 # https://www.nist.gov/si-redefinition/kilogram-kibble-balance
276 # https://en.wikipedia.org/wiki/Kibble_balance
277
278 k_SI 1.380649e-23
279 boltzmann 1.380649e-23 J/K # Boltzmann constant (exact)
280 k boltzmann
281
282 K ! # The kelvin, symbol K, is the SI unit of thermodynamic
283 kelvin K # temperature. It is defined by taking the fixed numerical
284 # value of the Boltzmann constant, k, to be 1.380 649 * 10^-23
285 # when expressed in the unit J/K, which is equal to
286 # kg m^2/s^2 K.
287 #
288 # The boltzmann constant establishes the relationship between
289 # energy and temperature. The average thermal energy carried
290 # by each degree of freedom is kT/2. A monatomic ideal gas
291 # has three degrees of freedom corresponding to the three
292 # spatial directions, which means its thermal energy is
293 # (3/2) k T.
294 #
295 # The previous definition of the kelvin was based on the
296 # triple point of water. The change in the definition of the
297 # kelvin will not have much effect on measurement practice.
298 # Practical temperature calibration makes use of two scales,
299 # the International Temperature Scale of 1990 (ITS-90), which
300 # covers the range of 0.65 K to 1357.77K and the Provisional
301 # Low Temperature Scale of 2000 (PLTS-2000), which covers the
302 # range of 0.9 mK to 1 K.
303 # https://www.bipm.org/en/committees/cc/cct/publications-cc.html
304 #
305 # The ITS-90 contains 17 reference points including things
306 # like the triple point of hydrogen (13.8033 K) or the
307 # freezing point of gold (1337.33 K), and of course the triple
308 # point of water. The PLTS-2000 specifies four reference
309 # points, all based on properties of helium-3.
310 #
311 # The redefinition of the kelvin will not affect the values of
312 # these reference points, which have been determined by
313 # primary thermometry, using thermometers that rely only on
314 # relationships that allow temperature to be calculated
315 # directly without using any unknown quantities. Examples
316 # include acoustic thermometers, which measure the speed of
317 # sound in a gas, or electronic thermometers, which measure
318 # tiny voltage fluctuations in resistors. Both variables
319 # depend directly on temperature.
320
321 e_SI 1.602176634e-19
322 e 1.602176634e-19 C # electron charge (exact)
323
324 A ! # The ampere, symbol A, is the SI unit of electric current.
325 ampere A # It is defined by taking the fixed numerical value of the
326 amp ampere # elementary charge, e, to be 1.602 176 634 * 10^-19 when
327 # expressed in the unit C, which is equal to A*s.
328 #
329 # The previous definition was the current which produces a
330 # force of 2e-7 N/m between two infinitely long wires a meter
331 # apart. This definition was difficult to realize accurately.
332 #
333 # The ampere is actually realized by establishing the volt and
334 # the ohm, since A = V / ohm. These measurements can be done
335 # using the Josephson effect and the quantum Hall effect,
336 # which accurately measure voltage and resistance, respectively,
337 # with reference to two fixed constants, the Josephson
338 # constant, K_J=2e/h and the von Klitzing constant, R_K=h/e^2.
339 # Under the previous SI system, these constants had official
340 # fixed values, defined in 1990. This created a situation
341 # where the standard values for the volt and ohm were in some
342 # sense outside of SI because they depended primarily on
343 # constants different from the ones used to define SI. After
344 # the revision, since e and h have exact definitions, the
345 # Josephson and von Klitzing constants will also have exact
346 # definitions that derive from SI instead of the conventional
347 # 1990 values.
348 #
349 # In fact we know that there is a small offset between the
350 # conventional values of the electrical units based on the
351 # conventional 1990 values and the SI values. The new
352 # definition, which brings the practical electrical units back
353 # into SI, will lead to a one time change of +0.1ppm for
354 # voltage values and +0.02ppm for resistance values.
355 #
356 # The previous definition resulted in fixed exact values for
357 # the vacuum permeability (mu0), the impedance of free space
358 # (Z0), the vacuum permittivity (epsilon0), and the Coulomb
359 # constant. With the new definition, these four values are
360 # subject to experimental error.
361
362 avogadro 6.02214076e23 / mol # Size of a mole (exact)
363 N_A avogadro
364
365 mol ! # The mole, symbol mol, is the SI unit of amount of
366 mole mol # substance. One mole contains exactly 6.022 140 76 * 10^23
367 # elementary entities. This number is the fixed numerical
368 # value of the Avogadro constant, N_A, when expressed in the
369 # unit 1/mol and is called the Avogadro number. The amount of
370 # substance, symbol n, of a system is a measure of the number
371 # of specified elementary entities. An elementary entity may
372 # be an atom, a molecule, an ion, an electron, any other
373 # particle or specified group of particles.
374 #
375 # The atomic mass unit (u) is defined as 1/12 the mass of
376 # carbon-12. Previously the mole was defined so that a mole
377 # of carbon-12 weighed exactly 12g, or N_A u = 1 g/mol
378 # exactly. This relationship is now an experimental,
379 # approximate relationship.
380 #
381 # To determine the size of the mole, researchers used spheres
382 # of very pure silicon-28 that weighed a kilogram. They
383 # measured the molar mass of Si-28 using mass spectrometry and
384 # used X-ray diffraction interferometry to determine the
385 # spacing of the silicon atoms in the sphere. Using the
386 # sphere's volume it was then possible to determine the number
387 # of silicon atoms in the sphere, and hence determine the
388 # Avogadro constant. The results of this experiment were used to
389 # define N_A, which is henceforth a fixed, unchanging quantity.
390
391 cd ! # The candela, symbol cd, is the SI unit of luminous intensity
392 candela cd # in a given direction. It is defined by taking the fixed
393 # numerical value of the luminous efficacy of monochromatic
394 # radiation of the frequency 540e12 Hz to be 683 when
395 # expressed in the unit lumen/watt, which is equal to
396 # cd sr/W, or cd sr s^3/kg m^2
397 #
398 # This definition is a rewording of the previous definition.
399 # Luminous intensity differs from radiant intensity (W/sr) in
400 # that it is adjusted for human perceptual dependence on
401 # wavelength. The frequency of 540e12 Hz (yellow;
402 # wavelength approximately 555 nm in vacuum) is where human
403 # perception is most efficient.
404 #
405 # The radian and steradian are defined as dimensionless primitive units.
406 # The radian is equal to m/m and the steradian to m^2/m^2 so these units are
407 # dimensionless. Retaining them as named units is useful because it allows
408 # clarity in expressions and makes the meaning of unit definitions more clear.
409 # These units will reduce to 1 in conversions but not for sums of units or for
410 # arguments to functions.
411 #
412
413 radian !dimensionless # The angle subtended at the center of a circle by
414 # an arc equal in length to the radius of the
415 # circle
416 sr !dimensionless # Solid angle which cuts off an area of the surface
417 steradian sr # of the sphere equal to that of a square with
418 # sides of length equal to the radius of the
419 # sphere
420
421 #
422 # A primitive non-SI unit
423 #
424
425 bit ! # Basic unit of information (entropy). The entropy in bits
426 # of a random variable over a finite alphabet is defined
427 # to be the sum of -p(i)*log2(p(i)) over the alphabet where
428 # p(i) is the probability that the random variable takes
429 # on the value i.
430
431 #
432 # Currency: the primitive unit of currency is defined in currency.units.
433 # It is usually the US$ or the euro, but it is user selectable.
434 #
435
436 ###########################################################################
437 # #
438 # Prefixes (longer names must come first) #
439 # #
440 ###########################################################################
441
442 yotta- 1e24 # Greek or Latin octo, "eight"
443 zetta- 1e21 # Latin septem, "seven"
444 exa- 1e18 # Greek hex, "six"
445 peta- 1e15 # Greek pente, "five"
446 tera- 1e12 # Greek teras, "monster"
447 giga- 1e9 # Greek gigas, "giant"
448 mega- 1e6 # Greek megas, "large"
449 myria- 1e4 # Not an official SI prefix
450 kilo- 1e3 # Greek chilioi, "thousand"
451 hecto- 1e2 # Greek hekaton, "hundred"
452 deca- 1e1 # Greek deka, "ten"
453 deka- deca
454 deci- 1e-1 # Latin decimus, "tenth"
455 centi- 1e-2 # Latin centum, "hundred"
456 milli- 1e-3 # Latin mille, "thousand"
457 micro- 1e-6 # Latin micro or Greek mikros, "small"
458 nano- 1e-9 # Latin nanus or Greek nanos, "dwarf"
459 pico- 1e-12 # Spanish pico, "a bit"
460 femto- 1e-15 # Danish-Norwegian femten, "fifteen"
461 atto- 1e-18 # Danish-Norwegian atten, "eighteen"
462 zepto- 1e-21 # Latin septem, "seven"
463 yocto- 1e-24 # Greek or Latin octo, "eight"
464
465 quarter- 1|4
466 semi- 0.5
467 demi- 0.5
468 hemi- 0.5
469 half- 0.5
470 double- 2
471 triple- 3
472 treble- 3
473
474 kibi- 2^10 # In response to the convention of illegally
475 mebi- 2^20 # and confusingly using metric prefixes for
476 gibi- 2^30 # powers of two, the International
477 tebi- 2^40 # Electrotechnical Commission aproved these
478 pebi- 2^50 # binary prefixes for use in 1998. If you
479 exbi- 2^60 # want to refer to "megabytes" using the
480 Ki- kibi # binary definition, use these prefixes.
481 Mi- mebi
482 Gi- gibi
483 Ti- tebi
484 Pi- pebi
485 Ei- exbi
486
487 Y- yotta
488 Z- zetta
489 E- exa
490 P- peta
491 T- tera
492 G- giga
493 M- mega
494 k- kilo
495 h- hecto
496 da- deka
497 d- deci
498 c- centi
499 m- milli
500 u- micro # it should be a mu but u is easy to type
501 n- nano
502 p- pico
503 f- femto
504 a- atto
505 z- zepto
506 y- yocto
507
508 #
509 # Names of some numbers
510 #
511
512 one 1
513 two 2
514 double 2
515 couple 2
516 three 3
517 triple 3
518 four 4
519 quadruple 4
520 five 5
521 quintuple 5
522 six 6
523 seven 7
524 eight 8
525 nine 9
526 ten 10
527 eleven 11
528 twelve 12
529 thirteen 13
530 fourteen 14
531 fifteen 15
532 sixteen 16
533 seventeen 17
534 eighteen 18
535 nineteen 19
536 twenty 20
537 thirty 30
538 forty 40
539 fifty 50
540 sixty 60
541 seventy 70
542 eighty 80
543 ninety 90
544 hundred 100
545 thousand 1000
546 million 1e6
547
548 twoscore two score
549 threescore three score
550 fourscore four score
551 fivescore five score
552 sixscore six score
553 sevenscore seven score
554 eightscore eight score
555 ninescore nine score
556 tenscore ten score
557 twelvescore twelve score
558
559 # These number terms were described by N. Chuquet and De la Roche in the 16th
560 # century as being successive powers of a million. These definitions are still
561 # used in most European countries. The current US definitions for these
562 # numbers arose in the 17th century and don't make nearly as much sense. These
563 # numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric
564 # W. Weisstein.
565
566 shortbillion 1e9
567 shorttrillion 1e12
568 shortquadrillion 1e15
569 shortquintillion 1e18
570 shortsextillion 1e21
571 shortseptillion 1e24
572 shortoctillion 1e27
573 shortnonillion 1e30
574 shortnoventillion shortnonillion
575 shortdecillion 1e33
576 shortundecillion 1e36
577 shortduodecillion 1e39
578 shorttredecillion 1e42
579 shortquattuordecillion 1e45
580 shortquindecillion 1e48
581 shortsexdecillion 1e51
582 shortseptendecillion 1e54
583 shortoctodecillion 1e57
584 shortnovemdecillion 1e60
585 shortvigintillion 1e63
586
587 centillion 1e303
588 googol 1e100
589
590 longbillion million^2
591 longtrillion million^3
592 longquadrillion million^4
593 longquintillion million^5
594 longsextillion million^6
595 longseptillion million^7
596 longoctillion million^8
597 longnonillion million^9
598 longnoventillion longnonillion
599 longdecillion million^10
600 longundecillion million^11
601 longduodecillion million^12
602 longtredecillion million^13
603 longquattuordecillion million^14
604 longquindecillion million^15
605 longsexdecillion million^16
606 longseptdecillion million^17
607 longoctodecillion million^18
608 longnovemdecillion million^19
609 longvigintillion million^20
610
611 # These numbers fill the gaps left by the long system above.
612
613 milliard 1000 million
614 billiard 1000 million^2
615 trilliard 1000 million^3
616 quadrilliard 1000 million^4
617 quintilliard 1000 million^5
618 sextilliard 1000 million^6
619 septilliard 1000 million^7
620 octilliard 1000 million^8
621 nonilliard 1000 million^9
622 noventilliard nonilliard
623 decilliard 1000 million^10
624
625 # For consistency
626
627 longmilliard milliard
628 longbilliard billiard
629 longtrilliard trilliard
630 longquadrilliard quadrilliard
631 longquintilliard quintilliard
632 longsextilliard sextilliard
633 longseptilliard septilliard
634 longoctilliard octilliard
635 longnonilliard nonilliard
636 longnoventilliard noventilliard
637 longdecilliard decilliard
638
639 # The long centillion would be 1e600. The googolplex is another
640 # familiar large number equal to 10^googol. These numbers give overflows.
641
642 #
643 # The short system prevails in English speaking countries
644 #
645
646 billion shortbillion
647 trillion shorttrillion
648 quadrillion shortquadrillion
649 quintillion shortquintillion
650 sextillion shortsextillion
651 septillion shortseptillion
652 octillion shortoctillion
653 nonillion shortnonillion
654 noventillion shortnoventillion
655 decillion shortdecillion
656 undecillion shortundecillion
657 duodecillion shortduodecillion
658 tredecillion shorttredecillion
659 quattuordecillion shortquattuordecillion
660 quindecillion shortquindecillion
661 sexdecillion shortsexdecillion
662 septendecillion shortseptendecillion
663 octodecillion shortoctodecillion
664 novemdecillion shortnovemdecillion
665 vigintillion shortvigintillion
666
667 #
668 # Numbers used in India
669 #
670
671 lakh 1e5
672 crore 1e7
673 arab 1e9
674 kharab 1e11
675 neel 1e13
676 padm 1e15
677 shankh 1e17
678
679 #############################################################################
680 # #
681 # Derived units which can be reduced to the primitive units #
682 # #
683 #############################################################################
684
685
686
687 #
688 # Named SI derived units (officially accepted)
689 #
690
691 newton kg m / s^2 # force
692 N newton
693 pascal N/m^2 # pressure or stress
694 Pa pascal
695 joule N m # energy
696 J joule
697 watt J/s # power
698 W watt
699 coulomb A s # charge
700 C coulomb
701 volt W/A # potential difference
702 V volt
703 ohm V/A # electrical resistance
704 siemens A/V # electrical conductance
705 S siemens
706 farad C/V # capacitance
707 F farad
708 weber V s # magnetic flux
709 Wb weber
710 henry V s / A # inductance
711 H henry
712 tesla Wb/m^2 # magnetic flux density
713 T tesla
714 hertz /s # frequency
715 Hz hertz
716
717 #
718 # Dimensions. These are here to help with dimensional analysis and
719 # because they will appear in the list produced by hitting '?' at the
720 # "You want:" prompt to tell the user the dimension of the unit.
721 #
722
723 LENGTH meter
724 AREA LENGTH^2
725 VOLUME LENGTH^3
726 MASS kilogram
727 AMOUNT mole
728 ANGLE radian
729 SOLID_ANGLE steradian
730 MONEY US$
731 FORCE newton
732 PRESSURE FORCE / AREA
733 STRESS FORCE / AREA
734 FREQUENCY hertz
735 VELOCITY LENGTH / TIME
736 ACCELERATION VELOCITY / TIME
737 DENSITY MASS / VOLUME
738 LINEAR_DENSITY MASS / LENGTH
739 VISCOSITY FORCE TIME / AREA
740 KINEMATIC_VISCOSITY VISCOSITY / DENSITY
741 CURRENT ampere
742 CHARGE coulomb
743 CAPACITANCE farad
744 RESISTANCE ohm
745 CONDUCTANCE siemens
746 # It may be easier to understand the relationship by considering
747 # an object with specified dimensions and resistivity, whose
748 # resistance is given by the resistivity * length / area.
749 RESISTIVITY RESISTANCE AREA / LENGTH
750 CONDUCTIVITY CONDUCTANCE LENGTH / AREA
751 INDUCTANCE henry
752 E_FIELD ELECTRIC_POTENTIAL / LENGTH
753 B_FIELD tesla
754 # The D and H fields are related to the E and B fields by factors of
755 # epsilon and mu respectively, so their units can be found by
756 # multiplying/dividing by the epsilon0 and mu0. The more complex
757 # definitions below make it possible to use D_FIELD and E_FIELD to
758 # convert between SI and CGS units for these dimensions.
759 D_FIELD E_FIELD epsilon0 / epsilon0_SI # mu0_SI c^2 F / m
760 H_FIELD B_FIELD / (mu0/mu0_SI)
761 ELECTRIC_DIPOLE_MOMENT C m
762 MAGNETIC_DIPOLE_MOMENT J / T
763 POLARIZATION ELECTRIC_DIPOLE_MOMENT / VOLUME
764 MAGNETIZATION MAGNETIC_DIPOLE_MOMENT / VOLUME
765 ELECTRIC_POTENTIAL ENERGY / CHARGE #volt
766 VOLTAGE ELECTRIC_POTENTIAL
767 E_FLUX E_FIELD AREA
768 D_FLUX D_FIELD AREA
769 B_FLUX B_FIELD AREA
770 H_FLUX H_FIELD AREA
771
772 #
773 # units derived easily from SI units
774 #
775
776 gram millikg
777 gm gram
778 g gram
779 tonne 1000 kg
780 t tonne
781 metricton tonne
782 sthene tonne m / s^2
783 funal sthene
784 pieze sthene / m^2
785 quintal 100 kg
786 bar 1e5 Pa # About 1 atm
787 b bar
788 vac millibar
789 micron micrometer # One millionth of a meter
790 bicron picometer # One brbillionth of a meter
791 cc cm^3
792 are 100 m^2
793 a are
794 liter 1000 cc # The liter was defined in 1901 as the
795 oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at
796 L liter # the temperature of its maximum density
797 l liter # under a pressure of 1 atm. This was
798 # supposed to be 1000 cubic cm, but it
799 # was discovered that the original
800 # measurement was off. In 1964, the
801 # liter was redefined to be exactly 1000
802 # cubic centimeters.
803 mho siemens # Inverse of ohm, hence ohm spelled backward
804 galvat ampere # Named after Luigi Galvani
805 angstrom 1e-10 m # Convenient for describing molecular sizes
806 xunit xunit_cu # Used for measuring x-ray wavelengths.
807 siegbahn xunit # Originally defined to be 1|3029.45 of
808 xunit_cu 1.00207697e-13 m # the spacing of calcite planes at 18
809 xunit_mo 1.00209952e-13 m # degC. It was intended to be exactly
810 # 1e-13 m, but was later found to be
811 # slightly off. Current usage is with
812 # reference to common x-ray lines, either
813 # the K-alpha 1 line of copper or the
814 # same line of molybdenum.
815 angstromstar 1.00001495 angstrom # Defined by JA Bearden in 1965 to replace
816 # the X unit. The wavelength of the
817 # tungsten K alpha1 line was defined as
818 # exactly 0.20901 angstrom star, with the
819 # valule chosen to try to make the new
820 # unit close to the angstrom.
821 silicon_d220 1.920155716e-10 m # Silicon lattice spacing
822 siliconlattice sqrt(8) silicon_d220# Silicon lattice parameter, (a), the side
823 # length of the unit cell for the diamond
824 # centered cubic structure of silicon.
825 fermi 1e-15 m # Convenient for describing nuclear sizes
826 # Nuclear radius is from 1 to 10 fermis
827 barn 1e-28 m^2 # Used to measure cross section for
828 # particle physics collision, said to
829 # have originated in the phrase "big as
830 # a barn".
831 shed 1e-24 barn # Defined to be a smaller companion to the
832 # barn, but it's too small to be of
833 # much use.
834 brewster micron^2/N # measures stress-optical coef
835 diopter /m # measures reciprocal of lens focal length
836 fresnel 1e12 Hz # occasionally used in spectroscopy
837 shake 1e-8 sec
838 svedberg 1e-13 s # Used for measuring the sedimentation
839 # coefficient for centrifuging.
840 gamma microgram # Also used for 1e-9 tesla
841 lambda microliter
842 spat 1e12 m # Rarely used for astronomical measurements
843 preece 1e13 ohm m # resistivity
844 planck J s # action of one joule over one second
845 sturgeon /henry # magnetic reluctance
846 daraf 1/farad # elastance (farad spelled backwards)
847 leo 10 m/s^2
848 poiseuille N s / m^2 # viscosity
849 mayer J/g K # specific heat
850 mired / microK # reciprocal color temperature. The name
851 # abbreviates micro reciprocal degree.
852 crocodile megavolt # used informally in UK physics labs
853 metricounce 25 g
854 mounce metricounce
855 finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light
856 # with wavelength 296.7 nm.
857 fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure
858 # the energy incident on the receiving
859 # body across a specified frequency
860 # bandwidth. [12]
861 jansky fluxunit # K. G. Jansky identified radio waves coming
862 Jy jansky # from outer space in 1931.
863 flick W / cm^2 sr micrometer # Spectral radiance or irradiance
864 pfu / cm^2 sr s # particle flux unit -- Used to measure
865 # rate at which particles are received by
866 # a spacecraft as particles per solid
867 # angle per detector area per second. [18]
868 pyron cal_IT / cm^2 min # Measures heat flow from solar radiation,
869 # from Greek work "pyr" for fire.
870 katal mol/sec # Measure of the amount of a catalyst. One
871 kat katal # katal of catalyst enables the reaction
872 # to consume or produce on mol/sec.
873 solarluminosity 382.8e24 W # A common yardstick for comparing the
874 # output of different stars.
875 # http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
876 # at mean earth-sun distance
877 solarirradiance solarluminosity / (4 pi sundist^2)
878 solarconstant solarirradiance
879 TSI solarirradiance # total solar irradiance
880
881 #
882 # time
883 #
884
885 sec s
886 minute 60 s
887 min minute
888 hour 60 min
889 hr hour
890 day 24 hr
891 d day
892 da day
893 week 7 day
894 wk week
895 sennight 7 day
896 fortnight 14 day
897 blink 1e-5 day # Actual human blink takes 1|3 second
898 ce 1e-2 day
899 cron 1e6 years
900 watch 4 hours # time a sentry stands watch or a ship's
901 # crew is on duty.
902 bell 1|8 watch # Bell would be sounded every 30 minutes.
903
904 # French Revolutionary Time or Decimal Time. It was Proposed during
905 # the French Revolution. A few clocks were made, but it never caught
906 # on. In 1998 Swatch defined a time measurement called ".beat" and
907 # sold some watches that displayed time in this unit.
908
909 decimalhour 1|10 day
910 decimalminute 1|100 decimalhour
911 decimalsecond 1|100 decimalminute
912 beat decimalminute # Swatch Internet Time
913
914 #
915 # angular measure
916 #
917
918 circle 2 pi radian
919 degree 1|360 circle
920 deg degree
921 arcdeg degree
922 arcmin 1|60 degree
923 arcminute arcmin
924 ' arcmin
925 arcsec 1|60 arcmin
926 arcsecond arcsec
927 " arcsec
928 '' "
929 rightangle 90 degrees
930 quadrant 1|4 circle
931 quintant 1|5 circle
932 sextant 1|6 circle
933
934 sign 1|12 circle # Angular extent of one sign of the zodiac
935 turn circle
936 revolution turn
937 rev turn
938 pulsatance radian / sec
939 gon 1|100 rightangle # measure of grade
940 grade gon
941 centesimalminute 1|100 grade
942 centesimalsecond 1|100 centesimalminute
943 milangle 1|6400 circle # Official NIST definition.
944 # Another choice is 1e-3 radian.
945 pointangle 1|32 circle # Used for reporting compass readings
946 centrad 0.01 radian # Used for angular deviation of light
947 # through a prism.
948 mas milli arcsec # Used by astronomers
949 seclongitude circle (seconds/day) # Astronomers measure longitude
950 # (which they call right ascension) in
951 # time units by dividing the equator into
952 # 24 hours instead of 360 degrees.
953 #
954 # Some geometric formulas
955 #
956
957 circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
958 spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \
959 cuberoot(spherevolume/4|3 pi)
960 spherevol() spherevolume
961 square(x) range=[0,) x^2 ; sqrt(square)
962
963 #
964 # Solid angle measure
965 #
966
967 sphere 4 pi sr
968 squaredegree 1|180^2 pi^2 sr
969 squareminute 1|60^2 squaredegree
970 squaresecond 1|60^2 squareminute
971 squarearcmin squareminute
972 squarearcsec squaresecond
973 sphericalrightangle 0.5 pi sr
974 octant 0.5 pi sr
975
976 #
977 # Concentration measures
978 #
979
980 percent 0.01
981 % percent
982 mill 0.001 # Originally established by Congress in 1791
983 # as a unit of money equal to 0.001 dollars,
984 # it has come to refer to 0.001 in general.
985 # Used by some towns to set their property
986 # tax rate, and written with a symbol similar
987 # to the % symbol but with two 0's in the
988 # denominator. [18]
989 proof 1|200 # Alcohol content measured by volume at
990 # 60 degrees Fahrenheit. This is a USA
991 # measure. In Europe proof=percent.
992 ppm 1e-6
993 partspermillion ppm
994 ppb 1e-9
995 partsperbillion ppb # USA billion
996 ppt 1e-12
997 partspertrillion ppt # USA trillion
998 karat 1|24 # measure of gold purity
999 caratgold karat
1000 gammil mg/l
1001 basispoint 0.01 % # Used in finance
1002 fine 1|1000 # Measure of gold purity
1003
1004 # The pH scale is used to measure the concentration of hydronium (H3O+) ions in
1005 # a solution. A neutral solution has a pH of 7 as a result of dissociated
1006 # water molecules.
1007
1008 pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol))
1009
1010
1011 #
1012 # Temperature
1013 #
1014 # Two types of units are defined: units for converting temperature differences
1015 # and functions for converting absolute temperatures. Conversions for
1016 # differences start with "deg" and conversions for absolute temperature start
1017 # with "temp".
1018 #
1019 # If the temperature inside is 72 degrees Fahrenheit and you want to
1020 # convert this to degrees Celsius then you need absolute temperature:
1021 #
1022 # You have: tempF(72)
1023 # You want: tempC
1024 # 22.222222
1025 #
1026 # If the temperature rose 72 degrees Fahrenheit during the chemical reaction
1027 # then this is a temperature difference:
1028 #
1029 # You have: 72 degF
1030 # You want: degC
1031 # * 40
1032 # / 0.025
1033 #
1034
1035 TEMPERATURE kelvin
1036 TEMPERATURE_DIFFERENCE kelvin
1037
1038 # In 1741 Anders Celsius introduced a temperature scale with water boiling at
1039 # 0 degrees and freezing at 100 degrees at standard pressure. After his death
1040 # the fixed points were reversed and the scale was called the centigrade
1041 # scale. Due to the difficulty of accurately measuring the temperature of
1042 # melting ice at standard pressure, the centigrade scale was replaced in 1954
1043 # by the Celsius scale which is defined by subtracting 273.15 from the
1044 # temperature in Kelvins. This definition differed slightly from the old
1045 # centigrade definition, but the Kelvin scale depends on the triple point of
1046 # water rather than a melting point, so it can be measured accurately.
1047
1048 tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \
1049 x K + stdtemp ; (tempC +(-stdtemp))/K
1050 tempcelsius() tempC
1051 degcelsius K
1052 degC K
1053
1054 # Fahrenheit defined his temperature scale by setting 0 to the coldest
1055 # temperature he could produce in his lab with a salt water solution and by
1056 # setting 96 degrees to body heat. In Fahrenheit's words:
1057 #
1058 # Placing the thermometer in a mixture of sal ammoniac or sea
1059 # salt, ice, and water a point on the scale will be found which
1060 # is denoted as zero. A second point is obtained if the same
1061 # mixture is used without salt. Denote this position as 30. A
1062 # third point, designated as 96, is obtained if the thermometer
1063 # is placed in the mouth so as to acquire the heat of a healthy
1064 # man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724)
1065
1066 tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
1067 (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
1068 tempfahrenheit() tempF
1069 degfahrenheit 5|9 degC
1070 degF 5|9 degC
1071
1072
1073 degreesrankine degF # The Rankine scale has the
1074 degrankine degreesrankine # Fahrenheit degree, but its zero
1075 degreerankine degF # is at absolute zero.
1076 degR degrankine
1077 tempR degrankine
1078 temprankine degrankine
1079
1080 tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \
1081 x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur
1082 degreaumur 10|8 degC # The Reaumur scale was used in Europe and
1083 # particularly in France. It is defined
1084 # to be 0 at the freezing point of water
1085 # and 80 at the boiling point. Reaumur
1086 # apparently selected 80 because it is
1087 # divisible by many numbers.
1088
1089 degK K # "Degrees Kelvin" is forbidden usage.
1090 tempK K # For consistency
1091
1092 # Gas mark is implemented below but in a terribly ugly way. There is
1093 # a simple formula, but it requires a conditional which is not
1094 # presently supported.
1095 #
1096 # The formula to convert to degrees Fahrenheit is:
1097 #
1098 # 25 log2(gasmark) + k_f gasmark<=1
1099 # 25 (gasmark-1) + k_f gasmark>=1
1100 #
1101 # k_f = 275
1102 #
1103 gasmark[degR] \
1104 .0625 634.67 \
1105 .125 659.67 \
1106 .25 684.67 \
1107 .5 709.67 \
1108 1 734.67 \
1109 2 759.67 \
1110 3 784.67 \
1111 4 809.67 \
1112 5 834.67 \
1113 6 859.67 \
1114 7 884.67 \
1115 8 909.67 \
1116 9 934.67 \
1117 10 959.67
1118
1119
1120 # The Beaufort wind force scale was developed from 1805-1807 by Sir Francis
1121 # Beaufort to categorize wind conditions at sea. It is normally defined from
1122 # Beaufort 0, also called "Force 0," through Beaufort 12. Beaufort numbers
1123 # 13-17 were later defined for tropical cyclones but are rarely used. The
1124 # original Beaufort scale was qualitative and did not relate directly to wind
1125 # speed. In 1906, George Simpson of the British Met Office fit wind-speed
1126 # measurements to visual Beaufort estimates made from five coastal and inland
1127 # stations in Britain. Simpson's formula was adopted by the World Meterological
1128 # Organization in 1946 to produce a table, known as WMO Code 1100, giving mean
1129 # (and min/max) wind speed equivalents at a height of 10 meters for each
1130 # Beaufort number. This is the "operational" Beaufort scale that mariners
1131 # use. Meterological and climatic researchers typically use a "scientific"
1132 # Beaufort scale based on more recent and comprehensive fits. See Wallbrink and
1133 # Cook, Historical Wind Speed Equivalents Of The Beaufort Scale, 1850-1950, at
1134 # https://icoads.noaa.gov/reclaim/pdf/Hisklim13.pdf
1135 #
1136 beaufort_WMO1100(B) units=[1;m/s] domain=[0,17] range=[0,) \
1137 0.836 B^3|2 m/s; (beaufort_WMO1100 s / 0.836 m)^2|3
1138
1139 beaufort(B) units=[1;m/s] domain=[0,17] range=[0,) \
1140 beaufort_WMO1100(B); ~beaufort_WMO1100(beaufort)
1141
1142 # Units cannot handle wind chill or heat index because they are two-variable
1143 # functions, but they are included here for your edification. Clearly these
1144 # equations are the result of a model fitting operation.
1145 #
1146 # wind chill index (WCI) a measurement of the combined cooling effect of low
1147 # air temperature and wind on the human body. The index was first defined
1148 # by the American Antarctic explorer Paul Siple in 1939. As currently used
1149 # by U.S. meteorologists, the wind chill index is computed from the
1150 # temperature T (in °F) and wind speed V (in mi/hr) using the formula:
1151 # WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4.
1152 # For very low wind speeds, below 4 mi/hr, the WCI is actually higher than
1153 # the air temperature, but for higher wind speeds it is lower than the air
1154 # temperature.
1155 #
1156 # heat index (HI or HX) a measure of the combined effect of heat and
1157 # humidity on the human body. U.S. meteorologists compute the index
1158 # from the temperature T (in °F) and the relative humidity H (as a
1159 # value from 0 to 1).
1160 # HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH
1161 # - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2
1162 # - 0.0199 T^2 H^2.
1163
1164 #
1165 # Physical constants
1166 #
1167
1168 # Basic constants
1169
1170 pi 3.14159265358979323846
1171 light c
1172 mu0_SI 2 alpha h_SI / e_SI^2 c_SI # Vacuum magnetic permeability
1173 mu0 2 alpha h / e^2 c # Gets overridden in CGS modes
1174 epsilon0_SI 1/mu0_SI c_SI^2 # Vacuum electric permittivity
1175 epsilon0 1/mu0 c^2 # Also overridden in CGS modes
1176 Z0 mu0 c # Free space impedance
1177 energy c^2 # Convert mass to energy
1178 hbar h / 2 pi
1179 hbar_SI h_SI / 2 pi
1180 spin hbar
1181 G_SI 6.67430e-11
1182 G 6.67430e-11 N m^2 / kg^2 # Newtonian gravitational constant
1183 coulombconst 1/4 pi epsilon0 # Listed as k or k_C sometimes
1184 k_C coulombconst
1185
1186 # Physico-chemical constants
1187
1188 atomicmassunit_SI 1.66053906660e-27 # Unified atomic mass unit, defined as
1189 atomicmassunit 1.66053906660e-27 kg # Unified atomic mass unit, defined as
1190 u atomicmassunit # 1|12 of the mass of carbon 12.
1191 amu atomicmassunit # The relationship N_A u = 1 g/mol
1192 dalton u # is approximately, but not exactly
1193 Da dalton # true (with the 2019 SI).
1194 # Previously the mole was defined to
1195 # make this relationship exact.
1196 amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of
1197 # the 3 naturally occuring neutral
1198 # isotopes of oxygen
1199 amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral
1200 # oxygen 16 atom
1201 gasconstant k N_A # Molar gas constant (exact)
1202 R gasconstant
1203 kboltzmann boltzmann
1204 molarvolume mol R stdtemp / atm # Volume occupied by one mole of an
1205 # ideal gas at STP.
1206 loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an
1207 # ideal gas at STP. Loschmidt did
1208 # work similar to Avogadro.
1209 molarvolume_si N_A siliconlattice^3 / 8 # Volume of a mole of crystalline
1210 # silicon. The unit cell contains 8
1211 # silicon atoms and has a side
1212 # length of siliconlattice.
1213 stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a
1214 sigma stefanboltzmann # blackbody at temperature T is
1215 # given by sigma T^4. (exact)
1216 wiendisplacement (h c/k)/4.9651142317442763 # Wien's Displacement Law gives
1217 # the frequency at which the the
1218 # Planck spectrum has maximum
1219 # intensity. The relation is lambda
1220 # T = b where lambda is wavelength,
1221 # T is temperature and b is the Wien
1222 # displacement. This relation is
1223 # used to determine the temperature
1224 # of stars. The constant is the
1225 # solution to x=5(1-exp(-x)).
1226 # This expression has no experimental
1227 # error, and x is defined exactly
1228 # by the equation above, so it is
1229 # an exact definition.
1230 K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until
1231 K_J 2e/h # recently, laboratories kept Weston cadmium cells as
1232 # a reference, but they could drift. In 1987 the
1233 # CGPM officially recommended the use of the
1234 # Josephson effect as a laboratory representation of
1235 # the volt. The Josephson effect occurs when two
1236 # superconductors are separated by a thin insulating
1237 # layer. A "supercurrent" flows across the insulator
1238 # with a frequency that depends on the potential
1239 # applied across the superconductors. This frequency
1240 # can be very accurately measured. The Josephson
1241 # constant K_J relates the measured frequency to the
1242 # potential. Two values given, the conventional
1243 # (exact) value from 1990, which was used until the
1244 # 2019 SI revision, and the current exact value.
1245 R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties.
1246 R_K h/e^2 # The old approach involved maintaining resistances
1247 # that were subject to drift. The new standard is
1248 # based on the Hall effect. When a current carrying
1249 # ribbon is placed in a magnetic field, a potential
1250 # difference develops across the ribbon. The ratio
1251 # of the potential difference to the current is
1252 # called the Hall resistance. Klaus von Klitzing
1253 # discovered in 1980 that the Hall resistance varies
1254 # in discrete jumps when the magnetic field is very
1255 # large and the temperature very low. This enables
1256 # accurate realization of the resistance h/e^2 in the
1257 # lab. The 1990 value was an exact conventional
1258 # value used until the SI revision in 2019. This value
1259 # did not agree with measurements. The new value
1260 # is exact.
1261
1262 # The 2019 update to SI gives exact definitions for R_K and K_J. Previously
1263 # the electromagnetic units were realized using the 1990 conventional values
1264 # for these constants, and as a result, the standard definitions were in some
1265 # sense outside of SI. The revision corrects this problem. The definitions
1266 # below give the 1990 conventional values for the electromagnetic units in
1267 # terms of 2019 SI.
1268
1269 ampere90 (K_J90 R_K90 / K_J R_K) A
1270 coulomb90 (K_J90 R_K90 / K_J R_K) C
1271 farad90 (R_K90/R_K) F
1272 henry90 (R_K/R_K90) H
1273 ohm90 (R_K/R_K90) ohm
1274 volt90 (K_J90/K_J) V
1275 watt90 (K_J90^2 R_K90 / K_J^2 R_K) W
1276
1277 # Various conventional values
1278
1279 gravity 9.80665 m/s^2 # std acceleration of gravity (exact)
1280 force gravity # use to turn masses into forces
1281 atm 101325 Pa # Standard atmospheric pressure
1282 atmosphere atm
1283 Hg 13.5951 gram force / cm^3 # Standard weight of mercury (exact)
1284 water gram force/cm^3 # Standard weight of water (exact)
1285 waterdensity gram / cm^3 # Density of water
1286 H2O water
1287 wc water # water column
1288 mach 331.46 m/s # speed of sound in dry air at STP
1289 standardtemp 273.15 K # standard temperature
1290 stdtemp standardtemp
1291 normaltemp tempF(70) # for gas density, from NIST
1292 normtemp normaltemp # Handbook 44
1293
1294 # Weight of mercury and water at different temperatures using the standard
1295 # force of gravity.
1296
1297 Hg10C 13.5708 force gram / cm^3 # These units, when used to form
1298 Hg20C 13.5462 force gram / cm^3 # pressure measures, are not accurate
1299 Hg23C 13.5386 force gram / cm^3 # because of considerations of the
1300 Hg30C 13.5217 force gram / cm^3 # revised practical temperature scale.
1301 Hg40C 13.4973 force gram / cm^3
1302 Hg60F 13.5574 force gram / cm^3
1303 H2O0C 0.99987 force gram / cm^3
1304 H2O5C 0.99999 force gram / cm^3
1305 H2O10C 0.99973 force gram / cm^3
1306 H2O15C 0.99913 force gram / cm^3
1307 H2O18C 0.99862 force gram / cm^3
1308 H2O20C 0.99823 force gram / cm^3
1309 H2O25C 0.99707 force gram / cm^3
1310 H2O50C 0.98807 force gram / cm^3
1311 H2O100C 0.95838 force gram / cm^3
1312
1313 # Atomic constants
1314
1315
1316
1317 Rinfinity m_e c alpha^2 / 2 h # The wavelengths of a spectral series
1318 R_H 10967760 /m # can be expressed as
1319 # 1/lambda = R (1/m^2 - 1/n^2).
1320 # where R is a number that various
1321 # slightly from element to element.
1322 # For hydrogen, R_H is the value,
1323 # and for heavy elements, the value
1324 # approaches Rinfinity.
1325 alpha 7.2973525693e-3 # The fine structure constant was
1326 # introduced to explain fine
1327 # structure visible in spectral
1328 # lines.
1329 bohrradius alpha / 4 pi Rinfinity
1330 prout 185.5 keV # nuclear binding energy equal to 1|12
1331 # binding energy of the deuteron
1332 conductancequantum 2 e^2 / h
1333
1334
1335 # Particle radius
1336
1337 electronradius coulombconst e^2 / electronmass c^2 # Classical
1338 deuteronchargeradius 2.12799e-15 m
1339 protonchargeradius 0.8751e-15 m
1340
1341 # Masses of elementary particles
1342
1343 electronmass_SI electronmass_u atomicmassunit_SI
1344 electronmass_u 5.48579909065e-4
1345 electronmass 5.48579909065e-4 u
1346 m_e electronmass
1347 muonmass 0.1134289259 u
1348 m_mu muonmass
1349 taumass 1.90754 u
1350 m_tau taumass
1351 protonmass 1.007276466621 u
1352 m_p protonmass
1353 neutronmass 1.00866491595 u
1354 m_n neutronmass
1355 deuteronmass 2.013553212745 u # Nucleus of deuterium, one
1356 m_d deuteronmass # proton and one neutron
1357 alphaparticlemass 4.001506179127 u # Nucleus of He, two protons
1358 m_alpha alphaparticlemass # and two neutrons
1359 tritonmass 3.01550071621 u # Nucleius of H3, one proton
1360 m_t tritonmass # and two neutrons
1361 helionmass 3.014932247175 u # Nucleus of He3, two protons
1362 m_h helionmass # and one neutron
1363
1364 # particle wavelengths: the compton wavelength of a particle is
1365 # defined as h / m c where m is the mass of the particle.
1366
1367 electronwavelength h / m_e c
1368 lambda_C electronwavelength
1369 protonwavelength h / m_p c
1370 lambda_C,p protonwavelength
1371 neutronwavelength h / m_n c
1372 lambda_C,n neutronwavelength
1373 muonwavelength h / m_mu c
1374 lambda_C,mu muonwavelength
1375
1376 # The g-factor or dimensionless magnetic moment is a quantity that
1377 # characterizes the magnetic moment of a particle. The electron g-factor is
1378 # one of the most precisely measured values in physics, with a relative
1379 # uncertainty of 1.7e-13.
1380
1381 g_d 0.8574382338 # Deuteron g-factor
1382 g_e -2.00231930436256 # Electron g-factor
1383 g_h -4.255250615 # Helion g-factor
1384 g_mu -2.0023318418 # Muon g-factor
1385 g_n -3.82608545 # Neutron g-factor
1386 g_p 5.5856946893 # Proton g-factor
1387 g_t 5.957924931 # Triton g-factor
1388
1389 fermicoupling 1.1663787e-5 / GeV^2
1390
1391 # Magnetic moments (derived from the more accurate g-factors)
1392 #
1393 # The magnetic moment is g * mu_ref * spin where in most cases
1394 # the reference is the nuclear magneton, and all of the particles
1395 # except the deuteron have spin 1/2.
1396
1397 bohrmagneton e hbar / 2 electronmass # Reference magnetic moment for
1398 mu_B bohrmagneton # the electron
1399 nuclearmagneton e hbar / 2 protonmass # Convenient reference magnetic
1400 mu_N nuclearmagneton # moment for heavy particles
1401 mu_e g_e mu_B / 2 # Electron spin magnet moment
1402 mu_mu g_mu e hbar / 4 muonmass # Muon spin magnetic moment
1403 mu_p g_p mu_N / 2 # Proton magnetic moment
1404 mu_n g_n mu_N / 2 # Neutron magnetic moment
1405 mu_t g_t mu_N / 2 # Triton magnetic moment
1406 mu_d g_d mu_N # Deuteron magnetic moment, spin 1
1407 mu_h g_h mu_N / 2 # Helion magnetic moment
1408
1409 #
1410 # Units derived from physical constants
1411 #
1412
1413 kgf kg force
1414 technicalatmosphere kgf / cm^2
1415 at technicalatmosphere
1416 hyl kgf s^2 / m # Also gram-force s^2/m according to [15]
1417 mmHg mm Hg
1418 torr atm / 760 # The torr, named after Evangelista
1419 # Torricelli, and is very close to the mm Hg
1420 tor Pa # Suggested in 1913 but seldom used [24].
1421 # Eventually renamed the Pascal. Don't
1422 # confuse the tor with the torr.
1423 inHg inch Hg
1424 inH2O inch water
1425 mmH2O mm water
1426 eV e V # Energy acquired by a particle with charge e
1427 electronvolt eV # when it is accelerated through 1 V
1428 lightyear c julianyear # The 365.25 day year is specified in
1429 ly lightyear # NIST publication 811
1430 lightsecond c s
1431 lightminute c min
1432 parsec au / tan(arcsec) # Unit of length equal to distance
1433 pc parsec # from the sun to a point having
1434 # heliocentric parallax of 1
1435 # arcsec (derived from parallax
1436 # second). A distant object with
1437 # parallax theta will be about
1438 # (arcsec/theta) parsecs from the
1439 # sun (using the approximation
1440 # that tan(theta) = theta).
1441 rydberg h c Rinfinity # Rydberg energy
1442 crith 0.089885 gram # The crith is the mass of one
1443 # liter of hydrogen at standard
1444 # temperature and pressure.
1445 amagatvolume molarvolume
1446 amagat mol/amagatvolume # Used to measure gas densities
1447 lorentz bohrmagneton / h c # Used to measure the extent
1448 # that the frequency of light
1449 # is shifted by a magnetic field.
1450 cminv h c / cm # Unit of energy used in infrared
1451 invcm cminv # spectroscopy.
1452 wavenumber cminv
1453 kcal_mol kcal_th / mol N_A # kcal/mol is used as a unit of
1454 # energy by physical chemists.
1455 #
1456 # CGS system based on centimeter, gram and second
1457 #
1458
1459 dyne cm gram / s^2 # force
1460 dyn dyne
1461 erg cm dyne # energy
1462 poise gram / cm s # viscosity, honors Jean Poiseuille
1463 P poise
1464 rhe /poise # reciprocal viscosity
1465 stokes cm^2 / s # kinematic viscosity
1466 St stokes
1467 stoke stokes
1468 lentor stokes # old name
1469 Gal cm / s^2 # acceleration, used in geophysics
1470 galileo Gal # for earth's gravitational field
1471 # (note that "gal" is for gallon
1472 # but "Gal" is the standard symbol
1473 # for the gal which is evidently a
1474 # shortened form of "galileo".)
1475 barye dyne/cm^2 # pressure
1476 barad barye # old name
1477 kayser 1/cm # Proposed as a unit for wavenumber
1478 balmer kayser # Even less common name than "kayser"
1479 kine cm/s # velocity
1480 bole g cm / s # momentum
1481 pond gram force
1482 glug gram force s^2 / cm # Mass which is accelerated at
1483 # 1 cm/s^2 by 1 gram force
1484 darcy centipoise cm^2 / s atm # Measures permeability to fluid flow.
1485 # One darcy is the permeability of a
1486 # medium that allows a flow of cc/s
1487 # of a liquid of centipoise viscosity
1488 # under a pressure gradient of
1489 # atm/cm. Named for H. Darcy.
1490 mobileohm cm / dyn s # mobile ohm, measure of mechanical
1491 # mobility
1492 mechanicalohm dyn s / cm # mechanical resistance
1493 acousticalohm dyn s / cm^5 # ratio of the sound pressure of
1494 # 1 dyn/cm^2 to a source of strength
1495 # 1 cm^3/s
1496 ray acousticalohm
1497 rayl dyn s / cm^3 # Specific acoustical resistance
1498 eotvos 1e-9 Gal/cm # Change in gravitational acceleration
1499 # over horizontal distance
1500 #
1501 # Electromagnetic CGS Units
1502 #
1503 # For measuring electromagnetic quantities in SI, we introduce the new base
1504 # dimension of current, define the ampere to measure current, and derive the
1505 # other electromagnetic units from the ampere. With the CGS units one approach
1506 # is to use the basic equations of electromagnetism to define units that
1507 # eliminate constants from those equations. Coulomb's law has the form
1508 #
1509 # F = k_C q1 q2 / r^2
1510 #
1511 # where k_C is the Coulomb constant equal to 1|4 pi epsilon0 in SI units.
1512 # Ampere's force law takes the form
1513 #
1514 # dF/dl = 2 k_A I1 I2 / r
1515 #
1516 # where k_A is the ampere constant. In the CGS system we force either k_C or
1517 # k_A to 1 which then defines either a unit for charge or a unit for current.
1518 # The other unit then becomes a derived unit. When k_C is 1 the ESU system
1519 # results. When k_A is 1 the EMU system results. Note that these parameters
1520 # are not independent of each other: Maxwell's equations indicate that
1521 #
1522 # k_C / k_A = c^2
1523 #
1524 # where c is the speed of light.
1525 #
1526 # One more choice is needed to define a complete system. Using Coulomb's law
1527 # we define the electric field as the force per unit charge
1528 #
1529 # E = k_C 1 / r^2.
1530 #
1531 # But what about the magnetic field? It is derived from Ampere's law but we
1532 # have the option of adding a proportionality constant, k_B, that may have
1533 # dimensions:
1534 #
1535 # B = 2 k_A k_B I / r
1536 #
1537 # We can choose k_B = 1, which is done in the SI, ESU and EMU systems. But if
1538 # instead we give k_B units of length/time then the magnetic field has
1539 # the same units as the electric field. This choice leads to the Gaussian
1540 # and Heaviside-Lorentz systems.
1541 #
1542 # The relations above are used to determine the dimensions, but the units are
1543 # derived from the base units of CGS, not directly from those formulas. We
1544 # will use the notation [unit] to refer to the dimension of the unit in
1545 # brackets. This same process gives rise to the SI units such as the tesla,
1546 # which is defined by
1547 #
1548 # [tesla] = [2 (1/4 pi c^2 epsilon0) amp / m] = [(mu0 / 2) amp / m]
1549 #
1550 # which gives kg / A s^2 as expected.
1551 #
1552 # References:
1553 #
1554 # Classical Electrodynamics by John David Jackson, 3rd edition.
1555 # Cardarelli, Francois. 1999. Scientific Unit Conversion. 2nd ed. Trans.
1556 # M.J. Shields. London: Springer-Verlag. ISBN 1-85233-043-0
1557 #
1558 #
1559 # All of the CGS systems result in electromagnetic units that involve the square
1560 # roots of the centimeter and gram. This requires a change in the primitive
1561 # units.
1562 #
1563
1564 !var UNITS_SYSTEM esu emu gaussian gauss hlu
1565 sqrt_cm !
1566 sqrt_centimeter sqrt_cm
1567 +m 100 sqrt_cm^2
1568 sqrt_g !
1569 sqrt_gram sqrt_g
1570 +kg kilo sqrt_g^2
1571 !endvar
1572
1573 # Electrostatic CGS (ESU)
1574 #
1575 # This system uses the statcoulomb as the fundamental unit of charge, with
1576 # derived units that parallel the conventional terminology but use the stat-
1577 # prefix. The statcoulomb is designed by setting k_C=1, which means
1578 #
1579 # dyne = statcoulomb^2 / cm^2.
1580 #
1581 # The statcoulomb is also called the franklin or esu.
1582 #
1583 # The ESU system was specified by a committee report in 1873 and rarely used.
1584
1585 statcoulomb 10 coulomb cm / s c # Charge such that two charges
1586 esu statcoulomb # of 1 statC separated by 1 cm
1587 statcoul statcoulomb # exert a force of 1 dyne
1588 statC statcoulomb
1589 stC statcoulomb
1590 franklin statcoulomb
1591 Fr franklin
1592
1593 !var UNITS_SYSTEM esu
1594 !message CGS-ESU units selected
1595 !prompt (ESU)
1596 +statcoulomb sqrt(dyne) cm
1597 +A 10 c_SI statamp
1598 +mu0 1/c^2
1599 +coulombconst 1
1600 !endvar
1601
1602 statampere statcoulomb / s
1603 statamp statampere
1604 statA statampere
1605 stA statampere
1606 statvolt dyne cm / statamp sec
1607 statV statvolt
1608 stV statvolt
1609 statfarad statamp sec / statvolt
1610 statF statfarad
1611 stF statfarad
1612 cmcapacitance statfarad
1613 stathenry statvolt sec / statamp
1614 statH stathenry
1615 stH stathenry
1616 statohm statvolt / statamp
1617 stohm statohm
1618 statmho /statohm
1619 stmho statmho
1620 statweber statvolt sec
1621 statWb statweber
1622 stWb statweber
1623 stattesla statWb/cm^2 # Defined by analogy with SI; rarely
1624 statT stattesla # if ever used
1625 stT stattesla
1626 debye 1e-10 statC angstrom # unit of electrical dipole moment
1627 helmholtz debye/angstrom^2 # Dipole moment per area
1628 jar 1000 statfarad # approx capacitance of Leyden jar
1629
1630 # Electromagnetic CGS (EMU)
1631 #
1632 # The abampere is the fundamental unit of this system, with the derived units
1633 # using the ab- prefix. The dimensions of the abampere are defined by assuming
1634 # that k_A=1, which
1635 #
1636 # [dyne / cm] = [2 abampere^2 / cm]
1637 #
1638 # where the brackets indicate taking the dimension of the unit in base units
1639 # and discarding any constant factors. This results in the definition from
1640 # base CGS units of:
1641 #
1642 # abampere = sqrt(dyne).
1643 #
1644 # The abampere is also called the biot. The magnetic field unit (the gauss)
1645 # follows from the assumption that k_B=1, which means
1646 #
1647 # B = 2 I / r,
1648 #
1649 # and hence the dimensions of the gauss are given by
1650 #
1651 # [gauss] = [2 abampere / cm]
1652 #
1653 # or rewriting in terms of the base units
1654 #
1655 # gauss = abampere / cm.
1656 #
1657 # The definition given below is different because it is in a form that
1658 # gives a valid reduction for SI and ESU and still gives the correct
1659 # result in EMU. (It can be derived from Faraday's law.)
1660 #
1661 # The EMU system was developed by Gauss and Weber and formalized as a system in
1662 # a committee report by the British Association for the Advancement of Science
1663 # in 1873.
1664
1665 abampere 10 A # Current which produces a force of
1666 abamp abampere # 2 dyne/cm between two infinitely
1667 aA abampere # long wires that are 1 cm apart
1668 abA abampere
1669 biot abampere
1670 Bi biot
1671
1672 !var UNITS_SYSTEM emu
1673 !message CGS-EMU units selected
1674 !prompt (EMU)
1675 +abampere sqrt(dyne)
1676 +A 0.1 abamp
1677 +mu0 1
1678 +coulombconst c^2
1679 !endvar
1680
1681 abcoulomb abamp sec
1682 abcoul abcoulomb
1683 abC abcoulomb
1684 abfarad abampere sec / abvolt
1685 abF abfarad
1686 abhenry abvolt sec / abamp
1687 abH abhenry
1688 abvolt dyne cm / abamp sec
1689 abV abvolt
1690 abohm abvolt / abamp
1691 abmho /abohm
1692 gauss abvolt sec / cm^2 # The magnetic field 2 cm from a wire
1693 Gs gauss # carrying a current of 1 abampere
1694 maxwell gauss cm^2 # Also called the "line"
1695 Mx maxwell
1696 oersted gauss / mu0 # From the relation H = B / mu
1697 Oe oersted
1698 gilbert gauss cm / mu0
1699 Gb gilbert
1700 Gi gilbert
1701 unitpole 4 pi maxwell # unit magnetic pole
1702 emu erg/gauss # "electro-magnetic unit", a measure of
1703 # magnetic moment, often used as emu/cm^3
1704 # to specify magnetic moment density.
1705
1706 # Electromagnetic CGS (Gaussian)
1707 #
1708 # The Gaussian system uses the statcoulomb and statamp from the ESU system
1709 # derived by setting k_C=1, but it defines the magnetic field unit differently
1710 # by taking k_B=c instead of k_B=1. As noted above, k_C and k_A are not
1711 # independent. With k_C=1 we must have k_A=c^-2. This results in the magnetic
1712 # field unit, the gauss, having dimensions give by:
1713 #
1714 # [gauss] = [2 (c^-2) c statamp / cm] = [statamp / c cm]
1715 #
1716 # We then define the gauss using base CGS units to obtain
1717 #
1718 # gauss = statamp / ((cm/s) cm) = statcoulomb / cm^2.
1719 #
1720 # Note that this definition happens to give the same result as the definition
1721 # for the EMU system, so the definitions of the gauss are consistent.
1722 #
1723 # This definition gives the same dimensions for the E and B fields and was also
1724 # known as the "symmetric system". This system was proposed by Hertz in 1888.
1725
1726 !var UNITS_SYSTEM gaussian gauss
1727 !message CGS-Gaussian units selected
1728 !prompt (Gaussian)
1729 !endvar
1730 !var UNITS_SYSTEM gaussian gauss natural-gauss
1731 +statcoulomb sqrt(dyne) cm
1732 +A 10 c_SI statamp
1733 +mu0 1
1734 +epsilon0 1
1735 +coulombconst 1 # The gauss is the B field produced
1736 +gauss statcoulomb / cm^2 # 1 cm from a wire carrying a current
1737 +weber 1e8 maxwell # of 0.5*(c/(cm/s)) stA = 1.5e10 stA
1738 +bohrmagneton e hbar / 2 electronmass c
1739 +nuclearmagneton e hbar / 2 protonmass c
1740 !endvar
1741
1742 # Electromagnetic CGS (Heaviside-Lorentz)
1743
1744 # The Heaviside-Lorentz system is similar to the Gaussian system, but it is
1745 # "rationalized" so that factors of 4 pi do not appear in Maxwell's equations.
1746 # The SI system is similarly rationalized, but the other CGS systems are not.
1747 #
1748 # The factor of 4 pi appears instead in Coulomb's law, so in this system
1749 # k_C = 1 / 4 pi, which means the charge unit is defined by
1750 #
1751 # dyne = (1 / 4 pi) hlu_charge^2 / cm^2.
1752 #
1753 # Since we have the leading constant of (1 / 4pi) the numerical value of the
1754 # charge number is larger by sqrt(4pi), which in turns means that the HLU
1755 # charge unit is smaller by this multiple. But note that the dimensions of the
1756 # charge unit are the same as the Gaussian system, so both systems measure
1757 # charge with cm^(3/2) g^(1/2) / s, but the amount of charge for this dimension
1758 # differs by a factor of sqrt(4pi) between the two systems.
1759 #
1760 # Ampere's law for the Heaviside-Lorentz system has the form
1761 #
1762 # B = 1/(2 pi c) * I/r
1763
1764 # The Heaviside-Lorentz system does not appear to have any named units, so we
1765 # use "hlu" for "Heaviside-Lorentz unit" so we can define values for the basic
1766 # units in this system.
1767
1768 hlu_charge statcoulomb / sqrt(4 pi)
1769 hlu_current hlu_charge / sec
1770 hlu_volt erg / hlu_charge
1771 hlu_efield hlu_volt / cm
1772 hlu_bfield sqrt(4 pi) gauss
1773
1774 !var UNITS_SYSTEM hlu
1775 !message CGS-Heaviside-Lorentz Units selected
1776 !prompt (HLU)
1777 !endvar
1778 !var UNITS_SYSTEM hlu natural planck planck-red
1779 +statcoulomb sqrt(dyne) cm sqrt(4 pi)
1780 +A 10 c_SI statamp
1781 +mu0 1
1782 +epsilon0 1
1783 # The gauss is the B field produced 1 cm from a wire carrying
1784 # a current of 0.5*(c/(cm/s)) stA, derived from Ampere's law
1785 +gauss (1/2 pi c) (0.5 c/(cm/s)) statamp / cm
1786 +weber 1e8 maxwell
1787 +bohrmagneton e hbar / 2 electronmass c
1788 +nuclearmagneton e hbar / 2 protonmass c
1789 !endvar
1790
1791 # "Natural units" (high energy physics and cosmology)
1792 #
1793 # In particle physics "natural units" (which don't seem to have a more specific
1794 # name) are defined by setting hbar = c = boltzmann = 1. In this system the
1795 # electron volt is the only base unit. The electromagnetic units can be
1796 # derived from the rationalized Heaviside-Lorentz units or from Gaussian units.
1797 # The default form is the rationalized HLU derived version.
1798
1799 # These are the Heaviside-Lorentz natural units
1800
1801 natural_length hbar c / eV
1802 natural_mass eV / c^2
1803 natural_time hbar / eV
1804 natural_temp eV / boltzmann
1805 natural_charge e / sqrt(4 pi alpha)
1806 natural_current natural_charge / natural_time
1807 natural_force natural_mass natural_length / natural_time^2
1808 natural_energy natural_force natural_length
1809 natural_power natural_energy / natural_time
1810 natural_volt natural_energy / natural_charge
1811 natural_Efield natural_volt / natural_length
1812 natural_Bfield natural_volt natural_time / natural_length^2
1813
1814 !var UNITS_SYSTEM natural
1815 !message Natural units selected (Heaviside-Lorentz based)
1816 !prompt (natural)
1817 +eV !
1818 +h 2 pi
1819 +c 1
1820 +boltzmann 1
1821 +m e_SI / hbar_SI c_SI eV
1822 +kg (c_SI^2 / e_SI) eV
1823 +s e_SI / hbar_SI eV
1824 +K (k_SI / e_SI) eV
1825 !endvar
1826
1827 !var UNITS_SYSTEM natural-gauss
1828 !message Natural units selected (Gaussian based)
1829 !prompt (natgauss)
1830 +eV !
1831 +h 2 pi
1832 +c 1
1833 +boltzmann 1
1834 +m e_SI / (h_SI / 2 pi) c_SI eV
1835 +kg (c_SI^2 / e_SI) eV
1836 +s e_SI / (h_SI / 2 pi) eV
1837 +K (k_SI / e_SI) eV
1838 !endvar
1839
1840 #
1841 # Planck units
1842 #
1843 # Planck units are a set of "natural" units based on physical constants c, G,
1844 # hbar, boltzmann's constant, and epsilon0, often used when working with
1845 # gravitational theory. In planck units, all quantities are dimensionless.
1846 # Some variations are possible for exactly how the units are defined. We
1847 # provide two variations, the rationalized planck units and the
1848 # rationalized-reduced planck units.
1849 #
1850 # In both forms the units are defined by c = hbar = boltzmann = 1.
1851 # But the choice of rationalized and reduced affects how epsilon0 and G
1852 # are treated.
1853 #
1854 # In the "rationalized" units, factors of 4 pi do not appear in Maxwell's
1855 # equation, and Coulomb's law bears a factor of 1/4 pi. See the section on
1856 # the Heaviside-Lorentz units for more about this. The choice of rationalized
1857 # units means that epsilon0 = 1. (In the unrationalized case, which is not
1858 # supported, 1/(4 pi epsilon0) = 1.)
1859 #
1860 # The "reduced" units similarly are defined to eliminate factors of 8 pi
1861 # from the Einstein field equations for gravitation. With reduced units
1862 # we set 8 pi G = 1 and with the unreduced units, simply G = 1.
1863
1864 # Rationalized, unreduced planck units
1865
1866 planckmass sqrt(hbar c / G)
1867 m_P planckmass
1868 plancktime hbar / planckmass c^2
1869 t_P plancktime
1870 plancklength plancktime c
1871 l_P plancklength
1872 plancktemperature hbar / k plancktime
1873 T_P plancktemperature
1874 planckenergy planckmass plancklength^2 / plancktime^2
1875 E_P planckenergy
1876 planckcharge sqrt(epsilon0 hbar c)
1877 planckcurrent planckcharge / plancktime
1878 planckvolt planckenergy / planckcharge
1879 planckEfield planckvolt / plancklength
1880 planckBfield planckvolt plancktime / plancklength^2
1881
1882 # Rationalized, reduced planck units
1883
1884 planckmass_red sqrt(hbar c / 8 pi G)
1885 plancktime_red hbar / planckmass_red c^2
1886 plancklength_red plancktime_red c
1887 plancktemperature_red hbar / k plancktime_red
1888 planckenergy_red planckmass_red plancklength_red^2 / plancktime_red^2
1889 planckcharge_red sqrt(epsilon0 hbar c)
1890 planckcurrent_red planckcharge_red / plancktime_red
1891 planckvolt_red planckenergy_red / planckcharge_red
1892 planckEfield_red planckvolt_red / plancklength_red
1893 planckBfield_red planckvolt_red plancktime_red / plancklength_red^2
1894
1895
1896 !var UNITS_SYSTEM planck
1897 !message Planck units selected
1898 !prompt (planck)
1899 +c 1
1900 +h 2 pi
1901 +G 1
1902 +boltzmann 1
1903 +kg sqrt(G_SI / hbar_SI c_SI)
1904 +s c_SI^2 / hbar_SI kg
1905 +m s / c_SI
1906 +K k_SI / hbar_SI s
1907 !endvar
1908
1909
1910 !var UNITS_SYSTEM planck-red
1911 !message Reduced planck units selected
1912 !prompt (planck reduced)
1913 +c 1
1914 +h 2 pi
1915 +G 1/8 pi
1916 +boltzmann 1
1917 +kg sqrt(8 pi G_SI / hbar_SI c_SI)
1918 +s c_SI^2 / hbar_SI kg
1919 +m s / c_SI
1920 +K k_SI / hbar_SI s
1921 !endvar
1922
1923 #
1924 # Some historical electromagnetic units
1925 #
1926
1927 intampere 0.999835 A # Defined as the current which in one
1928 intamp intampere # second deposits .001118 gram of
1929 # silver from an aqueous solution of
1930 # silver nitrate.
1931 intfarad 0.999505 F
1932 intvolt 1.00033 V
1933 intohm 1.000495 ohm # Defined as the resistance of a
1934 # uniform column of mercury containing
1935 # 14.4521 gram in a column 1.063 m
1936 # long and maintained at 0 degC.
1937 daniell 1.042 V # Meant to be electromotive force of a
1938 # Daniell cell, but in error by .04 V
1939 faraday N_A e mol # Charge that must flow to deposit or
1940 faraday_phys 96521.9 C # liberate one gram equivalent of any
1941 faraday_chem 96495.7 C # element. (The chemical and physical
1942 # values are off slightly from what is
1943 # obtained by multiplying by amu_chem
1944 # or amu_phys. These values are from
1945 # a 1991 NIST publication.) Note that
1946 # there is a Faraday constant which is
1947 # equal to N_A e and hence has units of
1948 # C/mol.
1949 kappline 6000 maxwell # Named by and for Gisbert Kapp
1950 siemensunit 0.9534 ohm # Resistance of a meter long column of
1951 # mercury with a 1 mm cross section.
1952 #
1953 # Printed circuit board units.
1954 #
1955 # http://www.ndt-ed.org/GeneralResources/IACS/IACS.htm.
1956 #
1957 # Conductivity is often expressed as a percentage of IACS. A copper wire a
1958 # meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at
1959 # 20 deg C. Copper density also has a standard IACS value at that temperature.
1960 #
1961
1962 copperconductivity 58 siemens m / mm^2 # A wire a meter long with
1963 IACS copperconductivity # a 1 mm^2 cross section
1964 copperdensity 8.89 g/cm^3 # The "ounce" measures the
1965 ouncecopper oz / ft^2 copperdensity # thickness of copper used
1966 ozcu ouncecopper # in circuitboard fabrication
1967
1968 #
1969 # Photometric units
1970 #
1971
1972 LUMINOUS_INTENSITY candela
1973 LUMINOUS_FLUX lumen
1974 LUMINOUS_ENERGY talbot
1975 ILLUMINANCE lux
1976 EXITANCE lux
1977
1978 candle 1.02 candela # Standard unit for luminous intensity
1979 hefnerunit 0.9 candle # in use before candela
1980 hefnercandle hefnerunit #
1981 violle 20.17 cd # luminous intensity of 1 cm^2 of
1982 # platinum at its temperature of
1983 # solidification (2045 K)
1984
1985 lumen cd sr # Luminous flux (luminous energy per
1986 lm lumen # time unit)
1987
1988 talbot lumen s # Luminous energy
1989 lumberg talbot # References give these values for
1990 lumerg talbot # lumerg and lumberg both. Note that
1991 # a paper from 1948 suggests that
1992 # lumerg should be 1e-7 talbots so
1993 # that lumergs/erg = talbots/joule.
1994 # lumerg = luminous erg
1995 lux lm/m^2 # Illuminance or exitance (luminous
1996 lx lux # flux incident on or coming from
1997 phot lumen / cm^2 # a surface)
1998 ph phot #
1999 footcandle lumen/ft^2 # Illuminance from a 1 candela source
2000 # at a distance of one foot
2001 metercandle lumen/m^2 # Illuminance from a 1 candela source
2002 # at a distance of one meter
2003
2004 mcs metercandle s # luminous energy per area, used to
2005 # measure photographic exposure
2006
2007 nox 1e-3 lux # These two units were proposed for
2008 skot 1e-3 apostilb # measurements relating to dark adapted
2009 # eyes.
2010 # Luminance measures
2011
2012 LUMINANCE nit
2013
2014 nit cd/m^2 # Luminance: the intensity per projected
2015 stilb cd / cm^2 # area of an extended luminous source.
2016 sb stilb # (nit is from latin nitere = to shine.)
2017
2018 apostilb cd/pi m^2
2019 asb apostilb
2020 blondel apostilb # Named after a French scientist.
2021
2022 # Equivalent luminance measures. These units are units which measure
2023 # the luminance of a surface with a specified exitance which obeys
2024 # Lambert's law. (Lambert's law specifies that luminous intensity of
2025 # a perfectly diffuse luminous surface is proportional to the cosine
2026 # of the angle at which you view the luminous surface.)
2027
2028 equivalentlux cd / pi m^2 # luminance of a 1 lux surface
2029 equivalentphot cd / pi cm^2 # luminance of a 1 phot surface
2030 lambert cd / pi cm^2
2031 footlambert cd / pi ft^2
2032
2033 # The bril is used to express "brilliance" of a source of light on a
2034 # logarithmic scale to correspond to subjective perception. An increase of 1
2035 # bril means doubling the luminance. A luminance of 1 lambert is defined to
2036 # have a brilliance of 1 bril.
2037
2038 bril(x) units=[1;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100
2039
2040 # Some luminance data from the IES Lighting Handbook, 8th ed, 1993
2041
2042 sunlum 1.6e9 cd/m^2 # at zenith
2043 sunillum 100e3 lux # clear sky
2044 sunillum_o 10e3 lux # overcast sky
2045 sunlum_h 6e6 cd/m^2 # value at horizon
2046 skylum 8000 cd/m^2 # average, clear sky
2047 skylum_o 2000 cd/m^2 # average, overcast sky
2048 moonlum 2500 cd/m^2
2049
2050 #
2051 # Photographic Exposure Value
2052 # This section by Jeff Conrad (jeff_conrad@msn.com)
2053 #
2054 # The Additive system of Photographic EXposure (APEX) proposed in ASA
2055 # PH2.5-1960 was an attempt to simplify exposure determination for people who
2056 # relied on exposure tables rather than exposure meters. Shortly thereafter,
2057 # nearly all cameras incorporated exposure meters, so the APEX system never
2058 # caught on, but the concept of exposure value remains in use. Though given as
2059 # 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'. EV is
2060 # related to exposure parameters by
2061 #
2062 # A^2 LS ES
2063 # 2^EV = --- = -- = --
2064 # t K C
2065 #
2066 # Where
2067 # A = Relative aperture (f-number)
2068 # t = Exposure time in seconds
2069 # L = Scene luminance in cd/m2
2070 # E = Scene illuminance in lux
2071 # S = Arithmetic ISO speed
2072 # K = Reflected-light meter calibration constant
2073 # C = Incident-light meter calibration constant
2074 #
2075 # Strictly, an exposure value is a combination of aperture and exposure time,
2076 # but it's also commonly used to indicate luminance (or illuminance).
2077 # Conversion to luminance or illuminance units depends on the ISO speed and the
2078 # meter calibration constant. Common practice is to use an ISO speed of 100.
2079 # Calibration constants vary among camera and meter manufacturers: Canon,
2080 # Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while
2081 # Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and Sekonic use
2082 # a value of 250 for incident-light meters with flat receptors.
2083 #
2084 # The values for in-camera meters apply only averaging, weighted-averaging, or
2085 # spot metering--the multi-segment metering incorporated in most current
2086 # cameras uses proprietary algorithms that evaluate many factors related to the
2087 # luminance distribution of what is being metered; they are not amenable to
2088 # simple conversions, and are usually not disclosed by the manufacturers.
2089
2090 s100 100 / lx s # ISO 100 speed
2091 iso100 s100
2092
2093 # Reflected-light meter calibration constant with ISO 100 speed
2094
2095 k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic
2096 k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax
2097
2098 # Incident-light meter calibration constant with ISO 100 film
2099
2100 c250 250 lx / lx s # flat-disc receptor
2101
2102 # Exposure value to scene luminance with ISO 100 imaging media
2103
2104 # For Kenko (Minolta) or Pentax
2105 #ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400)
2106 # For Canon, Nikon, or Sekonic
2107 ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250)
2108 EV100() ev100
2109
2110 # Exposure value to scene illuminance with ISO 100 imaging media
2111
2112 iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250)
2113
2114 # Other Photographic Exposure Conversions
2115 #
2116 # As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities
2117 # related by
2118 #
2119 # Ev = Av + Tv = Bv + Sv
2120 #
2121 # where
2122 # Av = log2(A^2) Aperture value
2123 # Tv = log2(1/t) Time value
2124 # Sv = log2(N Sx) Speed value
2125 # Bv = log2(B S / K) Luminance ("brightness") value
2126 # Iv = log2(I S / C) Illuminance value
2127 #
2128 # and
2129 # A = Relative aperture (f-number)
2130 # t = Exposure time in seconds
2131 # Sx = Arithmetic ISO speed in 1/lux s
2132 # B = luminance in cd/m2
2133 # I = luminance in lux
2134
2135 # The constant N derives from the arcane relationship between arithmetic
2136 # and logarithmic speed given in ASA PH2.5-1960. That relationship
2137 # apparently was not obvious--so much so that it was thought necessary
2138 # to explain it in PH2.12-1961. The constant has had several values
2139 # over the years, usually without explanation for the changes. Although
2140 # APEX had little impact on consumer cameras, it has seen a partial
2141 # resurrection in the Exif standards published by the Camera & Imaging
2142 # Products Association of Japan.
2143
2144 #N_apex 2^-1.75 lx s # precise value implied in ASA PH2.12-1961,
2145 # derived from ASA PH2.5-1960.
2146 #N_apex 0.30 lx s # rounded value in ASA PH2.5-1960,
2147 # ASA PH2.12-1961, and ANSI PH2.7-1986
2148 #N_apex 0.3162 lx s # value in ANSI PH2.7-1973
2149 N_exif 1|3.125 lx s # value in Exif 2.3 (2010), making Sv(5) = 100
2150 K_apex1961 11.4 (cd/m2) / lx s # value in ASA PH2.12-1961
2151 K_apex1971 12.5 (cd/m2) / lx s # value in ANSI PH3.49-1971; more common
2152 C_apex1961 224 lx / lx s # value in PH2.12-1961 (20.83 for I in
2153 # footcandles; flat sensor?)
2154 C_apex1971 322 lx / lx s # mean value in PH3.49-1971 (30 +/- 5 for I in
2155 # footcandles; hemispherical sensor?)
2156 N_speed N_exif
2157 K_lum K_apex1971
2158 C_illum C_apex1961
2159
2160 # Units for Photographic Exposure Variables
2161 #
2162 # Practical photography sometimes pays scant attention to units for exposure
2163 # variables. In particular, the "speed" of the imaging medium is treated as if
2164 # it were dimensionless when it should have units of reciprocal lux seconds;
2165 # this practice works only because "speed" is almost invariably given in
2166 # accordance with international standards (or similar ones used by camera
2167 # manufacturers)--so the assumed units are invariant. In calculating
2168 # logarithmic quantities--especially the time value Tv and the exposure value
2169 # EV--the units for exposure time ("shutter speed") are often ignored; this
2170 # practice works only because the units of exposure time are assumed to be in
2171 # seconds, and the missing units that make the argument to the logarithmic
2172 # function dimensionless are silently provided.
2173 #
2174 # In keeping with common practice, the definitions that follow treat "speeds"
2175 # as dimensionless, so ISO 100 speed is given simply as '100'. When
2176 # calculating the logarithmic APEX quantities Av and Tv, the definitions
2177 # provide the missing units, so the times can be given with any appropriate
2178 # units. For example, giving an exposure time of 1 minute as either '1 min' or
2179 # '60 s' will result in Tv of -5.9068906.
2180 #
2181 # Exposure Value from f-number and Exposure Time
2182 #
2183 # Because nonlinear unit conversions only accept a single quantity,
2184 # there is no direct conversion from f-number and exposure time to
2185 # exposure value EV. But the EV can be obtained from a combination of
2186 # Av and Tv. For example, the "sunny 16" rule states that correct
2187 # exposure for a sunlit scene can achieved by using f/16 and an exposure
2188 # time equal to the reciprocal of the ISO speed in seconds; this can be
2189 # calculated as
2190 #
2191 # ~Av(16) + ~Tv(1|100 s),
2192 #
2193 # which gives 14.643856. These conversions may be combined with the
2194 # ev100 conversion:
2195 #
2196 # ev100(~Av(16) + ~Tv(1|100 s))
2197 #
2198 # to yield the assumed average scene luminance of 3200 cd/m^2.
2199
2200 # convert relative aperture (f-number) to aperture value
2201 Av(A) units=[1;1] domain=[-2,) range=[0.5,) 2^(A/2); 2 log2(Av)
2202 # convert exposure time to time value
2203 Tv(t) units=[1;s] range=(0,) 2^(-t) s; log2(s / Tv)
2204 # convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed;
2205 # make arithmetic speed dimensionless
2206 # 'Sv' conflicts with the symbol for sievert; you can uncomment this function
2207 # definition if you don't need that symbol
2208 #Sv(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv)
2209 Sval(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval)
2210
2211 # convert luminance value Bv in ASA PH2.12-1961 to luminance
2212 Bv(x) units=[1;cd/m^2] range=(0,) \
2213 2^x K_lum N_speed ; log2(Bv / (K_lum N_speed))
2214
2215 # convert illuminance value Iv in ASA PH2.12-1961 to illuminance
2216 Iv(x) units=[1;lx] range=(0,) \
2217 2^x C_illum N_speed ; log2(Iv / (C_illum N_speed))
2218
2219 # convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in
2220 # ASA PH2.5-1960; make arithmetic speed dimensionless
2221 Sx(S) units=[1;1] domain=(0,) \
2222 log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s)
2223
2224 # convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed
2225 # for convenience, speed is treated here as if it were dimensionless
2226 Sdeg(S) units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg))
2227 Sdin() Sdeg
2228
2229 # Numerical Aperture and f-Number of a Lens
2230 #
2231 # The numerical aperture (NA) is given by
2232 #
2233 # NA = n sin(theta)
2234 #
2235 # where n is the index of refraction of the medium and theta is half
2236 # of the angle subtended by the aperture stop from a point in the image
2237 # or object plane. For a lens in air, n = 1, and
2238 #
2239 # NA = 0.5 / f-number
2240 #
2241 # convert NA to f-number
2242 numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \
2243 0.5 / x ; 0.5 / numericalaperture
2244 NA() numericalaperture
2245 #
2246 # convert f-number to itself; restrict values to those possible
2247 fnumber(x) units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber
2248
2249 # Referenced Photographic Standards
2250 #
2251 # ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome,
2252 # Continuous-Tone) Speed of Photographic Negative Materials.
2253 # ASA PH2.12-1961. American Standard, General-Purpose Photographic
2254 # Exposure Meters (photoelectric type).
2255 # ANSI PH3.49-1971. American National Standard for general-purpose
2256 # photographic exposure meters (photoelectric type).
2257 # ANSI PH2.7-1973. American National Standard Photographic Exposure Guide.
2258 # ANSI PH2.7-1986. American National Standard for Photography --
2259 # Photographic Exposure Guide.
2260 # CIPA DC-008-2010. Exchangeable image file format for digital still
2261 # cameras: Exif Version 2.3
2262 # ISO 6:1993. International Standard, Photography -- Black-and-white
2263 # pictorial still camera negative film/process systems --
2264 # Determination of ISO Speed.
2265
2266
2267 #
2268 # Astronomical time measurements
2269 #
2270 # Astronomical time measurement is a complicated matter. The length of the
2271 # true day at a given place can be 21 seconds less than 24 hours or 30 seconds
2272 # over 24 hours. The two main reasons for this are the varying speed of the
2273 # earth in its elliptical orbit and the fact that the sun moves on the ecliptic
2274 # instead of along the celestial equator. To devise a workable system for time
2275 # measurement, Simon Newcomb (1835-1909) used a fictitious "mean sun".
2276 # Consider a first fictitious sun traveling along the ecliptic at a constant
2277 # speed and coinciding with the true sun at perigee and apogee. Then
2278 # considering a second fictitious sun traveling along the celestial equator at
2279 # a constant speed and coinciding with the first fictitious sun at the
2280 # equinoxes. The second fictitious sun is the "mean sun". From this equations
2281 # can be written out to determine the length of the mean day, and the tropical
2282 # year. The length of the second was determined based on the tropical year
2283 # from such a calculation and was officially used from 1960-1967 until atomic
2284 # clocks replaced astronomical measurements for a standard of time. All of the
2285 # values below give the mean time for the specified interval.
2286 #
2287 # See "Mathematical Astronomy Morsels" by Jean Meeus for more details
2288 # and a description of how to compute the correction to mean time.
2289 #
2290
2291 TIME second
2292
2293 anomalisticyear 365.2596 days # The time between successive
2294 # perihelion passages of the
2295 # earth.
2296 siderealyear 365.256360417 day # The time for the earth to make
2297 # one revolution around the sun
2298 # relative to the stars.
2299 tropicalyear 365.242198781 day # The time needed for the mean sun
2300 # as defined above to increase
2301 # its longitude by 360 degrees.
2302 # Most references defined the
2303 # tropical year as the interval
2304 # between vernal equinoxes, but
2305 # this is misleading. The length
2306 # of the season changes over time
2307 # because of the eccentricity of
2308 # the earth's orbit. The time
2309 # between vernal equinoxes is
2310 # approximately 365.24237 days
2311 # around the year 2000. See
2312 # "Mathematical Astronomy
2313 # Morsels" for more details.
2314 eclipseyear 346.62 days # The line of nodes is the
2315 # intersection of the plane of
2316 # Earth's orbit around the sun
2317 # with the plane of the moon's
2318 # orbit around earth. Eclipses
2319 # can only occur when the moon
2320 # and sun are close to this
2321 # line. The line rotates and
2322 # appearances of the sun on the
2323 # line of nodes occur every
2324 # eclipse year.
2325 saros 223 synodicmonth # The earth, moon and sun appear in
2326 # the same arrangement every
2327 # saros, so if an eclipse occurs,
2328 # then one saros later, a similar
2329 # eclipse will occur. (The saros
2330 # is close to 19 eclipse years.)
2331 # The eclipse will occur about
2332 # 120 degrees west of the
2333 # preceding one because the
2334 # saros is not an even number of
2335 # days. After 3 saros, an
2336 # eclipse will occur at
2337 # approximately the same place.
2338 siderealday 86164.09054 s # The sidereal day is the interval
2339 siderealhour 1|24 siderealday # between two successive transits
2340 siderealminute 1|60 siderealhour # of a star over the meridian,
2341 siderealsecond 1|60 siderealminute # or the time required for the
2342 # earth to make one rotation
2343 # relative to the stars. The
2344 # more usual solar day is the
2345 # time required to make a
2346 # rotation relative to the sun.
2347 # Because the earth moves in its
2348 # orbit, it has to turn a bit
2349 # extra to face the sun again,
2350 # hence the solar day is slightly
2351 # longer.
2352 anomalisticmonth 27.55454977 day # Time for the moon to travel from
2353 # perigee to perigee
2354 nodicalmonth 27.2122199 day # The nodes are the points where
2355 draconicmonth nodicalmonth # an orbit crosses the ecliptic.
2356 draconiticmonth nodicalmonth # This is the time required to
2357 # travel from the ascending node
2358 # to the next ascending node.
2359 siderealmonth 27.321661 day # Time required for the moon to
2360 # orbit the earth
2361 lunarmonth 29 days + 12 hours + 44 minutes + 2.8 seconds
2362 # Mean time between full moons.
2363 synodicmonth lunarmonth # Full moons occur when the sun
2364 lunation synodicmonth # and moon are on opposite sides
2365 lune 1|30 lunation # of the earth. Since the earth
2366 lunour 1|24 lune # moves around the sun, the moon
2367 # has to revolve a bit extra to
2368 # get into the full moon
2369 # configuration.
2370 year tropicalyear
2371 yr year
2372 month 1|12 year
2373 mo month
2374 lustrum 5 years # The Lustrum was a Roman
2375 # purification ceremony that took
2376 # place every five years.
2377 # Classically educated Englishmen
2378 # used this term.
2379 decade 10 years
2380 century 100 years
2381 millennium 1000 years
2382 millennia millennium
2383 solaryear year
2384 lunaryear 12 lunarmonth
2385 calendaryear 365 day
2386 commonyear 365 day
2387 leapyear 366 day
2388 julianyear 365.25 day
2389 gregorianyear 365.2425 day
2390 islamicyear 354 day # A year of 12 lunar months. They
2391 islamicleapyear 355 day # began counting on July 16, AD 622
2392 # when Muhammad emigrated to Medina
2393 # (the year of the Hegira). They need
2394 # 11 leap days in 30 years to stay in
2395 # sync with the lunar year which is a
2396 # bit longer than the 29.5 days of the
2397 # average month. The months do not
2398 # keep to the same seasons, but
2399 # regress through the seasons every
2400 # 32.5 years.
2401 islamicmonth 1|12 islamicyear # They have 29 day and 30 day months.
2402
2403 # The Hebrew year is also based on lunar months, but synchronized to the solar
2404 # calendar. The months vary irregularly between 29 and 30 days in length, and
2405 # the years likewise vary. The regular year is 353, 354, or 355 days long. To
2406 # keep up with the solar calendar, a leap month of 30 days is inserted every
2407 # 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This
2408 # gives leap years that last 383, 384, or 385 days.
2409
2410
2411 # Sidereal days
2412
2413 mercuryday 58.6462 day
2414 venusday 243.01 day # retrograde
2415 earthday siderealday
2416 marsday 1.02595675 day
2417 jupiterday 0.41354 day
2418 saturnday 0.4375 day
2419 uranusday 0.65 day # retrograde
2420 neptuneday 0.768 day
2421 plutoday 6.3867 day
2422
2423 # Sidereal years from http://ssd.jpl.nasa.gov/phys_props_planets.html. Data
2424 # was updated in May 2001 based on the 1992 Explanatory Supplement to the
2425 # Astronomical Almanac and the mean longitude rates. Apparently the table of
2426 # years in that reference is incorrect.
2427
2428 mercuryyear 0.2408467 julianyear
2429 venusyear 0.61519726 julianyear
2430 earthyear siderealyear
2431 marsyear 1.8808476 julianyear
2432 jupiteryear 11.862615 julianyear
2433 saturnyear 29.447498 julianyear
2434 uranusyear 84.016846 julianyear
2435 neptuneyear 164.79132 julianyear
2436 plutoyear 247.92065 julianyear
2437
2438 # Objects on the earth are charted relative to a perfect ellipsoid whose
2439 # dimensions are specified by different organizations. The ellipsoid is
2440 # specified by an equatorial radius and a flattening value which defines the
2441 # polar radius. These values are the 1996 values given by the International
2442 # Earth Rotation Service (IERS) whose reference documents can be found at
2443 # http://maia.usno.navy.mil/
2444
2445 earthflattening 1|298.25642
2446 earthradius_equatorial 6378136.49 m
2447 earthradius_polar (-earthflattening+1) earthradius_equatorial
2448
2449 landarea 148.847e6 km^2
2450 oceanarea 361.254e6 km^2
2451
2452 moonradius 1738 km # mean value
2453 sunradius 6.96e8 m
2454
2455 # Many astronomical values can be measured most accurately in a system of units
2456 # using the astronomical unit and the mass of the sun as base units. The
2457 # uncertainty in the gravitational constant makes conversion to SI units
2458 # significantly less accurate.
2459
2460 # The astronomical unit was defined to be the length of the of the semimajor
2461 # axis of a massless object with the same year as the earth. With such a
2462 # definition in force, and with the mass of the sun set equal to one, Kepler's
2463 # third law can be used to solve for the value of the gravitational constant.
2464
2465 # Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital
2466 # period, a is the size of the semimajor axis, G is the gravitational constant
2467 # and M is the mass. With M = 1 and T and a chosen for the earth's orbit, we
2468 # find sqrt(G) = (2 pi / T) sqrt(AU^3). This constant is called the Gaussian
2469 # gravitational constant, apparently because Gauss originally did the
2470 # calculations. However, when the original calculation was done, the value
2471 # for the length of the earth's year was inaccurate. The value used is called
2472 # the Gaussian year. Changing the astronomical unit to bring it into
2473 # agreement with more accurate values for the year would have invalidated a
2474 # lot of previous work, so instead the astronomical unit has been kept equal
2475 # to this original value. This is accomplished by using a standard value for
2476 # the Gaussian gravitational constant. This constant is called k.
2477 # Many values below are from http://ssd.jpl.nasa.gov/?constants
2478
2479 gauss_k 0.01720209895 # This beast has dimensions of
2480 # au^(3|2) / day and is exact.
2481 gaussianyear (2 pi / gauss_k) days # Year that corresponds to the Gaussian
2482 # gravitational constant. This is a
2483 # fictional year, and doesn't
2484 # correspond to any celestial event.
2485 astronomicalunit 149597870700 m # IAU definition from 2012, exact
2486 au astronomicalunit # ephemeris for the above described
2487 # astronomical unit. (See the NASA
2488 # site listed above.)
2489 GMsun 1.32712440018e20 m^3 / s^2 # heliocentric gravitational constant
2490 solarmass GMsun/G # with uncertainty 8e9 is known more
2491 sunmass solarmass # accurately than G.
2492
2493
2494 sundist 1.0000010178 au # mean earth-sun distance
2495 moondist 3.844e8 m # mean earth-moon distance
2496 sundist_near 1.471e11 m # earth-sun distance at perihelion
2497 sundist_far 1.521e11 m # earth-sun distance at aphelion
2498 moondist_min 3.564e8 m # approximate least distance at
2499 # perigee 1901-2300
2500 moondist_max 4.067e8 m # approximate greatest distance at
2501 # apogee 1901-2300
2502
2503
2504 # The following are masses for planetary systems, not just the planet itself.
2505 # The comments give the uncertainty in the denominators. As noted above,
2506 # masses are given relative to the solarmass because this is more accurate.
2507 # The conversion to SI is uncertain because of uncertainty in G, the
2508 # gravitational constant.
2509 #
2510 # Values are from http://ssd.jpl.nasa.gov/astro_constants.html
2511
2512 mercurymass solarmass / 6023600 # 250
2513 venusmass solarmass / 408523.71 # 0.06
2514 earthmoonmass solarmass / 328900.56 # 0.02
2515 marsmass solarmass / 3098708 # 9
2516 jupitermass solarmass / 1047.3486 # 0.0008
2517 saturnmass solarmass / 3497.898 # 0.018
2518 uranusmass solarmass / 22902.98 # 0.03
2519 neptunemass solarmass / 19412.24 # 0.04
2520 plutomass solarmass / 1.35e8 # 0.07e8
2521
2522 moonearthmassratio 0.012300034 # uncertainty 3e-9
2523 earthmass earthmoonmass / ( 1 + moonearthmassratio)
2524 moonmass moonearthmassratio earthmass
2525
2526 # These are the old values for the planetary masses. They may give
2527 # the masses of the planets alone.
2528
2529 oldmercurymass 0.33022e24 kg
2530 oldvenusmass 4.8690e24 kg
2531 oldmarsmass 0.64191e24 kg
2532 oldjupitermass 1898.8e24 kg
2533 oldsaturnmass 568.5e24 kg
2534 olduranusmass 86.625e24 kg
2535 oldneptunemass 102.78e24 kg
2536 oldplutomass 0.015e24 kg
2537
2538 # Mean radius from http://ssd.jpl.nsaa.gov/phys_props_planets.html which in
2539 # turn cites Global Earth Physics by CF Yoder, 1995.
2540
2541 mercuryradius 2440 km
2542 venusradius 6051.84 km
2543 earthradius 6371.01 km
2544 marsradius 3389.92 km
2545 jupiterradius 69911 km
2546 saturnradius 58232 km
2547 uranusradius 25362 km
2548 neptuneradius 24624 km
2549 plutoradius 1151 km
2550
2551 moongravity 1.62 m/s^2
2552
2553 # The Hubble constant gives the speed at which distance galaxies are moving
2554 # away from the earth according to v = H0*d, where H0 is the hubble constant
2555 # and d is the distance to the galaxy.
2556
2557 hubble 70 km/s/Mpc # approximate
2558 H0 hubble
2559
2560 # Parallax is the angular difference between the topocentric (on Earth's
2561 # surface) and geocentric (at Earth's center) direction toward a celestial body
2562 # when the body is at a given altitude. When the body is on the horizon, the
2563 # parallax is the horizontal parallax; when the body is on the horizon and the
2564 # observer is on the equator, the parallax is the equatorial horizontal
2565 # parallax. When the body is at zenith, the parallax is zero.
2566
2567 lunarparallax asin(earthradius_equatorial / moondist) # Moon equatorial
2568 moonhp lunarparallax # horizontal parallax
2569 # at mean distance
2570
2571 # Light from celestial objects is attenuated by passage through Earth's
2572 # atmosphere. A body near the horizon passes through much more air than an
2573 # object at zenith, and is consequently less bright. Air mass is the ratio of
2574 # the length of the optical path at a given altitude (angle above the horizon)
2575 # to the length at zenith. Air mass at zenith is by definition unity; at the
2576 # horizon, air mass is approximately 38, though the latter value can vary
2577 # considerably with atmospheric conditions. The general formula is # E = E0
2578 # exp(-c X), where E0 is the value outside Earth's atmosphere, E is the value
2579 # seen by an observer, X is the air mass and c is the extinction coefficient.
2580 # A common value for c in reasonably clear air is 0.21, but values can be
2581 # considerably greater in urban areas. Apparent altitude is that perceived by
2582 # an observer; it includes the effect of atmospheric refraction. There is no
2583 # shortage of formulas for air mass
2584 # (https://en.wikipedia.org/wiki/Air_mass_(astronomy)); all are subject to
2585 # variations in local atmospheric conditions. The formula used here is simple
2586 # and is in good agreement with rigorously calculated values under standard
2587 # conditions.
2588 #
2589 # Extraterrestrial illuminance or luminance of an object at a given altitude
2590 # determined with vmag() or SB_xxx() below can be multiplied by
2591 # atm_transmission() or atm_transmissionz() to estimate the terrestrial value.
2592 #
2593 # Kasten and Young (1989) air mass formula. alt is apparent altitude
2594 # Reference:
2595 # Kasten, F., and A.T. Young. 1989. "Revised Optical Air Mass Tables
2596 # and Approximation Formula." Applied Optics. Vol. 28, 4735–4738.
2597 # Bibcode:1989ApOpt..28.4735K. doi:10.1364/AO.28.004735.
2598
2599 airmass(alt) units=[degree;1] domain=[0,90] noerror \
2600 1 / (sin(alt) + 0.50572 (alt / degree + 6.07995)^-1.6364)
2601
2602 # zenith is apparent zenith angle (zenith = 90 deg - alt)
2603 airmassz(zenith) units=[degree;1] domain=[0,90] noerror \
2604 1 / (cos(zenith) + 0.50572 (96.07995 - zenith / degree)^-1.6364)
2605
2606 # For reasonably clear air at sea level; values may need adjustment for
2607 # elevation and local atmospheric conditions
2608 # for scotopic vision (510 nm), appropriate for the dark-adapted eye
2609 # extinction_coeff 0.26
2610 # for photopic vision, appropriate for observing brighter objects such
2611 # as the full moon
2612 extinction_coeff 0.21
2613
2614 atm_transmission(alt) units=[degree;1] domain=[0,90] noerror \
2615 exp(-extinction_coeff airmass(alt))
2616
2617 # in terms of zenith angle (zenith = 90 deg - alt)
2618 atm_transmissionz(zenith) units=[degree;1] domain=[0,90] noerror \
2619 exp(-extinction_coeff airmassz(zenith))
2620
2621 # Moon and Sun data at mean distances
2622 moonvmag -12.74 # Moon apparent visual magnitude at mean distance
2623 sunvmag -26.74 # Sun apparent visual magnitude at mean distance
2624 moonsd asin(moonradius / moondist) # Moon angular semidiameter at mean distance
2625 sunsd asin(sunradius / sundist) # Sun angular semidiameter at mean distance
2626
2627 # Visual magnitude of star or other celestial object. The system of stellar
2628 # magnitudes, developed in ancient Greece, assigned magnitudes from 1
2629 # (brightest) to 6 (faintest visible to the naked eye). In 1856, British
2630 # astronomer Norman Pogson made the system precise, with a magnitude 1 object
2631 # 100 times as bright as a magnitude 6 object, and each magnitude differing
2632 # from the next by a constant ratio; the ratio, sometimes known as Pogson's
2633 # ratio, is thus 100^0.2, or approximately 2.5119. The logarithm of 100^0.2 is
2634 # 0.4, hence the common use of powers of 10 and base-10 logarithms.
2635 #
2636 # Reference:
2637 # Allen, C.W. 1976. Astrophysical Quantities, 3rd ed. 1973, reprinted
2638 # with corrections, 1976. London: Athlone.
2639 #
2640 # The function argument is the (dimensionless) visual magnitude; reference
2641 # illuminance of 2.54e-6 lx is from Allen (2000, 21), and is for outside
2642 # Earth's atmosphere. Illuminance values can be adjusted to terrestrial values
2643 # by multiplying by one of the atm_transmission functions above.
2644
2645 # Illuminance from apparent visual magnitude
2646 vmag(mag) units=[1;lx] domain=[,] range=(0,] \
2647 2.54e-6 lx 10^(-0.4 mag); -2.5 log(vmag / (2.54e-6 lx))
2648
2649 # Surface brightness of a celestial object of a given visual magnitude
2650 # is a logarithmic measure of the luminance the object would have if its
2651 # light were emitted by an object of specified solid angle; it is
2652 # expressed in magnitudes per solid angle. Surface brightness can be
2653 # obtained from the visual magnitude by
2654 # S = m + 2.5 log(pi pi k a b),
2655 # where k is the phase (fraction illuminated), a is the equatorial
2656 # radius, and b is the polar radius. For 100% illumination (e.g., full
2657 # moon), this is often simplified to
2658 # S = m + 2.5 log(pi k s^2),
2659 # where s is the object's angular semidiameter; the units of s determine
2660 # the units of solid angle. The visual magnitude and semidiameter must
2661 # be appropriate for the object's distance; for other than 100%
2662 # illumination, the visual magnitude must be appropriate for the phase.
2663 # Luminance values are for outside Earth's atmosphere; they can be
2664 # adjusted to terrestrial values by multiplying by one of the atm_transmission
2665 # functions above.
2666
2667 # luminance from surface brightness in magnitudes per square degree
2668 SB_degree(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
2669 vmag(sb) / squaredegree ; \
2670 ~vmag(SB_degree squaredegree)
2671
2672 # luminance from surface brightness in magnitudes per square minute
2673 SB_minute(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
2674 vmag(sb) / squareminute ; \
2675 ~vmag(SB_minute squareminute)
2676
2677 # luminance from surface brightness in magnitudes per square second
2678 SB_second(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
2679 vmag(sb) / squaresecond ; \
2680 ~vmag(SB_second squaresecond)
2681
2682 # luminance from surface brightness in magnitudes per steradian
2683 SB_sr(sb) units=[1;cd/m^2] domain=[,] range=(0,] \
2684 vmag(sb) / sr ; \
2685 ~vmag(SB_sr sr)
2686
2687 SB() SB_second
2688 SB_sec() SB_second
2689 SB_min() SB_minute
2690 SB_deg() SB_degree
2691
2692 # The brightness of one tenth-magnitude star per square degree outside
2693 # Earth's atmosphere; often used for night sky brightness.
2694 S10 SB_degree(10)
2695
2696 # Examples for magnitude and surface brightness functions
2697 # Sun illuminance from visual magnitude
2698 # You have: sunvmag
2699 # You want:
2700 # Definition: -26.74 = -26.74
2701 # You have: vmag(sunvmag)
2702 # You want: lx
2703 # * 126134.45
2704 # / 7.9280482e-06
2705 #
2706 # Moon surface brightness from visual magnitude and semidiameter at 100%
2707 # illumination (full moon):
2708 # You have: moonvmag
2709 # You want:
2710 # Definition: -12.74 = -12.74
2711 # You have: moonsd
2712 # You want: arcsec
2713 # * 932.59484
2714 # / 0.001072277
2715 # You have: moonvmag + 2.5 log(pi 932.59484^2)
2716 # You want:
2717 # Definition: 3.3513397
2718 #
2719 # Similar example with specific data obtained from another source (JPL
2720 # Horizons, https://ssd.jpl.nasa.gov/horizons.cgi); semidiameter is in
2721 # arcseconds
2722 #
2723 # You have: -12.9 + 2.5 log(pi 2023.201|2^2)
2724 # You want:
2725 # Definition: 3.3679199
2726 # You have: SB_second(-12.9 + 2.5 log(pi 2023.201|2^2))
2727 # You want:
2728 # Definition: 4858.6547 cd / m^2
2729 #
2730 # If surface brightness is provided by another source (e.g., Horizons),
2731 # it can simply be used directly:
2732 # You have: SB_second(3.3679199)
2733 # You want: cd/m^2
2734 # * 4858.6546
2735 # / 0.0002058183
2736 # The illuminance and luminance values are extraterrestrial (outside
2737 # Earth's atmosphere). The values at Earth's surface are less than these
2738 # because of atmospheric extinction. For example, in the last example
2739 # above, if the Moon were at an altitude of 55 degrees, the terrestrial
2740 # luminance could be calculated with
2741 # You have: SB_second(3.3679199)
2742 # You want: cd/m^2
2743 # * 4858.6546
2744 # / 0.0002058183
2745 # You have: _ atm_transmission(55 deg)
2746 # You want: cd/m^2
2747 # * 3760.6356
2748 # / 0.0002659125
2749 # If desired, photographic exposure can be determined with EV100(),
2750 # leading to acceptable combinations of aperture and exposure time.
2751 # For the example above, but with the Moon at 10 degrees,
2752 # You have: SB_second(3.3679199) atm_transmission(10 deg)
2753 # You want: EV100
2754 # 13.553962
2755
2756
2757 # The Hartree system of atomic units, derived from fundamental units
2758 # of mass (of electron), action (Planck's constant), charge, and
2759 # the Coulomb constant. This system is used in the fields of physical
2760 # chemistry and condensed matter physics.
2761 #
2762 # The Hartree energy can be derived from m_e, e, hbar, and coulombconst by
2763 # hartree = coulombconst^2 m_e e^4 / hbar^2
2764 # but due to correlations between the measurements for m_e and coulombconst
2765 # this results in a significant loss of precision. So we use an alternate
2766 # equivalent definition for the hartree and use energy instead of the
2767 # Coulomb constant to derive the other units. This method retains the
2768 # precision.
2769
2770 hartree 2 rydberg # Approximate electric potential energy of
2771 # the hydrogen atom in its ground state,
2772 # and approximately twice its ionization
2773 # energy.
2774 # Fundamental units
2775
2776 atomicmass electronmass
2777 atomiccharge e
2778 atomicaction hbar
2779 atomicenergy hartree
2780
2781 # Derived units
2782
2783 atomicvelocity sqrt(atomicenergy / atomicmass)
2784 atomictime atomicaction / atomicenergy
2785 atomiclength atomicvelocity atomictime
2786 atomicforce atomicenergy / atomiclength
2787 atomicmomentum atomicenergy / atomicvelocity
2788 atomiccurrent atomiccharge / atomictime
2789 atomicpotential atomicenergy / atomiccharge # electrical potential
2790 atomicvolt atomicpotential
2791 atomicEfield atomicpotential / atomiclength
2792 atomicBfield atomicvolt atomictime / atomiclength^2
2793 atomictemperature atomicenergy / boltzmann
2794
2795 !var UNITS_SYSTEM hartree
2796 !message Hartree units selected
2797 !prompt (hartree)
2798 +kg 1/electronmass_SI
2799 +K k_SI / hbar_SI s
2800 +m alpha c_SI electronmass_SI / hbar_SI
2801 +s alpha c_SI m
2802 +A 1 / s e_SI
2803 !endvar
2804
2805 #
2806 # These thermal units treat entropy as charge, from [5]
2807 #
2808
2809 thermalcoulomb J/K # entropy
2810 thermalampere W/K # entropy flow
2811 thermalfarad J/K^2
2812 thermalohm K^2/W # thermal resistance
2813 fourier thermalohm
2814 thermalhenry J K^2/W^2 # thermal inductance
2815 thermalvolt K # thermal potential difference
2816
2817
2818 #
2819 # United States units
2820 #
2821
2822 # linear measure
2823
2824 # The US Metric Law of 1866 legalized the metric system in the USA and
2825 # defined the meter in terms of the British system with the exact
2826 # 1 meter = 39.37 inches. On April 5, 1893 Thomas Corwin Mendenhall,
2827 # Superintendent of Weights and Measures, decided, in what has become
2828 # known as the "Mendenhall Order" that the meter and kilogram would be the
2829 # fundamental standards in the USA. The definition from 1866 was turned
2830 # around to give an exact definition of the yard as 3600|3937 meters This
2831 # definition was used until July of 1959 when the definition was changed
2832 # to bring the US and other English-speaking countries into agreement; the
2833 # Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it
2834 # was approximately halfway between the British and US values; it had the
2835 # added advantage of making 1 inch = 25.4 mm (exactly). Since 1959, the
2836 # "international" foot has been exactly 0.3048 meters. At the same time,
2837 # it was decided that any data expressed in feet derived from geodetic
2838 # surveys within the US would continue to use the old definition and call
2839 # the old unit the "survey foot." The US continues to define the statute
2840 # mile, furlong, chain, rod, link, and fathom in terms of the US survey
2841 # foot.
2842 # Sources:
2843 # NIST Special Publication 447, Sects. 5, 7, and 8.
2844 # NIST Handbook 44, 2011 ed., Appendix C.
2845 # Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014.
2846
2847 US 1200|3937 m/ft # These four values will convert
2848 US- US # international measures to
2849 survey- US # US Survey measures
2850 geodetic- US
2851 int 3937|1200 ft/m # Convert US Survey measures to
2852 int- int # international measures
2853
2854 inch 2.54 cm
2855 in inch
2856 foot 12 inch
2857 feet foot
2858 ft foot
2859 yard 3 ft
2860 yd yard
2861 mile 5280 ft # The mile was enlarged from 5000 ft
2862 # to this number in order to make
2863 # it an even number of furlongs.
2864 # (The Roman mile is 5000 romanfeet.)
2865 line 1|12 inch # Also defined as '.1 in' or as '1e-8 Wb'
2866 rod 5.5 yard
2867 perch rod
2868 furlong 40 rod # From "furrow long"
2869 statutemile mile
2870 league 3 mile # Intended to be an an hour's walk
2871
2872 # surveyor's measure
2873
2874 surveyorschain 66 surveyft
2875 surveychain surveyorschain
2876 surveyorspole 1|4 surveyorschain
2877 surveyorslink 1|100 surveyorschain
2878 chain 66 ft
2879 link 1|100 chain
2880 ch chain
2881 USacre 10 surveychain^2
2882 intacre 10 chain^2 # Acre based on international ft
2883 intacrefoot acre foot
2884 USacrefoot USacre surveyfoot
2885 acrefoot intacrefoot
2886 acre intacre
2887 section mile^2
2888 township 36 section
2889 homestead 160 acre # Area of land granted by the 1862 Homestead
2890 # Act of the United States Congress
2891 gunterschain surveyorschain
2892
2893 engineerschain 100 ft
2894 engineerslink 1|100 engineerschain
2895 ramsdenschain engineerschain
2896 ramsdenslink engineerslink
2897
2898 gurleychain 33 feet # Andrew Ellicott chain is the
2899 gurleylink 1|50 gurleychain # same length
2900
2901 wingchain 66 feet # Chain from 1664, introduced by
2902 winglink 1|80 wingchain # Vincent Wing, also found in a
2903 # 33 foot length with 40 links.
2904 # early US length standards
2905
2906 # The US has had four standards for the yard: one by Troughton of London
2907 # (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent
2908 # with the definition of the meter in the metric joint resolution of
2909 # Congress in 1866, but defining the yard in terms of the meter; and the
2910 # international yard (1959), which standardized definitions for Australia,
2911 # Canada, New Zealand, South Africa, the UK, and the US.
2912 # Sources: Pat Naughtin (2009), Which Inch?, www.metricationmatters.com;
2913 # Lewis E. Barbrow and Lewis V. Judson (1976). NBS Special Publication
2914 # 447, Weights and Measures Standards of the United States: A Brief
2915 # History.
2916
2917 troughtonyard 914.42190 mm
2918 bronzeyard11 914.39980 mm
2919 mendenhallyard surveyyard
2920 internationalyard yard
2921
2922 # nautical measure
2923
2924 fathom 6 ft # Originally defined as the distance from
2925 # fingertip to fingertip with arms fully
2926 # extended.
2927 nauticalmile 1852 m # Supposed to be one minute of latitude at
2928 # the equator. That value is about 1855 m.
2929 # Early estimates of the earth's circumference
2930 # were a bit off. The value of 1852 m was
2931 # made the international standard in 1929.
2932 # The US did not accept this value until
2933 # 1954. The UK switched in 1970.
2934
2935 cable 1|10 nauticalmile
2936 intcable cable # international cable
2937 cablelength cable
2938 UScable 100 USfathom
2939 navycablelength 720 USft # used for depth in water
2940 marineleague 3 nauticalmile
2941 geographicalmile brnauticalmile
2942 knot nauticalmile / hr
2943 click km # US military slang
2944 klick click
2945
2946 # Avoirdupois weight
2947
2948 pound 0.45359237 kg # The one normally used
2949 lb pound # From the latin libra
2950 grain 1|7000 pound # The grain is the same in all three
2951 # weight systems. It was originally
2952 # defined as the weight of a barley
2953 # corn taken from the middle of the
2954 # ear.
2955 ounce 1|16 pound
2956 oz ounce
2957 dram 1|16 ounce
2958 dr dram
2959 ushundredweight 100 pounds
2960 cwt hundredweight
2961 shorthundredweight ushundredweight
2962 uston shortton
2963 shortton 2000 lb
2964 quarterweight 1|4 uston
2965 shortquarterweight 1|4 shortton
2966 shortquarter shortquarterweight
2967
2968 # Troy Weight. In 1828 the troy pound was made the first United States
2969 # standard weight. It was to be used to regulate coinage.
2970
2971 troypound 5760 grain
2972 troyounce 1|12 troypound
2973 ozt troyounce
2974 pennyweight 1|20 troyounce # Abbreviated "d" in reference to a
2975 dwt pennyweight # Frankish coin called the "denier"
2976 # minted in the late 700's. There
2977 # were 240 deniers to the pound.
2978 assayton mg ton / troyounce # mg / assayton = troyounce / ton
2979 usassayton mg uston / troyounce
2980 brassayton mg brton / troyounce
2981 fineounce troyounce # A troy ounce of 99.5% pure gold
2982
2983 # Some other jewelers units
2984
2985 metriccarat 0.2 gram # Defined in 1907
2986 metricgrain 50 mg
2987 carat metriccarat
2988 ct carat
2989 jewelerspoint 1|100 carat
2990 silversmithpoint 1|4000 inch
2991 momme 3.75 grams # Traditional Japanese unit based
2992 # on the chinese mace. It is used for
2993 # pearls in modern times and also for
2994 # silk density. The definition here
2995 # was adopted in 1891.
2996 # Apothecaries' weight
2997
2998 appound troypound
2999 apounce troyounce
3000 apdram 1|8 apounce
3001 apscruple 1|3 apdram
3002
3003 # Liquid measure
3004
3005 usgallon 231 in^3 # US liquid measure is derived from
3006 gal gallon # the British wine gallon of 1707.
3007 quart 1|4 gallon # See the "winegallon" entry below
3008 pint 1|2 quart # more historical information.
3009 gill 1|4 pint
3010 usquart 1|4 usgallon
3011 uspint 1|2 usquart
3012 usgill 1|4 uspint
3013 usfluidounce 1|16 uspint
3014 fluiddram 1|8 usfloz
3015 minimvolume 1|60 fluiddram
3016 qt quart
3017 pt pint
3018 floz fluidounce
3019 usfloz usfluidounce
3020 fldr fluiddram
3021 liquidbarrel 31.5 usgallon
3022 usbeerbarrel 2 beerkegs
3023 beerkeg 15.5 usgallon # Various among brewers
3024 ponykeg 1|2 beerkeg
3025 winekeg 12 usgallon
3026 petroleumbarrel 42 usgallon # Originated in Pennsylvania oil
3027 barrel petroleumbarrel # fields, from the winetierce
3028 bbl barrel
3029 ushogshead 2 liquidbarrel
3030 usfirkin 9 usgallon
3031
3032 # Dry measures: The Winchester Bushel was defined by William III in 1702 and
3033 # legally adopted in the US in 1836.
3034
3035 usbushel 2150.42 in^3 # Volume of 8 inch cylinder with 18.5
3036 bu bushel # inch diameter (rounded)
3037 peck 1|4 bushel
3038 uspeck 1|4 usbushel
3039 brpeck 1|4 brbushel
3040 pk peck
3041 drygallon 1|2 uspeck
3042 dryquart 1|4 drygallon
3043 drypint 1|2 dryquart
3044 drybarrel 7056 in^3 # Used in US for fruits, vegetables,
3045 # and other dry commodities except for
3046 # cranberries.
3047 cranberrybarrel 5826 in^3 # US cranberry barrel
3048 heapedbushel 1.278 usbushel# The following explanation for this
3049 # value was provided by Wendy Krieger
3050 # <os2fan2@yahoo.com> based on
3051 # guesswork. The cylindrical vessel is
3052 # 18.5 inches in diameter and 1|2 inch
3053 # thick. A heaped bushel includes the
3054 # contents of this cylinder plus a heap
3055 # on top. The heap is a cone 19.5
3056 # inches in diameter and 6 inches
3057 # high. With these values, the volume
3058 # of the bushel is 684.5 pi in^3 and
3059 # the heap occupies 190.125 pi in^3.
3060 # Therefore, the heaped bushel is
3061 # 874.625|684.5 bushels. This value is
3062 # approximately 1.2777575 and it rounds
3063 # to the value listed for the size of
3064 # the heaped bushel. Sometimes the
3065 # heaped bushel is reported as 1.25
3066 # bushels. This same explanation gives
3067 # that value if the heap is taken to
3068 # have an 18.5 inch diameter.
3069
3070 # Grain measures. The bushel as it is used by farmers in the USA is actually
3071 # a measure of mass which varies for different commodities. Canada uses the
3072 # same bushel masses for most commodities, but not for oats.
3073
3074 wheatbushel 60 lb
3075 soybeanbushel 60 lb
3076 cornbushel 56 lb
3077 ryebushel 56 lb
3078 barleybushel 48 lb
3079 oatbushel 32 lb
3080 ricebushel 45 lb
3081 canada_oatbushel 34 lb
3082
3083 # Wine and Spirits measure
3084
3085 ponyvolume 1 usfloz
3086 jigger 1.5 usfloz # Can vary between 1 and 2 usfloz
3087 shot jigger # Sometimes 1 usfloz
3088 eushot 25 ml # EU standard spirits measure
3089 fifth 1|5 usgallon
3090 winebottle 750 ml # US industry standard, 1979
3091 winesplit 1|4 winebottle
3092 magnum 1.5 liter # Standardized in 1979, but given
3093 # as 2 qt in some references
3094 metrictenth 375 ml
3095 metricfifth 750 ml
3096 metricquart 1 liter
3097
3098 # Old British bottle size
3099
3100 reputedquart 1|6 brgallon
3101 reputedpint 1|2 reputedquart
3102 brwinebottle reputedquart # Very close to 1|5 winegallon
3103
3104 # French champagne bottle sizes
3105
3106 split 200 ml
3107 jeroboam 2 magnum
3108 rehoboam 3 magnum
3109 methuselah 4 magnum
3110 imperialbottle 4 magnum
3111 salmanazar 6 magnum
3112 balthazar 8 magnum
3113 nebuchadnezzar 10 magnum
3114 solomon 12 magnum
3115 melchior 12 magnum
3116 sovereign 17.5 magnum
3117 primat 18 magnum
3118 goliath 18 magnum
3119 melchizedek 20 magnum
3120 midas 20 magnum
3121
3122 # The wine glass doesn't seem to have an official standard, but the same value
3123 # is suggested by several organization.
3124
3125 # https://www.rethinkingdrinking.niaaa.nih.gov/
3126 # http://www.rethinkyourdrinking.ca/what-is-a-standard-drink/
3127 # https://www.drinkaware.co.uk/
3128 # https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/545937/UK_CMOs__report.pdf
3129 # http://www.alcohol.gov.au/internet/alcohol/publishing.nsf/content/drinksguide-cnt
3130
3131 wineglass 150 mL # the size of a "typical" serving
3132
3133 # A unit of alcohol is a specified mass of pure ethyl alcohol.
3134 # The term is used officially in the UK, but other countries use the same
3135 # concept but with different values. For example, the UK value of 8 g is
3136 # nominally the amount of alcohol that a typical adult can metabolize in
3137 # one hour. Values for several countries, converted to a volumetric basis:
3138
3139 alcoholunitus 14 g / ethanoldensity
3140 alcoholunitca 13.6 g / ethanoldensity
3141 alcoholunituk 8 g / ethanoldensity
3142 alcoholunitau 10 g / ethanoldensity
3143
3144 # Example: for 12% ABV (alcohol by volume)
3145 # alcoholunitus / 12% = 147.8 mL, close to the “standard” serving of 150 mL.
3146
3147
3148 # Coffee
3149 #
3150 # The recommended ratio of coffee to water. Values vary considerably;
3151 # one is from the Specialty Coffee Association of America
3152 # http://scaa.org/?page=resources&d=brewing-best-practices
3153
3154 coffeeratio 55 g/L # ± 10%
3155
3156 # other recommendations are more loose, e.g.,
3157 # http://www.ncausa.org/About-Coffee/How-to-Brew-Coffee
3158
3159
3160 #
3161 # Water is "hard" if it contains various minerals, expecially calcium
3162 # carbonate.
3163 #
3164
3165 clarkdegree grains/brgallon # Content by weigh of calcium carbonate
3166 gpg grains/usgallon # Divide by water's density to convert to
3167 # a dimensionless concentration measure
3168 #
3169 # Shoe measures
3170 #
3171
3172 shoeiron 1|48 inch # Used to measure leather in soles
3173 shoeounce 1|64 inch # Used to measure non-sole shoe leather
3174
3175 # USA shoe sizes. These express the length of the shoe or the length
3176 # of the "last", the form that the shoe is made on. But note that
3177 # this only captures the length. It appears that widths change 1/4
3178 # inch for each letter within the same size, and if you change the
3179 # length by half a size then the width changes between 1/8 inch and
3180 # 1/4 inch. But this may not be standard. If you know better, please
3181 # contact me.
3182
3183 shoesize_delta 1|3 inch # USA shoe sizes differ by this amount
3184 shoe_men0 8.25 inch
3185 shoe_women0 (7+11|12) inch
3186 shoe_boys0 (3+11|12) inch
3187 shoe_girls0 (3+7|12) inch
3188
3189 shoesize_men(n) units=[1;inch] shoe_men0 + n shoesize_delta ; \
3190 (shoesize_men+(-shoe_men0))/shoesize_delta
3191 shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \
3192 (shoesize_women+(-shoe_women0))/shoesize_delta
3193 shoesize_boys(n) units=[1;inch] shoe_boys0 + n shoesize_delta ; \
3194 (shoesize_boys+(-shoe_boys0))/shoesize_delta
3195 shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \
3196 (shoesize_girls+(-shoe_girls0))/shoesize_delta
3197
3198 # European shoe size. According to
3199 # http://www.shoeline.com/footnotes/shoeterm.shtml
3200 # shoe sizes in Europe are measured with Paris points which simply measure
3201 # the length of the shoe.
3202
3203 europeshoesize 2|3 cm
3204
3205 #
3206 # USA slang units
3207 #
3208
3209 buck US$
3210 fin 5 US$
3211 sawbuck 10 US$
3212 usgrand 1000 US$
3213 greenback US$
3214 key kg # usually of marijuana, 60's
3215 lid 1 oz # Another 60's weed unit
3216 footballfield usfootballfield
3217 usfootballfield 100 yards
3218 canadafootballfield 110 yards # And 65 yards wide
3219 marathon 26 miles + 385 yards
3220
3221 #
3222 # British
3223 #
3224
3225 # The length measure in the UK was defined by a bronze bar manufactured in
3226 # 1844. Various conversions were sanctioned for convenience at different
3227 # times, which makes conversions before 1963 a confusing matter. Apparently
3228 # previous conversions were never explicitly revoked. Four different
3229 # conversion factors appear below. Multiply them times an imperial length
3230 # units as desired. The Weights and Measures Act of 1963 switched the UK away
3231 # from their bronze standard and onto a definition of the yard in terms of the
3232 # meter. This happened after an international agreement in 1959 to align the
3233 # world's measurement systems.
3234
3235 UK UKlength_SJJ
3236 UK- UK
3237 british- UK
3238
3239 UKlength_B 0.9143992 meter / yard # Benoit found the yard to be
3240 # 0.9143992 m at a weights and
3241 # measures conference around
3242 # 1896. Legally sanctioned
3243 # in 1898.
3244 UKlength_SJJ 0.91439841 meter / yard # In 1922, Seers, Jolly and
3245 # Johnson found the yard to be
3246 # 0.91439841 meters.
3247 # Used starting in the 1930's.
3248 UKlength_K meter / 39.37079 inch # In 1816 Kater found this ratio
3249 # for the meter and inch. This
3250 # value was used as the legal
3251 # conversion ratio when the
3252 # metric system was legalized
3253 # for contract in 1864.
3254 UKlength_C meter / 1.09362311 yard # In 1866 Clarke found the meter
3255 # to be 1.09362311 yards. This
3256 # conversion was legalized
3257 # around 1878.
3258 brnauticalmile 6080 ft # Used until 1970 when the UK
3259 brknot brnauticalmile / hr # switched to the international
3260 brcable 1|10 brnauticalmile # nautical mile.
3261 admiraltymile brnauticalmile
3262 admiraltyknot brknot
3263 admiraltycable brcable
3264 seamile 6000 ft
3265 shackle 15 fathoms # Adopted 1949 by British navy
3266
3267 # British Imperial weight is mostly the same as US weight. A few extra
3268 # units are added here.
3269
3270 clove 7 lb
3271 stone 14 lb
3272 tod 28 lb
3273 brquarterweight 1|4 brhundredweight
3274 brhundredweight 8 stone
3275 longhundredweight brhundredweight
3276 longton 20 brhundredweight
3277 brton longton
3278
3279 # British Imperial volume measures
3280
3281 brminim 1|60 brdram
3282 brscruple 1|3 brdram
3283 fluidscruple brscruple
3284 brdram 1|8 brfloz
3285 brfluidounce 1|20 brpint
3286 brfloz brfluidounce
3287 brgill 1|4 brpint
3288 brpint 1|2 brquart
3289 brquart 1|4 brgallon
3290 brgallon 4.54609 l # The British Imperial gallon was
3291 # defined in 1824 to be the volume of
3292 # water which weighed 10 pounds at 62
3293 # deg F with a pressure of 30 inHg.
3294 # It was also defined as 277.274 in^3,
3295 # Which is slightly in error. In
3296 # 1963 it was defined to be the volume
3297 # occupied by 10 pounds of distilled
3298 # water of density 0.998859 g/ml weighed
3299 # in air of density 0.001217 g/ml
3300 # against weights of density 8.136 g/ml.
3301 # This gives a value of approximately
3302 # 4.5459645 liters, but the old liter
3303 # was in force at this time. In 1976
3304 # the definition was changed to exactly
3305 # 4.54609 liters using the new
3306 # definition of the liter (1 dm^3).
3307 brbarrel 36 brgallon # Used for beer
3308 brbushel 8 brgallon
3309 brheapedbushel 1.278 brbushel
3310 brquarter 8 brbushel
3311 brchaldron 36 brbushel
3312
3313 # Obscure British volume measures. These units are generally traditional
3314 # measures whose definitions have fluctuated over the years. Often they
3315 # depended on the quantity being measured. They are given here in terms of
3316 # British Imperial measures. For example, the puncheon may have historically
3317 # been defined relative to the wine gallon or beer gallon or ale gallon
3318 # rather than the British Imperial gallon.
3319
3320 bag 4 brbushel
3321 bucket 4 brgallon
3322 kilderkin 2 brfirkin
3323 last 40 brbushel
3324 noggin brgill
3325 pottle 0.5 brgallon
3326 pin 4.5 brgallon
3327 puncheon 72 brgallon
3328 seam 8 brbushel
3329 coomb 4 brbushel
3330 boll 6 brbushel
3331 firlot 1|4 boll
3332 brfirkin 9 brgallon # Used for ale and beer
3333 cran 37.5 brgallon # measures herring, about 750 fish
3334 brwinehogshead 52.5 brgallon # This value is approximately equal
3335 brhogshead brwinehogshead # to the old wine hogshead of 63
3336 # wine gallons. This adjustment
3337 # is listed in the OED and in
3338 # "The Weights and Measures of
3339 # England" by R. D. Connor
3340 brbeerhogshead 54 brgallon
3341 brbeerbutt 2 brbeerhogshead
3342 registerton 100 ft^3 # Used for internal capacity of ships
3343 shippington 40 ft^3 # Used for ship's cargo freight or timber
3344 brshippington 42 ft^3 #
3345 freightton shippington # Both register ton and shipping ton derive
3346 # from the "tun cask" of wine.
3347 displacementton 35 ft^3 # Approximate volume of a longton weight of
3348 # sea water. Measures water displaced by
3349 # ships.
3350 waterton 224 brgallon
3351 strike 70.5 l # 16th century unit, sometimes
3352 # defined as .5, 2, or 4 bushels
3353 # depending on the location. It
3354 # probably doesn't make a lot of
3355 # sense to define in terms of imperial
3356 # bushels. Zupko gives a value of
3357 # 2 Winchester grain bushels or about
3358 # 70.5 liters.
3359 amber 4 brbushel# Used for dry and liquid capacity [18]
3360
3361 # British volume measures with "imperial"
3362
3363 imperialminim brminim
3364 imperialscruple brscruple
3365 imperialdram brdram
3366 imperialfluidounce brfluidounce
3367 imperialfloz brfloz
3368 imperialgill brgill
3369 imperialpint brpint
3370 imperialquart brquart
3371 imperialgallon brgallon
3372 imperialbarrel brbarrel
3373 imperialbushel brbushel
3374 imperialheapedbushel brheapedbushel
3375 imperialquarter brquarter
3376 imperialchaldron brchaldron
3377 imperialwinehogshead brwinehogshead
3378 imperialhogshead brhogshead
3379 imperialbeerhogshead brbeerhogshead
3380 imperialbeerbutt brbeerbutt
3381 imperialfirkin brfirkin
3382
3383 # obscure British lengths
3384
3385 barleycorn 1|3 UKinch # Given in Realm of Measure as the
3386 # difference between successive shoe sizes
3387 nail 1|16 UKyard # Originally the width of the thumbnail,
3388 # or 1|16 ft. This took on the general
3389 # meaning of 1|16 and settled on the
3390 # nail of a yard or 1|16 yards as its
3391 # final value. [12]
3392 pole 16.5 UKft # This was 15 Saxon feet, the Saxon
3393 rope 20 UKft # foot (aka northern foot) being longer
3394 englishell 45 UKinch
3395 flemishell 27 UKinch
3396 ell englishell # supposed to be measure from elbow to
3397 # fingertips
3398 span 9 UKinch # supposed to be distance from thumb
3399 # to pinky with full hand extension
3400 goad 4.5 UKft # used for cloth, possibly named after the
3401 # stick used for prodding animals.
3402
3403 # misc obscure British units
3404
3405 hide 120 acre # English unit of land area dating to the 7th
3406 # century, originally the amount of land
3407 # that a single plowman could cultivate,
3408 # which varied from 60-180 acres regionally.
3409 # Standardized at Normon conquest.
3410 virgate 1|4 hide
3411 nook 1|2 virgate
3412 rood furlong rod # Area of a strip a rod by a furlong
3413 englishcarat troyounce/151.5 # Originally intended to be 4 grain
3414 # but this value ended up being
3415 # used in the London diamond market
3416 mancus 2 oz
3417 mast 2.5 lb
3418 nailkeg 100 lbs
3419 basebox 31360 in^2 # Used in metal plating
3420
3421 # alternate spellings
3422
3423 gramme gram
3424 litre liter
3425 dioptre diopter
3426 aluminium aluminum
3427 sulphur sulfur
3428
3429 #
3430 # Units derived the human body (may not be very accurate)
3431 #
3432
3433 geometricpace 5 ft # distance between points where the same
3434 # foot hits the ground
3435 pace 2.5 ft # distance between points where alternate
3436 # feet touch the ground
3437 USmilitarypace 30 in # United States official military pace
3438 USdoubletimepace 36 in # United States official doubletime pace
3439 fingerbreadth 7|8 in # The finger is defined as either the width
3440 fingerlength 4.5 in # or length of the finger
3441 finger fingerbreadth
3442 palmwidth hand # The palm is a unit defined as either the width
3443 palmlength 8 in # or the length of the hand
3444 hand 4 inch # width of hand
3445 shaftment 6 inch # Distance from tip of outstretched thumb to the
3446 # opposite side of the palm of the hand. The
3447 # ending -ment is from the old English word
3448 # for hand. [18]
3449 smoot 5 ft + 7 in # Created as part of an MIT fraternity prank.
3450 # In 1958 Oliver Smoot was used to measure
3451 # the length of the Harvard Bridge, which was
3452 # marked off in Smoot lengths. These
3453 # markings have been maintained on the bridge
3454 # since then and repainted by subsequent
3455 # incoming fraternity members. During a
3456 # bridge renovation the new sidewalk was
3457 # scored every Smoot rather than at the
3458 # customary 6 ft spacing.
3459 tomcruise 5 ft + 7.75 in # Height of Tom Cruise
3460
3461 #
3462 # Cooking measures
3463 #
3464
3465 # Common abbreviations
3466
3467 tbl tablespoon
3468 tbsp tablespoon
3469 tblsp tablespoon
3470 Tb tablespoon
3471 tsp teaspoon
3472 saltspoon 1|4 tsp
3473
3474 # US measures
3475
3476 uscup 8 usfloz
3477 ustablespoon 1|16 uscup
3478 usteaspoon 1|3 ustablespoon
3479 ustbl ustablespoon
3480 ustbsp ustablespoon
3481 ustblsp ustablespoon
3482 ustsp usteaspoon
3483 metriccup 250 ml
3484 stickbutter 1|4 lb # Butter in the USA is sold in one
3485 # pound packages that contain four
3486 # individually wrapped pieces. The
3487 # pieces are marked into tablespoons,
3488 # making it possible to measure out
3489 # butter by volume by slicing the
3490 # butter.
3491
3492 legalcup 240 ml # The cup used on nutrition labeling
3493 legaltablespoon 1|16 legalcup
3494 legaltbsp legaltablespoon
3495
3496 # Scoop size. Ice cream scoops in the US are marked with numbers
3497 # indicating the number of scoops required to fill a US quart.
3498
3499 scoop(n) units=[1;cup] domain=[4,100] range=[0.04,1] \
3500 32 usfloz / n ; 32 usfloz / scoop
3501
3502
3503 # US can sizes.
3504
3505 number1can 10 usfloz
3506 number2can 19 usfloz
3507 number2.5can 3.5 uscups
3508 number3can 4 uscups
3509 number5can 7 uscups
3510 number10can 105 usfloz
3511
3512 # British measures
3513
3514 brcup 1|2 brpint
3515 brteacup 1|3 brpint
3516 brtablespoon 15 ml # Also 5|8 brfloz, approx 17.7 ml
3517 brteaspoon 1|3 brtablespoon # Also 1|4 brtablespoon
3518 brdessertspoon 2 brteaspoon
3519 dessertspoon brdessertspoon
3520 dsp dessertspoon
3521 brtsp brteaspoon
3522 brtbl brtablespoon
3523 brtbsp brtablespoon
3524 brtblsp brtablespoon
3525
3526 # Australian
3527
3528 australiatablespoon 20 ml
3529 austbl australiatablespoon
3530 austbsp australiatablespoon
3531 austblsp australiatablespoon
3532 australiateaspoon 1|4 australiatablespoon
3533 austsp australiateaspoon
3534
3535 # Italian
3536
3537 etto 100 g # Used for buying items like meat and
3538 etti etto # cheese.
3539
3540 # Chinese
3541
3542 catty 0.5 kg
3543 oldcatty 4|3 lbs # Before metric conversion.
3544 tael 1|16 oldcatty # Should the tael be defined both ways?
3545 mace 0.1 tael
3546 oldpicul 100 oldcatty
3547 picul 100 catty # Chinese usage
3548
3549 # Indian
3550
3551 seer 14400 grain # British Colonial standard
3552 ser seer
3553 maund 40 seer
3554 pakistanseer 1 kg
3555 pakistanmaund 40 pakistanseer
3556 chittak 1|16 seer
3557 tola 1|5 chittak
3558 ollock 1|4 liter # Is this right?
3559
3560 # Japanese
3561
3562 japancup 200 ml
3563
3564 # densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum
3565 # so you can convert '2 cups sugar' to grams, for example, or in the other
3566 # direction grams could be converted to 'cup flour_scooped'.
3567
3568 butter 8 oz/uscup
3569 butter_clarified 6.8 oz/uscup
3570 cocoa_butter 9 oz/uscup
3571 shortening 6.75 oz/uscup # vegetable shortening
3572 oil 7.5 oz/uscup
3573 cakeflour_sifted 3.5 oz/uscup # The density of flour depends on the
3574 cakeflour_spooned 4 oz/uscup # measuring method. "Scooped", or
3575 cakeflour_scooped 4.5 oz/uscup # "dip and sweep" refers to dipping a
3576 flour_sifted 4 oz/uscup # measure into a bin, and then sweeping
3577 flour_spooned 4.25 oz/uscup # the excess off the top. "Spooned"
3578 flour_scooped 5 oz/uscup # means to lightly spoon into a measure
3579 breadflour_sifted 4.25 oz/uscup # and then sweep the top. Sifted means
3580 breadflour_spooned 4.5 oz/uscup # sifting the flour directly into a
3581 breadflour_scooped 5.5 oz/uscup # measure and then sweeping the top.
3582 cornstarch 120 grams/uscup
3583 dutchcocoa_sifted 75 g/uscup # These are for Dutch processed cocoa
3584 dutchcocoa_spooned 92 g/uscup
3585 dutchcocoa_scooped 95 g/uscup
3586 cocoa_sifted 75 g/uscup # These are for nonalkalized cocoa
3587 cocoa_spooned 82 g/uscup
3588 cocoa_scooped 95 g/uscup
3589 heavycream 232 g/uscup
3590 milk 242 g/uscup
3591 sourcream 242 g/uscup
3592 molasses 11.25 oz/uscup
3593 cornsyrup 11.5 oz/uscup
3594 honey 11.75 oz/uscup
3595 sugar 200 g/uscup
3596 powdered_sugar 4 oz/uscup
3597 brownsugar_light 217 g/uscup # packed
3598 brownsugar_dark 239 g/uscup
3599
3600 baking_powder 4.6 grams / ustsp
3601 salt 6 g / ustsp
3602 koshersalt 2.8 g / ustsp # Diamond Crystal kosher salt
3603 koshersalt_morton 4.8 g / ustsp # Morton kosher salt
3604 # Values are from the nutrition info
3605 # on the packages
3606
3607
3608 # Egg weights and volumes for a USA large egg
3609
3610 egg 50 grams # without shell
3611 eggwhite 30 grams
3612 eggyolk 18.6 grams
3613 eggvolume 3 ustablespoons + 1|2 ustsp
3614 eggwhitevolume 2 ustablespoons
3615 eggyolkvolume 3.5 ustsp
3616
3617 # Alcohol density
3618
3619 ethanoldensity 0.7893 g/cm^3 # From CRC Handbook, 91st Edition
3620 alcoholdensity ethanoldensity
3621
3622 #
3623 # Density measures. Density has traditionally been measured on a variety of
3624 # bizarre nonlinear scales.
3625 #
3626
3627 # Density of a sugar syrup is frequently measured in candy making procedures.
3628 # In the USA the boiling point of the syrup is measured. Some recipes instead
3629 # specify the density using degrees Baume. Conversion between degrees Baume
3630 # and the boiling point measure has proved elusive. This table appeared in one
3631 # text, and provides a fragmentary relationship to the concentration.
3632 #
3633 # temp(C) conc (%)
3634 # 100 30
3635 # 101 40
3636 # 102 50
3637 # 103 60
3638 # 106 70
3639 # 112 80
3640 # 123 90
3641 # 140 95
3642 # 151 97
3643 # 160 98.2
3644 # 166 99.5
3645 # 171 99.6
3646 #
3647 # The best source identified to date came from "Boiling point elevation of
3648 # technical sugarcane solutions and its use in automatic pan boiling" by
3649 # Michael Saska. International Sugar Journal, 2002, 104, 1247, pp 500-507.
3650 #
3651 # But I'm using equation (3) which is credited to Starzak and Peacock,
3652 # "Water activity coefficient in aqueous solutions of sucrose--A comprehensive
3653 # data analysis. Zuckerindustrie, 122, 380-387. (I couldn't find this
3654 # document.)
3655 #
3656 # Note that the range of validity is uncertain, but answers are in agreement
3657 # with the above table all the way to 99.6.
3658 #
3659 # The original equation has a parameter for the boiling point of water, which
3660 # of course varies with altitude. It also includes various other model
3661 # parameters. The input is the molar concentration of sucrose in the solution,
3662 # (moles sucrose) / (total moles).
3663 #
3664 # Bsp 3797.06 degC
3665 # Csp 226.28 degC
3666 # QQ -17638 J/mol
3667 # asp -1.0038
3668 # bsp -0.24653
3669 # tbw 100 degC # boiling point of water
3670 # sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \
3671 # /(tbw+stdtemp)) / (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp)
3672 #
3673 # To convert mass concentration (brix) to molar concentration
3674 #
3675 # sc(x) (x / 342.3) / (( x/342.3) + (100-x)/18.02); \
3676 # 100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1)
3677 #
3678 # Here is a simplified version of this equation where the temperature of boiling
3679 # water has been fixed at 100 degrees Celsius and the argument is now the
3680 # concentration (brix).
3681 #
3682 # sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \
3683 # / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K
3684 #
3685 #
3686 # The formula is not invertible, so to implement it in units we unfortunately
3687 # must turn it into a table.
3688
3689 # This table gives the boiling point elevation as a function of the sugar syrup
3690 # concentration expressed as a percentage.
3691
3692 sugar_conc_bpe[K] \
3693 0 0.0000 5 0.0788 10 0.1690 15 0.2729 20 0.3936 25 0.5351 \
3694 30 0.7027 35 0.9036 40 1.1475 42 1.2599 44 1.3825 46 1.5165 \
3695 48 1.6634 50 1.8249 52 2.0031 54 2.2005 56 2.4200 58 2.6651 \
3696 60 2.9400 61 3.0902 62 3.2499 63 3.4198 64 3.6010 65 3.7944 \
3697 66 4.0012 67 4.2227 68 4.4603 69 4.7156 70 4.9905 71 5.2870 \
3698 72 5.6075 73 5.9546 74 6.3316 75 6.7417 76 7.1892 77 7.6786 \
3699 78.0 8.2155 79.0 8.8061 80.0 9.4578 80.5 9.8092 81.0 10.1793 \
3700 81.5 10.5693 82.0 10.9807 82.5 11.4152 83.0 11.8743 83.5 12.3601 \
3701 84.0 12.8744 84.5 13.4197 85.0 13.9982 85.5 14.6128 86.0 15.2663 \
3702 86.5 15.9620 87.0 16.7033 87.5 17.4943 88.0 18.3391 88.5 19.2424 \
3703 89.0 20.2092 89.5 21.2452 90.0 22.3564 90.5 23.5493 91.0 24.8309 \
3704 91.5 26.2086 92.0 27.6903 92.5 29.2839 93.0 30.9972 93.5 32.8374 \
3705 94.0 34.8104 94.5 36.9195 95.0 39.1636 95.5 41.5348 96.0 44.0142 \
3706 96.5 46.5668 97.0 49.1350 97.5 51.6347 98.0 53.9681 98.1 54.4091 \
3707 98.2 54.8423 98.3 55.2692 98.4 55.6928 98.5 56.1174 98.6 56.5497 \
3708 98.7 56.9999 98.8 57.4828 98.9 58.0206 99.0 58.6455 99.1 59.4062 \
3709 99.2 60.3763 99.3 61.6706 99.4 63.4751 99.5 66.1062 99.6 70.1448 \
3710 99.7 76.7867
3711
3712 # Using the brix table we can use this to produce a mapping from boiling point
3713 # to density which makes all of the units interconvertible. Because the brix
3714 # table stops at 95 this approach works up to a boiling point elevation of 39 K
3715 # or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy
3716 # making. The "hard crack" stage continues up to 310 F.
3717
3718 # Boiling point elevation
3719 sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \
3720 brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe))
3721 # Absolute boiling point (produces an absolute temperature)
3722 sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \
3723 range=[0.99717,1.5144619] \
3724 brix(~sugar_conc_bpe(T-tempC(100))) ;\
3725 sugar_conc_bpe(~brix(sugar_bp))+tempC(100)
3726
3727 # In practice dealing with the absolute temperature is annoying because it is
3728 # not possible to convert to a nested function, so you're stuck retyping the
3729 # absolute temperature in Kelvins to convert to celsius or Fahrenheit. To
3730 # prevent this we supply definitions that build in the temperature conversion
3731 # and produce results in the Fahrenheit and Celsius scales. So using these
3732 # measures, to convert 46 degrees Baume to a Fahrenheit boiling point:
3733 #
3734 # You have: baume(45)
3735 # You want: sugar_bpF
3736 # 239.05647
3737 #
3738 sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\
3739 brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\
3740 ~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100))
3741 sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\
3742 brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\
3743 ~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100))
3744
3745 # Degrees Baume is used in European recipes to specify the density of a sugar
3746 # syrup. An entirely different definition is used for densities below
3747 # 1 g/cm^3. An arbitrary constant appears in the definition. This value is
3748 # equal to 145 in the US, but was according to [], the old scale used in
3749 # Holland had a value of 144, and the new scale or Gerlach scale used 146.78.
3750
3751 baumeconst 145 # US value
3752 baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \
3753 (baumeconst/(baumeconst+-d)) g/cm^3 ; \
3754 (baume+((-g)/cm^3)) baumeconst / baume
3755
3756 # It's not clear if this value was ever used with negative degrees.
3757 twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \
3758 (1 + 0.005 x) g / cm^3 ; \
3759 200 (twaddell / (g/cm^3) +- 1)
3760
3761 # The degree quevenne is a unit for measuring the density of milk.
3762 # Similarly it's unclear if negative values were allowed here.
3763 quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \
3764 (1 + 0.001 x) g / cm^3 ; \
3765 1000 (quevenne / (g/cm^3) +- 1)
3766
3767 # Degrees brix measures sugar concentration by weigh as a percentage, so a
3768 # solution that is 3 degrees brix is 3% sugar by weight. This unit was named
3769 # after Adolf Brix who invented a hydrometer that read this percentage
3770 # directly. This data is from Table 114 of NIST Circular 440, "Polarimetry,
3771 # Saccharimetry and the Sugars". It gives apparent specific gravity at 20
3772 # degrees Celsius of various sugar concentrations. As rendered below this
3773 # data is converted to apparent density at 20 degrees Celsius using the
3774 # density figure for water given in the same NIST reference. They use the
3775 # word "apparent" to refer to measurements being made in air with brass
3776 # weights rather than vacuum.
3777
3778 brix[0.99717g/cm^3]\
3779 0 1.00000 1 1.00390 2 1.00780 3 1.01173 4 1.01569 5 1.01968 \
3780 6 1.02369 7 1.02773 8 1.03180 9 1.03590 10 1.04003 11 1.04418 \
3781 12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \
3782 18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \
3783 24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \
3784 30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \
3785 36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \
3786 42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \
3787 48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \
3788 54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \
3789 60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \
3790 66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \
3791 72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \
3792 78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \
3793 84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \
3794 90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876
3795
3796 # Density measure invented by the American Petroleum Institute. Lighter
3797 # petroleum products are more valuable, and they get a higher API degree.
3798 #
3799 # The intervals of range and domain should be open rather than closed.
3800 #
3801 apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \
3802 141.5 g/cm^3 / (x+131.5) ; \
3803 141.5 (g/cm^3) / apidegree + (-131.5)
3804 #
3805 # Average densities of various woods (dried)
3806 # Data from The Wood Database https://www.wood-database.com
3807 #
3808
3809 # North American Hardwoods
3810
3811 wood_cherry 35 lb/ft^3
3812 wood_redoak 44 lb/ft^3
3813 wood_whiteoak 47 lb/ft^3
3814 wood_blackwalnut 38 lb/ft^3
3815 wood_walnut wood_blackwalnut
3816 wood_birch 43 lb/ft^3
3817 wood_hardmaple 44 lb/ft^3
3818
3819 wood_bigleafmaple 34 lb/ft^3
3820 wood_boxeldermaple 30 lb/ft^3
3821 wood_redmaple 38 lb/ft^3
3822 wood_silvermaple 33 lb/ft^3
3823 wood_stripedmaple 32 lb/ft^3
3824 wood_softmaple (wood_bigleafmaple \
3825 + wood_boxeldermaple \
3826 + wood_redmaple \
3827 + wood_silvermaple \
3828 + wood_stripedmaple) / 5
3829 wood_poplar 29 lb/ft^3
3830 wood_beech 45 lb/ft^3
3831
3832 # North American Softwoods
3833
3834 wood_jeffreypine 28 lb/ft^3
3835 wood_ocotepine 44 lb/ft^3
3836 wood_ponderosapine 28 lb/ft^3
3837
3838 wood_loblollypine 35 lb/ft^3
3839 wood_longleafpine 41 lb/ft^3
3840 wood_shortleafpine 35 lb/ft^3
3841 wood_slashpine 41 lb/ft^3
3842 wood_yellowpine (wood_loblollypine \
3843 + wood_longleafpine \
3844 + wood_shortleafpine \
3845 + wood_slashpine) / 4
3846 wood_redpine 34 lb/ft^3
3847
3848 wood_easternwhitepine 25 lb/ft^3
3849 wood_westernwhitepine 27 lb/ft^3
3850 wood_whitepine (wood_easternwhitepine + wood_westernwhitepine) / 2
3851
3852 wood_douglasfir 32 lb/ft^3
3853
3854 wood_blackspruce 28 lb/ft^3
3855 wood_engelmannspruce 24 lb/ft^3
3856 wood_redspruce 27 lb/ft^3
3857 wood_sitkaspruce 27 lb/ft^3
3858 wood_whitespruce 27 lb/ft^3
3859 wood_spruce (wood_blackspruce \
3860 + wood_engelmannspruce \
3861 + wood_redspruce \
3862 + wood_sitkaspruce \
3863 + wood_whitespruce) / 5
3864
3865 # Other woods
3866
3867 wood_basswood 26 lb/ft^3
3868 wood_balsa 9 lb/ft^3
3869 wood_ebony_gaboon 60 lb/ft^3
3870 wood_ebony_macassar 70 lb/ft^3
3871 wood_mahogany 37 lb/ft^3 # True (Honduran) mahogany,
3872 # Swietenia macrophylla
3873 wood_teak 41 lb/ft^3
3874 wood_rosewood_brazilian 52 lb/ft^3
3875 wood_rosewood_honduran 64 lb/ft^3
3876 wood_rosewood_indian 52 lb/ft^3
3877 wood_cocobolo 69 lb/ft^3
3878 wood_bubinga 56 lb/ft^3
3879 wood_zebrawood 50 lb/ft^3
3880 wood_koa 38 lb/ft^3
3881 wood_snakewood 75.7 lb/ft^3
3882 wood_lignumvitae 78.5 lb/ft^3
3883 wood_blackwood 79.3 lb/ft^3
3884 wood_blackironwood 84.5 lb/ft^3 # Krugiodendron ferreum, listed
3885 # in database as the heaviest wood
3886
3887 #
3888 # Modulus of elasticity of selected woods.
3889 # Data from The Wood Database https://www.wood-database.com
3890 #
3891
3892 # North American Hardwoods
3893
3894 wood_mod_beech 1.720e6 lbf/in^2
3895 wood_mod_birchyellow 2.010e6 lbf/in^2
3896 wood_mod_birch wood_mod_birchyellow
3897 wood_mod_cherry 1.490e6 lbf/in^2
3898 wood_mod_hardmaple 1.830e6 lbf/in^2
3899
3900 wood_mod_bigleafmaple 1.450e6 lbf/in^2
3901 wood_mod_boxeldermaple 1.050e6 lbf/in^2
3902 wood_mod_redmaple 1.640e6 lbf/in^2
3903 wood_mod_silvermaple 1.140e6 lbf/in^2
3904 wood_mod_softmaple (wood_mod_bigleafmaple \
3905 + wood_mod_boxeldermaple \
3906 + wood_mod_redmaple \
3907 + wood_mod_silvermaple) / 4
3908
3909 wood_mod_redoak 1.761e6 lbf/in^2
3910 wood_mod_whiteoak 1.762e6 lbf/in^2
3911 wood_mod_poplar 1.580e6 lbf/in^2
3912 wood_mod_blackwalnut 1.680e6 lbf/in^2
3913 wood_mod_walnut wood_mod_blackwalnut
3914
3915 # North American Softwoods
3916
3917 wood_mod_jeffreypine 1.240e6 lbf/in^2
3918 wood_mod_ocotepine 2.209e6 lbf/in^2
3919 wood_mod_ponderosapine 1.290e6 lbf/in^2
3920
3921 wood_mod_loblollypine 1.790e6 lbf/in^2
3922 wood_mod_longleafpine 1.980e6 lbf/in^2
3923 wood_mod_shortleafpine 1.750e6 lbf/in^2
3924 wood_mod_slashpine 1.980e6 lbf/in^2
3925 wood_mod_yellowpine (wood_mod_loblollypine \
3926 + wood_mod_longleafpine \
3927 + wood_mod_shortleafpine \
3928 + wood_mod_slashpine) / 4
3929
3930 wood_mod_redpine 1.630e6 lbf/in^2
3931
3932 wood_mod_easternwhitepine 1.240e6 lbf/in^2
3933 wood_mod_westernwhitepine 1.460e6 lbf/in^2
3934 wood_mod_whitepine (wood_mod_easternwhitepine + \
3935 wood_mod_westernwhitepine) / 2
3936
3937 wood_mod_douglasfir 1.765e6 lbf/in^2
3938
3939 wood_mod_blackspruce 1.523e6 lbf/in^2
3940 wood_mod_englemannspruce 1.369e6 lbf/in^2
3941 wood_mod_redspruce 1.560e6 lbf/in^2
3942 wood_mod_sitkaspruce 1.600e6 lbf/in^2
3943 wood_mod_whitespruce 1.315e6 lbf/in^2
3944 wood_mod_spruce (wood_mod_blackspruce \
3945 + wood_mod_englemannspruce \
3946 + wood_mod_redspruce + wood_mod_sitkaspruce \
3947 + wood_mod_whitespruce) / 5
3948
3949 # Other woods
3950
3951 wood_mod_balsa 0.538e6 lbf/in^2
3952 wood_mod_basswood 1.460e6 lbf/in^2
3953 wood_mod_blackwood 2.603e6 lbf/in^2 # African, Dalbergia melanoxylon
3954 wood_mod_bubinga 2.670e6 lbf/in^2
3955 wood_mod_cocobolo 2.712e6 lbf/in^2
3956 wood_mod_ebony_gaboon 2.449e6 lbf/in^2
3957 wood_mod_ebony_macassar 2.515e6 lbf/in^2
3958 wood_mod_blackironwood 2.966e6 lbf/in^2 # Krugiodendron ferreum
3959 wood_mod_koa 1.503e6 lbf/in^2
3960 wood_mod_lignumvitae 2.043e6 lbf/in^2
3961 wood_mod_mahogany 1.458e6 lbf/in^2 # True (Honduran) mahogany,
3962 # Swietenia macrophylla
3963 wood_mod_rosewood_brazilian 2.020e6 lbf/in^2
3964 wood_mod_rosewood_honduran 3.190e6 lbf/in^2
3965 wood_mod_rosewood_indian 1.668e6 lbf/in^2
3966 wood_mod_snakewood 3.364e6 lbf/in^2
3967 wood_mod_teak 1.781e6 lbf/in^2
3968 wood_mod_zebrawood 2.374e6 lbf/in^2
3969
3970 #
3971 # Area of countries and other regions. This is the "total area" which
3972 # includes land and water areas within international boundaries and
3973 # coastlines. Data from January, 2019.
3974 #
3975 # except as noted, sources are
3976 # https://en.wikipedia.org/wiki/List_of_countries_and_dependencies_by_area
3977 # https://www.cia.gov/library/publications/the-world-factbook)
3978
3979 area_russia 17098246 km^2
3980 area_antarctica 14000000 km^2
3981 # area_canada is covered below as sum of province and territory areas
3982 area_china 9596961 km^2
3983 # area_unitedstates is covered below as sum of state areas
3984 # includes only the 50 states and District of Columbia
3985 area_us area_unitedstates
3986 area_brazil 8515767 km^2
3987 area_australia 7692024 km^2
3988 # area_europeanunion is covered below as sum of member areas
3989 area_india 3287263 km^2
3990 area_argentina 2780400 km^2
3991 area_kazakhstan 2724900 km^2
3992 area_algeria 2381741 km^2
3993 area_drcongo 2344858 km^2
3994 area_greenland 2166086 km^2
3995 area_saudiarabia 2149690 km^2
3996 area_mexico 1964375 km^2
3997 area_indonesia 1910931 km^2
3998 area_sudan 1861484 km^2
3999 area_libya 1759540 km^2
4000 area_iran 1648195 km^2
4001 area_mongolia 1564110 km^2
4002 area_peru 1285216 km^2
4003 area_chad 1284000 km^2
4004 area_niger 1267000 km^2
4005 area_angola 1246700 km^2
4006 area_mali 1240192 km^2
4007 area_southafrica 1221037 km^2
4008 area_colombia 1141748 km^2
4009 area_ethiopia 1104300 km^2
4010 area_bolivia 1098581 km^2
4011 area_mauritania 1030700 km^2
4012 area_egypt 1002450 km^2
4013 area_tanzania 945087 km^2
4014 area_nigeria 923768 km^2
4015 area_venezuela 916445 km^2
4016 area_pakistan 881912 km^2
4017 area_namibia 825615 km^2
4018 area_mozambique 801590 km^2
4019 area_turkey 783562 km^2
4020 area_chile 756102 km^2
4021 area_zambia 752612 km^2
4022 area_myanmar 676578 km^2
4023 area_burma area_myanmar
4024 area_afghanistan 652230 km^2
4025 area_southsudan 644329 km^2
4026 area_france 640679 km^2
4027 area_somalia 637657 km^2
4028 area_centralafrica 622984 km^2
4029 area_ukraine 603500 km^2
4030 area_crimea 27000 km^2 # occupied by Russia; included in
4031 # (Encyclopedia Britannica)
4032 area_madagascar 587041 km^2
4033 area_botswana 581730 km^2
4034 area_kenya 580367 km^2
4035 area_yemen 527968 km^2
4036 area_thailand 513120 km^2
4037 area_spain 505992 km^2
4038 area_turkmenistan 488100 km^2
4039 area_cameroon 475422 km^2
4040 area_papuanewguinea 462840 km^2
4041 area_sweden 450295 km^2
4042 area_uzbekistan 447400 km^2
4043 area_morocco 446550 km^2
4044 area_iraq 438317 km^2
4045 area_paraguay 406752 km^2
4046 area_zimbabwe 390757 km^2
4047 area_japan 377973 km^2
4048 area_germany 357114 km^2
4049 area_congorepublic 342000 km^2
4050 area_finland 338424 km^2
4051 area_vietnam 331212 km^2
4052 area_malaysia 330803 km^2
4053 area_norway 323802 km^2
4054 area_ivorycoast 322463 km^2
4055 area_poland 312696 km^2
4056 area_oman 309500 km^2
4057 area_italy 301339 km^2
4058 area_philippines 300000 km^2
4059 area_ecuador 276841 km^2
4060 area_burkinafaso 274222 km^2
4061 area_newzealand 270467 km^2
4062 area_gabon 267668 km^2
4063 area_westernsahara 266000 km^2
4064 area_guinea 245857 km^2
4065 # area_unitedkingdom is covered below
4066 area_uganda 241550 km^2
4067 area_ghana 238533 km^2
4068 area_romania 238397 km^2
4069 area_laos 236800 km^2
4070 area_guyana 214969 km^2
4071 area_belarus 207600 km^2
4072 area_kyrgyzstan 199951 km^2
4073 area_senegal 196722 km^2
4074 area_syria 185180 km^2
4075 area_golanheights 1150 km^2 # occupied by Israel; included in
4076 # Syria (Encyclopedia Britannica)
4077 area_cambodia 181035 km^2
4078 area_uruguay 176215 km^2
4079 area_somaliland 176120 km^2
4080 area_suriname 163820 km^2
4081 area_tunisia 163610 km^2
4082 area_bangladesh 147570 km^2
4083 area_nepal 147181 km^2
4084 area_tajikistan 143100 km^2
4085 area_greece 131990 km^2
4086 area_nicaragua 130373 km^2
4087 area_northkorea 120540 km^2
4088 area_malawi 118484 km^2
4089 area_eritrea 117600 km^2
4090 area_benin 114763 km^2
4091 area_honduras 112492 km^2
4092 area_liberia 111369 km^2
4093 area_bulgaria 110879 km^2
4094 area_cuba 109884 km^2
4095 area_guatemala 108889 km^2
4096 area_iceland 103000 km^2
4097 area_southkorea 100210 km^2
4098 area_hungary 93028 km^2
4099 area_portugal 92090 km^2
4100 area_jordan 89342 km^2
4101 area_serbia 88361 km^2
4102 area_azerbaijan 86600 km^2
4103 area_austria 83871 km^2
4104 area_uae 83600 km^2
4105 area_czechia 78865 km^2
4106 area_czechrepublic area_czechia
4107 area_panama 75417 km^2
4108 area_sierraleone 71740 km^2
4109 area_ireland 70273 km^2
4110 area_georgia 69700 km^2
4111 area_srilanka 65610 km^2
4112 area_lithuania 65300 km^2
4113 area_latvia 64559 km^2
4114 area_togo 56785 km^2
4115 area_croatia 56594 km^2
4116 area_bosnia 51209 km^2
4117 area_costarica 51100 km^2
4118 area_slovakia 49037 km^2
4119 area_dominicanrepublic 48671 km^2
4120 area_estonia 45227 km^2
4121 area_denmark 43094 km^2
4122 area_netherlands 41850 km^2
4123 area_switzerland 41284 km^2
4124 area_bhutan 38394 km^2
4125 area_taiwan 36193 km^2
4126 area_guineabissau 36125 km^2
4127 area_moldova 33846 km^2
4128 area_belgium 30528 km^2
4129 area_lesotho 30355 km^2
4130 area_armenia 29743 km^2
4131 area_solomonislands 28896 km^2
4132 area_albania 28748 km^2
4133 area_equitorialguinea 28051 km^2
4134 area_burundi 27834 km^2
4135 area_haiti 27750 km^2
4136 area_rwanda 26338 km^2
4137 area_northmacedonia 25713 km^2
4138 area_djibouti 23200 km^2
4139 area_belize 22966 km^2
4140 area_elsalvador 21041 km^2
4141 area_israel 20770 km^2
4142 area_slovenia 20273 km^2
4143 area_fiji 18272 km^2
4144 area_kuwait 17818 km^2
4145 area_eswatini 17364 km^2
4146 area_easttimor 14919 km^2
4147 area_bahamas 13943 km^2
4148 area_montenegro 13812 km^2
4149 area_vanatu 12189 km^2
4150 area_qatar 11586 km^2
4151 area_gambia 11295 km^2
4152 area_jamaica 10991 km^2
4153 area_kosovo 10887 km^2
4154 area_lebanon 10452 km^2
4155 area_cyprus 9251 km^2
4156 area_puertorico 9104 km^2 # United States territory; not included
4157 # in United States area
4158 area_westbank 5860 km^2 # (CIA World Factbook)
4159 area_hongkong 2755 km^2
4160 area_luxembourg 2586 km^2
4161 area_singapore 716 km^2
4162 area_gazastrip 360 km^2 # (CIA World Factbook)
4163 area_malta 316 km^2 # smallest EU country
4164 area_liechtenstein 160 km^2
4165 area_monaco 2.02 km^2
4166 area_vaticancity 0.44 km^2
4167
4168 # Members as of 1 Feb 2020
4169 area_europeanunion area_austria + area_belgium + area_bulgaria \
4170 + area_croatia + area_cyprus + area_czechia + area_denmark \
4171 + area_estonia + area_finland + area_france + area_germany \
4172 + area_greece + area_hungary + area_ireland + area_italy \
4173 + area_latvia + area_lithuania + area_luxembourg \
4174 + area_malta + area_netherlands + area_poland \
4175 + area_portugal + area_romania + area_slovakia \
4176 + area_slovenia + area_spain + area_sweden
4177 area_eu area_europeanunion
4178
4179 #
4180 # Areas of the individual US states
4181 #
4182 # https://en.wikipedia.org/wiki/List_of_U.S._states_and_territories_by_area
4183 #
4184 # United States Summary: 2010, Population and Housing Unit Counts, Table 18, p. 41
4185 # Issued September 2012
4186
4187 area_alaska 1723336.8 km^2
4188 area_texas 695661.6 km^2
4189 area_california 423967.4 km^2
4190 area_montana 380831.1 km^2
4191 area_newmexico 314917.4 km^2
4192 area_arizona 295233.5 km^2
4193 area_nevada 286379.7 km^2
4194 area_colorado 269601.4 km^2
4195 area_oregon 254799.2 km^2
4196 area_wyoming 253334.5 km^2
4197 area_michigan 250486.8 km^2
4198 area_minnesota 225162.8 km^2
4199 area_utah 219881.9 km^2
4200 area_idaho 216442.6 km^2
4201 area_kansas 213100.0 km^2
4202 area_nebraska 200329.9 km^2
4203 area_southdakota 199728.7 km^2
4204 area_washington 184660.8 km^2
4205 area_northdakota 183107.8 km^2
4206 area_oklahoma 181037.2 km^2
4207 area_missouri 180540.3 km^2
4208 area_florida 170311.7 km^2
4209 area_wisconsin 169634.8 km^2
4210 area_georgia_us 153910.4 km^2
4211 area_illinois 149995.4 km^2
4212 area_iowa 145745.9 km^2
4213 area_newyork 141296.7 km^2
4214 area_northcarolina 139391.0 km^2
4215 area_arkansas 137731.8 km^2
4216 area_alabama 135767.4 km^2
4217 area_louisiana 135658.7 km^2
4218 area_mississippi 125437.7 km^2
4219 area_pennsylvania 119280.2 km^2
4220 area_ohio 116097.7 km^2
4221 area_virginia 110786.6 km^2
4222 area_tennessee 109153.1 km^2
4223 area_kentucky 104655.7 km^2
4224 area_indiana 94326.2 km^2
4225 area_maine 91633.1 km^2
4226 area_southcarolina 82932.7 km^2
4227 area_westvirginia 62755.5 km^2
4228 area_maryland 32131.2 km^2
4229 area_hawaii 28313.0 km^2
4230 area_massachusetts 27335.7 km^2
4231 area_vermont 24906.3 km^2
4232 area_newhampshire 24214.2 km^2
4233 area_newjersey 22591.4 km^2
4234 area_connecticut 14357.4 km^2
4235 area_delaware 6445.8 km^2
4236 area_rhodeisland 4001.2 km^2
4237 area_districtofcolumbia 177.0 km^2
4238
4239 area_unitedstates area_alabama + area_alaska + area_arizona \
4240 + area_arkansas + area_california + area_colorado \
4241 + area_connecticut + area_delaware \
4242 + area_districtofcolumbia + area_florida \
4243 + area_georgia_us + area_hawaii + area_idaho \
4244 + area_illinois + area_indiana + area_iowa \
4245 + area_kansas + area_kentucky + area_louisiana \
4246 + area_maine + area_maryland + area_massachusetts \
4247 + area_michigan + area_minnesota + area_mississippi \
4248 + area_missouri + area_montana + area_nebraska \
4249 + area_nevada + area_newhampshire + area_newjersey \
4250 + area_newmexico + area_newyork + area_northcarolina \
4251 + area_northdakota + area_ohio + area_oklahoma \
4252 + area_oregon + area_pennsylvania + area_rhodeisland \
4253 + area_southcarolina + area_southdakota \
4254 + area_tennessee + area_texas + area_utah \
4255 + area_vermont + area_virginia + area_washington \
4256 + area_westvirginia + area_wisconsin + area_wyoming
4257
4258 # Total area of Canadian province and territories
4259 #
4260 # Statistics Canada, "Land and freshwater area, by province and territory",
4261 # 2016-10-07:
4262 #
4263 # https://www150.statcan.gc.ca/n1/pub/11-402-x/2012000/chap/geo/tbl/tbl06-eng.htm
4264
4265 area_ontario 1076395 km^2 # confederated 1867-Jul-01
4266 area_quebec 1542056 km^2 # confederated 1867-Jul-01
4267 area_novascotia 55284 km^2 # confederated 1867-Jul-01
4268 area_newbrunswick 72908 km^2 # confederated 1867-Jul-01
4269 area_canada_original area_ontario + area_quebec + area_novascotia \
4270 + area_newbrunswick
4271 area_manitoba 647797 km^2 # confederated 1870-Jul-15
4272 area_britishcolumbia 944735 km^2 # confederated 1871-Jul-20
4273 area_princeedwardisland 5660 km^2 # confederated 1873-Jul-01
4274 area_canada_additional area_manitoba + area_britishcolumbia \
4275 + area_princeedwardisland
4276 area_alberta 661848 km^2 # confederated 1905-Sep-01
4277 area_saskatchewan 651036 km^2 # confederated 1905-Sep-01
4278 area_newfoundlandandlabrador 405212 km^2 # confederated 1949-Mar-31
4279 area_canada_recent area_alberta + area_saskatchewan \
4280 + area_newfoundlandandlabrador
4281 area_canada_provinces area_canada_original + area_canada_additional \
4282 + area_canada_recent
4283 area_northwestterritories 1346106 km^2 # NT confederated 1870-Jul-15
4284 area_yukon 482443 km^2 # YT confederated 1898-Jun-13
4285 area_nunavut 2093190 km^2 # NU confederated 1999-Apr-01
4286 area_canada_territories area_northwestterritories + area_yukon \
4287 + area_nunavut
4288 area_canada area_canada_provinces + area_canada_territories
4289
4290 # area-uk-countries.units - UK country (/province) total areas
4291 # https://en.wikipedia.org/wiki/Countries_of_the_United_Kingdom#Statistics
4292 # GB is official UK country code for some purposes but internally is a Kingdom
4293 #
4294 # areas from A Beginners Guide to UK Geography 2019 v1.0, Office for National Statistics
4295 # England: country; 0927-Jul-12 united; 1603-Mar-24 union of crowns
4296 area_england 132947.76 km^2
4297 #
4298 # Wales: 1282 conquered; 1535 union; principality until 2011
4299 area_wales 21224.48 km^2
4300 #
4301 # England and Wales: nation; 1535 union
4302 area_englandwales area_england + area_wales
4303 #
4304 # Scotland: country; ~900 united; 1603-Mar-24 union of crowns
4305 area_scotland 80226.36 km^2
4306 #
4307 # Great Britain: kingdom; excludes NI;
4308 # 1707 Treaty and Acts of Union: union of parliaments
4309 area_greatbritain area_england + area_wales + area_scotland
4310 area_gb area_greatbritain
4311 #
4312 # Northern Ireland: province; Ireland: 1177 Henry II lordship;
4313 # 1542 Henry VIII kingdom; 1652 Cromwell commonwealth;
4314 # 1691 William III kingdom; 1800 Acts of Union: UK of GB & Ireland;
4315 # 1921 Irish Free State independent of UK
4316 area_northernireland 14133.38 km^2
4317 #
4318 # United Kingdom of GB & NI: 1800 Acts of Union: UK of GB & Ireland;
4319 # 1921 Irish Free State independent of UK
4320 area_unitedkingdom area_greatbritain + area_northernireland
4321 area_uk area_unitedkingdom
4322
4323 #
4324 # Units derived from imperial system
4325 #
4326
4327 ouncedal oz ft / s^2 # force which accelerates an ounce
4328 # at 1 ft/s^2
4329 poundal lb ft / s^2 # same thing for a pound
4330 tondal longton ft / s^2 # and for a ton
4331 pdl poundal
4332 osi ounce force / inch^2 # used in aviation
4333 psi pound force / inch^2
4334 psia psi # absolute pressure
4335 # Note that gauge pressure can be given
4336 # using the gaugepressure() and
4337 # psig() nonlinear unit definitions
4338 tsi ton force / inch^2
4339 reyn psi sec
4340 slug lbf s^2 / ft
4341 slugf slug force
4342 slinch lbf s^2 / inch # Mass unit derived from inch second
4343 slinchf slinch force # pound-force system. Used in space
4344 # applications where in/sec^2 was a
4345 # natural acceleration measure.
4346 geepound slug
4347 lbf lb force
4348 tonf ton force
4349 lbm lb
4350 kip 1000 lbf # from kilopound
4351 ksi kip / in^2
4352 mil 0.001 inch
4353 thou 0.001 inch
4354 tenth 0.0001 inch # one tenth of one thousandth of an inch
4355 millionth 1e-6 inch # one millionth of an inch
4356 circularinch 1|4 pi in^2 # area of a one-inch diameter circle
4357 circleinch circularinch # A circle with diameter d inches has
4358 # an area of d^2 circularinches
4359 cylinderinch circleinch inch # Cylinder h inch tall, d inches diameter
4360 # has volume d^2 h cylinder inches
4361 circularmil 1|4 pi mil^2 # area of one-mil diameter circle
4362 cmil circularmil
4363
4364 cental 100 pound
4365 centner cental
4366 caliber 0.01 inch # for measuring bullets
4367 duty ft lbf
4368 celo ft / s^2
4369 jerk ft / s^3
4370 australiapoint 0.01 inch # The "point" is used to measure rainfall
4371 # in Australia
4372 sabin ft^2 # Measure of sound absorption equal to the
4373 # absorbing power of one square foot of
4374 # a perfectly absorbing material. The
4375 # sound absorptivity of an object is the
4376 # area times a dimensionless
4377 # absorptivity coefficient.
4378 standardgauge 4 ft + 8.5 in # Standard width between railroad track
4379 flag 5 ft^2 # Construction term referring to sidewalk.
4380 rollwallpaper 30 ft^2 # Area of roll of wall paper
4381 fillpower in^3 / ounce # Density of down at standard pressure.
4382 # The best down has 750-800 fillpower.
4383 pinlength 1|16 inch # A #17 pin is 17/16 in long in the USA.
4384 buttonline 1|40 inch # The line was used in 19th century USA
4385 # to measure width of buttons.
4386 beespace 1|4 inch # Bees will fill any space that is smaller
4387 # than the bee space and leave open
4388 # spaces that are larger. The size of
4389 # the space varies with species.
4390 diamond 8|5 ft # Marking on US tape measures that is
4391 # useful to carpenters who wish to place
4392 # five studs in an 8 ft distance. Note
4393 # that the numbers appear in red every
4394 # 16 inches as well, giving six
4395 # divisions in 8 feet.
4396 retmaunit 1.75 in # Height of rack mountable equipment.
4397 U retmaunit # Equipment should be 1|32 inch narrower
4398 RU U # than its U measurement indicates to
4399 # allow for clearance, so 4U=(6+31|32)in
4400 # RETMA stands for the former name of
4401 # the standardizing organization, Radio
4402 # Electronics Television Manufacturers
4403 # Association. This organization is now
4404 # called the Electronic Industries
4405 # Alliance (EIA) and the rack standard
4406 # is specified in EIA RS-310-D.
4407 count per pound # For measuring the size of shrimp
4408 flightlevel 100 ft # Flight levels are used to ensure safe
4409 FL flightlevel # vertical separation between aircraft
4410 # despite variations in local air
4411 # pressure. Flight levels define
4412 # altitudes based on a standard air
4413 # pressure so that altimeter calibration
4414 # is not needed. This means that
4415 # aircraft at separated flight levels
4416 # are guaranteed to be separated.
4417 # Hence the definition of 100 feet is
4418 # a nominal, not true, measure.
4419 # Customarily written with no space in
4420 # the form FL290, which will not work in
4421 # units. But note "FL 290" will work.
4422
4423 #
4424 # Other units of work, energy, power, etc
4425 #
4426
4427 ENERGY joule
4428 WORK joule
4429
4430 # Calorie: approximate energy to raise a gram of water one degree celsius
4431
4432 calorie cal_th # Default is the thermochemical calorie
4433 cal calorie
4434 calorie_th 4.184 J # Thermochemical calorie, defined in 1930
4435 thermcalorie calorie_th # by Frederick Rossini as 4.1833 J to
4436 cal_th calorie_th # avoid difficulties associated with the
4437 # uncertainty in the heat capacity of
4438 # water. In 1948 the value of the joule
4439 # was changed, so the thermochemical
4440 # calorie was redefined to 4.184 J.
4441 # This kept the energy measured by this
4442 # unit the same.
4443 calorie_IT 4.1868 J # International (Steam) Table calorie,
4444 cal_IT calorie_IT # defined in 1929 as watt-hour/860 or
4445 # equivalently 180|43 joules. At this
4446 # time the international joule had a
4447 # different value than the modern joule,
4448 # and the values were different in the
4449 # USA and in Europe. In 1956 at the
4450 # Fifth International Conference on
4451 # Properties of Steam the exact
4452 # definition given here was adopted.
4453 calorie_15 4.18580 J # Energy to go from 14.5 to 15.5 degC
4454 cal_15 calorie_15
4455 calorie_fifteen cal_15
4456 calorie_20 4.18190 J # Energy to go from 19.5 to 20.5 degC
4457 cal_20 calorie_20
4458 calorie_twenty calorie_20
4459 calorie_4 4.204 J # Energy to go from 3.5 to 4.5 degC
4460 cal_4 calorie_4
4461 calorie_four calorie_4
4462 cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC
4463 Calorie kilocalorie # the food Calorie
4464 thermie 1e6 cal_15 # Heat required to raise the
4465 # temperature of a tonne of
4466 # water from 14.5 to 15.5 degC.
4467
4468 # btu definitions: energy to raise a pound of water 1 degF
4469
4470 btu btu_IT # International Table BTU is the default
4471 britishthermalunit btu
4472 btu_IT cal_IT lb degF / gram K
4473 btu_th cal_th lb degF / gram K
4474 btu_mean cal_mean lb degF / gram K
4475 btu_15 cal_15 lb degF / gram K
4476 btu_ISO 1055.06 J # Exact, rounded ISO definition based
4477 # on the IT calorie
4478 quad quadrillion btu
4479
4480 ECtherm 1e5 btu_ISO # Exact definition
4481 UStherm 1.054804e8 J # Exact definition,
4482 therm UStherm
4483
4484 # Water latent heat from [23]
4485
4486 water_fusion_heat 6.01 kJ/mol / (18.015 g/mol) # At 0 deg C
4487 water_vaporization_heat 2256.4 J/g # At saturation, 100 deg C, 101.42 kPa
4488
4489 # Specific heat capacities of various substances
4490
4491 specificheat_water calorie / g K
4492 water_specificheat specificheat_water
4493 # Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html
4494 specificheat_aluminum 0.91 J/g K
4495 specificheat_antimony 0.21 J/g K
4496 specificheat_barium 0.20 J/g K
4497 specificheat_beryllium 1.83 J/g K
4498 specificheat_bismuth 0.13 J/g K
4499 specificheat_cadmium 0.23 J/g K
4500 specificheat_cesium 0.24 J/g K
4501 specificheat_chromium 0.46 J/g K
4502 specificheat_cobalt 0.42 J/g K
4503 specificheat_copper 0.39 J/g K
4504 specificheat_gallium 0.37 J/g K
4505 specificheat_germanium 0.32 J/g K
4506 specificheat_gold 0.13 J/g K
4507 specificheat_hafnium 0.14 J/g K
4508 specificheat_indium 0.24 J/g K
4509 specificheat_iridium 0.13 J/g K
4510 specificheat_iron 0.45 J/g K
4511 specificheat_lanthanum 0.195 J/g K
4512 specificheat_lead 0.13 J/g K
4513 specificheat_lithium 3.57 J/g K
4514 specificheat_lutetium 0.15 J/g K
4515 specificheat_magnesium 1.05 J/g K
4516 specificheat_manganese 0.48 J/g K
4517 specificheat_mercury 0.14 J/g K
4518 specificheat_molybdenum 0.25 J/g K
4519 specificheat_nickel 0.44 J/g K
4520 specificheat_osmium 0.13 J/g K
4521 specificheat_palladium 0.24 J/g K
4522 specificheat_platinum 0.13 J/g K
4523 specificheat_plutonum 0.13 J/g K
4524 specificheat_potassium 0.75 J/g K
4525 specificheat_rhenium 0.14 J/g K
4526 specificheat_rhodium 0.24 J/g K
4527 specificheat_rubidium 0.36 J/g K
4528 specificheat_ruthenium 0.24 J/g K
4529 specificheat_scandium 0.57 J/g K
4530 specificheat_selenium 0.32 J/g K
4531 specificheat_silicon 0.71 J/g K
4532 specificheat_silver 0.23 J/g K
4533 specificheat_sodium 1.21 J/g K
4534 specificheat_strontium 0.30 J/g K
4535 specificheat_tantalum 0.14 J/g K
4536 specificheat_thallium 0.13 J/g K
4537 specificheat_thorium 0.13 J/g K
4538 specificheat_tin 0.21 J/g K
4539 specificheat_titanium 0.54 J/g K
4540 specificheat_tungsten 0.13 J/g K
4541 specificheat_uranium 0.12 J/g K
4542 specificheat_vanadium 0.39 J/g K
4543 specificheat_yttrium 0.30 J/g K
4544 specificheat_zinc 0.39 J/g K
4545 specificheat_zirconium 0.27 J/g K
4546 specificheat_ethanol 2.3 J/g K
4547 specificheat_ammonia 4.6 J/g K
4548 specificheat_freon 0.91 J/g K # R-12 at 0 degrees Fahrenheit
4549 specificheat_gasoline 2.22 J/g K
4550 specificheat_iodine 2.15 J/g K
4551 specificheat_oliveoil 1.97 J/g K
4552
4553 # en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
4554 specificheat_hydrogen 14.3 J/g K
4555 specificheat_helium 5.1932 J/g K
4556 specificheat_argon 0.5203 J/g K
4557 specificheat_tissue 3.5 J/g K
4558 specificheat_diamond 0.5091 J/g K
4559 specificheat_granite 0.79 J/g K
4560 specificheat_graphite 0.71 J/g K
4561 specificheat_ice 2.11 J/g K
4562 specificheat_asphalt 0.92 J/g K
4563 specificheat_brick 0.84 J/g K
4564 specificheat_concrete 0.88 J/g K
4565 specificheat_glass_silica 0.84 J/g K
4566 specificheat_glass_flint 0.503 J/g K
4567 specificheat_glass_pyrex 0.753 J/g K
4568 specificheat_gypsum 1.09 J/g K
4569 specificheat_marble 0.88 J/g K
4570 specificheat_sand 0.835 J/g K
4571 specificheat_soil 0.835 J/g K
4572 specificheat_wood 1.7 J/g K
4573
4574 specificheat_sucrose 1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php
4575
4576
4577 # Energy densities of various fuels
4578 #
4579 # Most of these fuels have varying compositions or qualities and hence their
4580 # actual energy densities vary. These numbers are hence only approximate.
4581 #
4582 # E1. http://bioenergy.ornl.gov/papers/misc/energy_conv.html
4583 # E2. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm
4584 # E3. http://www.ior.com.au/ecflist.html
4585
4586 tonoil 1e10 cal_IT # Ton oil equivalent. A conventional
4587 # value for the energy released by
4588 toe tonoil # burning one metric ton of oil. [18,E2]
4589 # Note that energy per mass of petroleum
4590 # products is fairly constant.
4591 # Variations in volumetric energy
4592 # density result from variations in the
4593 # density (kg/m^3) of different fuels.
4594 # This definition is given by the
4595 # IEA/OECD.
4596 toncoal 7e9 cal_IT # Energy in metric ton coal from [18].
4597 # This is a nominal value which
4598 # is close to the heat content
4599 # of coal used in the 1950's
4600 barreloil 5.8 Mbtu # Conventional value for barrel of crude
4601 # oil [E2]. Actual range is 5.6 - 6.3.
4602 naturalgas_HHV 1027 btu/ft3 # Energy content of natural gas. HHV
4603 naturalgas_LHV 930 btu/ft3 # is for Higher Heating Value and
4604 naturalgas naturalgas_HHV # includes energy from condensation
4605 # combustion products. LHV is for Lower
4606 # Heating Value and excludes these.
4607 # American publications typically report
4608 # HHV whereas European ones report LHV.
4609 charcoal 30 GJ/tonne
4610 woodenergy_dry 20 GJ/tonne # HHV, a cord weights about a tonne
4611 woodenergy_airdry 15 GJ/tonne # 20% moisture content
4612 coal_bituminous 27 GJ / tonne
4613 coal_lignite 15 GJ / tonne
4614 coal_US 22 GJ / uston # Average for US coal (short ton), 1995
4615 ethanol_HHV 84000 btu/usgallon
4616 ethanol_LHV 75700 btu/usgallon
4617 diesel 130500 btu/usgallon
4618 gasoline_LHV 115000 btu/usgallon
4619 gasoline_HHV 125000 btu/usgallon
4620 gasoline gasoline_HHV
4621 heating 37.3 MJ/liter
4622 fueloil 39.7 MJ/liter # low sulphur
4623 propane 93.3 MJ/m^3
4624 butane 124 MJ/m^3
4625
4626 # These values give total energy from uranium fission. Actual efficiency
4627 # of nuclear power plants is around 30%-40%. Note also that some reactors
4628 # use enriched uranium around 3% U-235. Uranium during processing or use
4629 # may be in a compound of uranium oxide or uranium hexafluoride, in which
4630 # case the energy density would be lower depending on how much uranium is
4631 # in the compound.
4632
4633 uranium_pure 200 MeV avogadro / (235.0439299 g/mol) # Pure U-235
4634 uranium_natural 0.7% uranium_pure # Natural uranium: 0.7% U-235
4635
4636 # Celsius heat unit: energy to raise a pound of water 1 degC
4637
4638 celsiusheatunit cal lb degC / gram K
4639 chu celsiusheatunit
4640
4641 POWER watt
4642
4643 # "Apparent" average power in an AC circuit, the product of rms voltage
4644 # and rms current, equal to the true power in watts when voltage and
4645 # current are in phase. In a DC circuit, always equal to the true power.
4646
4647 VA volt ampere
4648
4649 kWh kilowatt hour
4650
4651 # The horsepower is supposedly the power of one horse pulling. Obviously
4652 # different people had different horses.
4653
4654 horsepower 550 foot pound force / sec # Invented by James Watt
4655 mechanicalhorsepower horsepower
4656 hp horsepower
4657 metrichorsepower 75 kilogram force meter / sec # PS=Pferdestaerke in
4658 electrichorsepower 746 W # Germany
4659 boilerhorsepower 9809.50 W
4660 waterhorsepower 746.043 W
4661 brhorsepower horsepower # Value corrected Dec, 2019. Was 745.7 W.
4662 donkeypower 250 W
4663 chevalvapeur metrichorsepower
4664
4665 #
4666 # Heat Transfer
4667 #
4668 # Thermal conductivity, K, measures the rate of heat transfer across
4669 # a material. The heat transfered is
4670 # Q = K dT A t / L
4671 # where dT is the temperature difference across the material, A is the
4672 # cross sectional area, t is the time, and L is the length (thickness).
4673 # Thermal conductivity is a material property.
4674
4675 THERMAL_CONDUCTIVITY POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH)
4676 THERMAL_RESISTIVITY 1/THERMAL_CONDUCTIVITY
4677
4678 # Thermal conductance is the rate at which heat flows across a given
4679 # object, so the area and thickness have been fixed. It depends on
4680 # the size of the object and is hence not a material property.
4681
4682 THERMAL_CONDUCTANCE POWER / TEMPERATURE_DIFFERENCE
4683 THERMAL_RESISTANCE 1/THERMAL_CONDUCTANCE
4684
4685 # Thermal admittance is the rate of heat flow per area across an
4686 # object whose thickness has been fixed. Its reciprocal, thermal
4687 # insulation, is used to for measuring the heat transfer per area
4688 # of sheets of insulation or cloth that are of specified thickness.
4689
4690 THERMAL_ADMITTANCE THERMAL_CONDUCTIVITY / LENGTH
4691 THERMAL_INSULANCE THERMAL_RESISTIVITY LENGTH
4692 THERMAL_INSULATION THERMAL_RESISTIVITY LENGTH
4693
4694 Rvalue degF ft^2 hr / btu
4695 Uvalue 1/Rvalue
4696 europeanUvalue watt / m^2 K
4697 RSI degC m^2 / W
4698 clo 0.155 degC m^2 / W # Supposed to be the insulance
4699 # required to keep a resting person
4700 # comfortable indoors. The value
4701 # given is from NIST and the CRC,
4702 # but [5] gives a slightly different
4703 # value of 0.875 ft^2 degF hr / btu.
4704 tog 0.1 degC m^2 / W # Also used for clothing.
4705
4706
4707 # Thermal Conductivity of a few materials
4708
4709 diamond_natural_thermal_conductivity 2200 W / m K
4710 diamond_synthetic_thermal_conductivity 3320 W / m K # 99% pure C12
4711 silver_thermal_conductivity 406 W / m K
4712 aluminum_thermal_conductivity 205 W / m K
4713 copper_thermal_conductivity 385 W / m K
4714 gold_thermal_conductivity 314 W / m K
4715 iron_thermal_conductivity 79.5 W / m K
4716 stainless_304_thermal_conductivity 15.5 W / m K # average value
4717
4718 # The bel was defined by engineers of Bell Laboratories to describe the
4719 # reduction in audio level over a length of one mile. It was originally
4720 # called the transmission unit (TU) but was renamed around 1923 to honor
4721 # Alexander Graham Bell. The bel proved inconveniently large so the decibel
4722 # has become more common. The decibel is dimensionless since it reports a
4723 # ratio, but it is used in various contexts to report a signal's power
4724 # relative to some reference level.
4725
4726 bel(x) units=[1;1] range=(0,) 10^(x); log(bel) # Basic bel definition
4727 decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel
4728 dB() decibel # Abbreviation
4729 dBW(x) units=[1;W] range=(0,) dB(x) W ; ~dB(dBW/W) # Reference = 1 W
4730 dBk(x) units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW
4731 dBf(x) units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW
4732 dBm(x) units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW
4733 dBmW(x) units=[1;W] range=(0,) dBm(x) ; ~dBm(dBmW) # Reference = 1 mW
4734 dBJ(x) units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J) # Energy relative
4735 # to 1 joule. Used for power spectral
4736 # density since W/Hz = J
4737
4738 # When used to measure amplitude, voltage, or current the signal is squared
4739 # because power is proportional to the square of these measures. The root
4740 # mean square (RMS) voltage is typically used with these units.
4741
4742 dBV(x) units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V
4743 dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV
4744 dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2)
4745 # Reference = 1 microvolt
4746
4747 # Here are dB measurements for current. Be aware that dbA is also
4748 # a unit for frequency weighted sound pressure.
4749 dBA(x) units=[1;A] range=(0,) dB(0.5 x) A;~dB(dBA^2 / A^2) # Reference = 1 A
4750 dBmA(x) units=[1;A] range=(0,) dB(0.5 x) mA;~dB(dBmA^2/mA^2)# Reference = 1 mA
4751 dBuA(x) units=[1;A] range=(0,) dB(0.5 x) microA ; ~dB(dBuA^2 / microA^2)
4752 # Reference = 1 microamp
4753
4754 # Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load.
4755 # Originally defined as dBv but changed to prevent confusion with dBV.
4756 # The "u" is for unloaded.
4757 dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \
4758 ~dB(dBu^2 / mW 600 ohm)
4759 dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv) # Synonym for dBu
4760
4761 # Measurements for sound in air, referenced to the threshold of human hearing
4762 # Note that sound in other media typically uses 1 micropascal as a reference
4763 # for sound pressure. Units dBA, dBB, dBC, refer to different frequency
4764 # weightings meant to approximate the human ear's response.
4765
4766 dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ; \
4767 ~dB(dBSPL^2 / (20 microPa)^2) # pressure
4768 dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \
4769 ~dB(dBSIL / (1e-12 W/m^2)) # intensity
4770 dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W)
4771
4772
4773 # Misc other measures
4774
4775 ENTROPY ENERGY / TEMPERATURE
4776 clausius 1e3 cal/K # A unit of physical entropy
4777 langley thermcalorie/cm^2 # Used in radiation theory
4778 poncelet 100 kg force m / s
4779 tonrefrigeration uston 144 btu / lb day # One ton refrigeration is
4780 # the rate of heat extraction required
4781 # turn one ton of water to ice in
4782 # a day. Ice is defined to have a
4783 # latent heat of 144 btu/lb.
4784 tonref tonrefrigeration
4785 refrigeration tonref / ton
4786 frigorie 1000 cal_15 # Used in refrigeration engineering.
4787 tnt 1e9 cal_th / ton# So you can write tons tnt. This
4788 # is a defined, not measured, value.
4789 airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as
4790 # pressure times air flow.
4791
4792 # Nuclear weapon yields
4793
4794 davycrocket 10 ton tnt # lightest US tactical nuclear weapon
4795 hiroshima 15.5 kiloton tnt # Uranium-235 fission bomb
4796 nagasaki 21 kiloton tnt # Plutonium-239 fission bomb
4797 fatman nagasaki
4798 littleboy hiroshima
4799 ivyking 500 kiloton tnt # most powerful fission bomb
4800 castlebravo 15 megaton tnt # most powerful US test
4801 tsarbomba 50 megaton tnt # most powerful test ever: USSR,
4802 # 30 October 1961
4803 b53bomb 9 megaton tnt
4804 # http://rarehistoricalphotos.com/gadget-first-atomic-bomb/
4805 trinity 18 kiloton tnt # July 16, 1945
4806 gadget trinity
4807
4808 #
4809 # Permeability: The permeability or permeance, n, of a substance determines
4810 # how fast vapor flows through the substance. The formula W = n A dP
4811 # holds where W is the rate of flow (in mass/time), n is the permeability,
4812 # A is the area of the flow path, and dP is the vapor pressure difference.
4813 #
4814
4815 perm_0C grain / hr ft^2 inHg
4816 perm_zero perm_0C
4817 perm_0 perm_0C
4818 perm perm_0C
4819 perm_23C grain / hr ft^2 in Hg23C
4820 perm_twentythree perm_23C
4821
4822 #
4823 # Counting measures
4824 #
4825
4826 pair 2
4827 brace 2
4828 nest 3 # often used for items like bowls that
4829 # nest together
4830 hattrick 3 # Used in sports, especially cricket and ice
4831 # hockey to report the number of goals.
4832 dicker 10
4833 dozen 12
4834 bakersdozen 13
4835 score 20
4836 flock 40
4837 timer 40
4838 shock 60
4839 toncount 100 # Used in sports in the UK
4840 longhundred 120 # From a germanic counting system
4841 gross 144
4842 greatgross 12 gross
4843 tithe 1|10 # From Anglo-Saxon word for tenth
4844
4845 # Paper counting measure
4846
4847 shortquire 24
4848 quire 25
4849 shortream 480
4850 ream 500
4851 perfectream 516
4852 bundle 2 reams
4853 bale 5 bundles
4854
4855 #
4856 # Paper measures
4857 #
4858
4859 # USA paper sizes
4860
4861 lettersize 8.5 inch 11 inch
4862 legalsize 8.5 inch 14 inch
4863 ledgersize 11 inch 17 inch
4864 executivesize 7.25 inch 10.5 inch
4865 Apaper 8.5 inch 11 inch
4866 Bpaper 11 inch 17 inch
4867 Cpaper 17 inch 22 inch
4868 Dpaper 22 inch 34 inch
4869 Epaper 34 inch 44 inch
4870
4871 # Correspondence envelope sizes. #10 is the standard business
4872 # envelope in the USA.
4873
4874 envelope6_25size 3.5 inch 6 inch
4875 envelope6_75size 3.625 inch 6.5 inch
4876 envelope7size 3.75 inch 6.75 inch
4877 envelope7_75size 3.875 inch 7.5 inch
4878 envelope8_625size 3.625 inch 8.625 inch
4879 envelope9size 3.875 inch 8.875 inch
4880 envelope10size 4.125 inch 9.5 inch
4881 envelope11size 4.5 inch 10.375 inch
4882 envelope12size 4.75 inch 11 inch
4883 envelope14size 5 inch 11.5 inch
4884 envelope16size 6 inch 12 inch
4885
4886 # Announcement envelope sizes (no relation to metric paper sizes like A4)
4887
4888 envelopeA1size 3.625 inch 5.125 inch # same as 4bar
4889 envelopeA2size 4.375 inch 5.75 inch
4890 envelopeA6size 4.75 inch 6.5 inch
4891 envelopeA7size 5.25 inch 7.25 inch
4892 envelopeA8size 5.5 inch 8.125 inch
4893 envelopeA9size 5.75 inch 8.75 inch
4894 envelopeA10size 6 inch 9.5 inch
4895
4896 # Baronial envelopes
4897
4898 envelope4bar 3.625 inch 5.125 inch # same as A1
4899 envelope5_5bar 4.375 inch 5.75 inch
4900 envelope6bar 4.75 inch 6.5 inch
4901
4902 # Coin envelopes
4903
4904 envelope1baby 2.25 inch 3.5 inch # same as #1 coin
4905 envelope00coin 1.6875 inch 2.75 inch
4906 envelope1coin 2.25 inch 3.5 inch
4907 envelope3coin 2.5 inch 4.25 inch
4908 envelope4coin 3 inch 4.5 inch
4909 envelope4_5coin 3 inch 4.875 inch
4910 envelope5coin 2.875 inch 5.25 inch
4911 envelope5_5coin 3.125 inch 5.5 inch
4912 envelope6coin 3.375 inch 6 inch
4913 envelope7coin 3.5 inch 6.5 inch
4914
4915 # The metric paper sizes are defined so that if a sheet is cut in half
4916 # along the short direction, the result is two sheets which are
4917 # similar to the original sheet. This means that for any metric size,
4918 # the long side is close to sqrt(2) times the length of the short
4919 # side. Each series of sizes is generated by repeated cuts in half,
4920 # with the values rounded down to the nearest millimeter.
4921
4922 A0paper 841 mm 1189 mm # The basic size in the A series
4923 A1paper 594 mm 841 mm # is defined to have an area of
4924 A2paper 420 mm 594 mm # one square meter.
4925 A3paper 297 mm 420 mm
4926 A4paper 210 mm 297 mm
4927 A5paper 148 mm 210 mm
4928 A6paper 105 mm 148 mm
4929 A7paper 74 mm 105 mm
4930 A8paper 52 mm 74 mm
4931 A9paper 37 mm 52 mm
4932 A10paper 26 mm 37 mm
4933
4934 B0paper 1000 mm 1414 mm # The basic B size has an area
4935 B1paper 707 mm 1000 mm # of sqrt(2) square meters.
4936 B2paper 500 mm 707 mm
4937 B3paper 353 mm 500 mm
4938 B4paper 250 mm 353 mm
4939 B5paper 176 mm 250 mm
4940 B6paper 125 mm 176 mm
4941 B7paper 88 mm 125 mm
4942 B8paper 62 mm 88 mm
4943 B9paper 44 mm 62 mm
4944 B10paper 31 mm 44 mm
4945
4946 C0paper 917 mm 1297 mm # The basic C size has an area
4947 C1paper 648 mm 917 mm # of sqrt(sqrt(2)) square meters.
4948 C2paper 458 mm 648 mm
4949 C3paper 324 mm 458 mm # Intended for envelope sizes
4950 C4paper 229 mm 324 mm
4951 C5paper 162 mm 229 mm
4952 C6paper 114 mm 162 mm
4953 C7paper 81 mm 114 mm
4954 C8paper 57 mm 81 mm
4955 C9paper 40 mm 57 mm
4956 C10paper 28 mm 40 mm
4957
4958 # gsm (Grams per Square Meter), a sane, metric paper weight measure
4959
4960 gsm grams / meter^2
4961
4962 # In the USA, a collection of crazy historical paper measures are used. Paper
4963 # is measured as a weight of a ream of that particular type of paper. This is
4964 # sometimes called the "substance" or "basis" (as in "substance 20" paper).
4965 # The standard sheet size or "basis size" varies depending on the type of
4966 # paper. As a result, 20 pound bond paper and 50 pound text paper are actually
4967 # about the same weight. The different sheet sizes were historically the most
4968 # convenient for printing or folding in the different applications. These
4969 # different basis weights are standards maintained by American Society for
4970 # Testing Materials (ASTM) and the American Forest and Paper Association
4971 # (AF&PA).
4972
4973 poundbookpaper lb / 25 inch 38 inch ream
4974 lbbook poundbookpaper
4975 poundtextpaper poundbookpaper
4976 lbtext poundtextpaper
4977 poundoffsetpaper poundbookpaper # For offset printing
4978 lboffset poundoffsetpaper
4979 poundbiblepaper poundbookpaper # Designed to be lightweight, thin,
4980 lbbible poundbiblepaper # strong and opaque.
4981 poundtagpaper lb / 24 inch 36 inch ream
4982 lbtag poundtagpaper
4983 poundbagpaper poundtagpaper
4984 lbbag poundbagpaper
4985 poundnewsprintpaper poundtagpaper
4986 lbnewsprint poundnewsprintpaper
4987 poundposterpaper poundtagpaper
4988 lbposter poundposterpaper
4989 poundtissuepaper poundtagpaper
4990 lbtissue poundtissuepaper
4991 poundwrappingpaper poundtagpaper
4992 lbwrapping poundwrappingpaper
4993 poundwaxingpaper poundtagpaper
4994 lbwaxing poundwaxingpaper
4995 poundglassinepaper poundtagpaper
4996 lbglassine poundglassinepaper
4997 poundcoverpaper lb / 20 inch 26 inch ream
4998 lbcover poundcoverpaper
4999 poundindexpaper lb / 25.5 inch 30.5 inch ream
5000 lbindex poundindexpaper
5001 poundindexbristolpaper poundindexpaper
5002 lbindexbristol poundindexpaper
5003 poundbondpaper lb / 17 inch 22 inch ream # Bond paper is stiff and
5004 lbbond poundbondpaper # durable for repeated
5005 poundwritingpaper poundbondpaper # filing, and it resists
5006 lbwriting poundwritingpaper # ink penetration.
5007 poundledgerpaper poundbondpaper
5008 lbledger poundledgerpaper
5009 poundcopypaper poundbondpaper
5010 lbcopy poundcopypaper
5011 poundblottingpaper lb / 19 inch 24 inch ream
5012 lbblotting poundblottingpaper
5013 poundblankspaper lb / 22 inch 28 inch ream
5014 lbblanks poundblankspaper
5015 poundpostcardpaper lb / 22.5 inch 28.5 inch ream
5016 lbpostcard poundpostcardpaper
5017 poundweddingbristol poundpostcardpaper
5018 lbweddingbristol poundweddingbristol
5019 poundbristolpaper poundweddingbristol
5020 lbbristol poundbristolpaper
5021 poundboxboard lb / 1000 ft^2
5022 lbboxboard poundboxboard
5023 poundpaperboard poundboxboard
5024 lbpaperboard poundpaperboard
5025
5026 # When paper is marked in units of M, it means the weight of 1000 sheets of the
5027 # given size of paper. To convert this to paper weight, divide by the size of
5028 # the paper in question.
5029
5030 paperM lb / 1000
5031
5032 # In addition paper weight is reported in "caliper" which is simply the
5033 # thickness of one sheet, typically in inches. Thickness is also reported in
5034 # "points" where a point is 1|1000 inch. These conversions are supplied to
5035 # convert these units roughly (using an approximate density) into the standard
5036 # paper weight values.
5037
5038 pointthickness 0.001 in
5039 paperdensity 0.8 g/cm^3 # approximate--paper densities vary!
5040 papercaliper in paperdensity
5041 paperpoint pointthickness paperdensity
5042
5043 #
5044 # Printing
5045 #
5046
5047 fournierpoint 0.1648 inch / 12 # First definition of the printers
5048 # point made by Pierre Fournier who
5049 # defined it in 1737 as 1|12 of a
5050 # cicero which was 0.1648 inches.
5051 olddidotpoint 1|72 frenchinch # François Ambroise Didot, one of
5052 # a family of printers, changed
5053 # Fournier's definition around 1770
5054 # to fit to the French units then in
5055 # use.
5056 bertholdpoint 1|2660 m # H. Berthold tried to create a
5057 # metric version of the didot point
5058 # in 1878.
5059 INpoint 0.4 mm # This point was created by a
5060 # group directed by Fermin Didot in
5061 # 1881 and is associated with the
5062 # imprimerie nationale. It doesn't
5063 # seem to have been used much.
5064 germandidotpoint 0.376065 mm # Exact definition appears in DIN
5065 # 16507, a German standards document
5066 # of 1954. Adopted more broadly in
5067 # 1966 by ???
5068 metricpoint 3|8 mm # Proposed in 1977 by Eurograf
5069 oldpoint 1|72.27 inch # The American point was invented
5070 printerspoint oldpoint # by Nelson Hawks in 1879 and
5071 texpoint oldpoint # dominates USA publishing.
5072 # It was standardized by the American
5073 # Typefounders Association at the
5074 # value of 0.013837 inches exactly.
5075 # Knuth uses the approximation given
5076 # here (which is very close). The
5077 # comp.fonts FAQ claims that this
5078 # value is supposed to be 1|12 of a
5079 # pica where 83 picas is equal to 35
5080 # cm. But this value differs from
5081 # the standard.
5082 texscaledpoint 1|65536 texpoint # The TeX typesetting system uses
5083 texsp texscaledpoint # this for all computations.
5084 computerpoint 1|72 inch # The American point was rounded
5085 point computerpoint
5086 computerpica 12 computerpoint # to an even 1|72 inch by computer
5087 postscriptpoint computerpoint # people at some point.
5088 pspoint postscriptpoint
5089 twip 1|20 point # TWentieth of an Imperial Point
5090 Q 1|4 mm # Used in Japanese phototypesetting
5091 # Q is for quarter
5092 frenchprinterspoint olddidotpoint
5093 didotpoint germandidotpoint # This seems to be the dominant value
5094 europeanpoint didotpoint # for the point used in Europe
5095 cicero 12 didotpoint
5096
5097 stick 2 inches
5098
5099 # Type sizes
5100
5101 excelsior 3 oldpoint
5102 brilliant 3.5 oldpoint
5103 diamondtype 4 oldpoint
5104 pearl 5 oldpoint
5105 agate 5.5 oldpoint # Originally agate type was 14 lines per
5106 # inch, giving a value of 1|14 in.
5107 ruby agate # British
5108 nonpareil 6 oldpoint
5109 mignonette 6.5 oldpoint
5110 emerald mignonette # British
5111 minion 7 oldpoint
5112 brevier 8 oldpoint
5113 bourgeois 9 oldpoint
5114 longprimer 10 oldpoint
5115 smallpica 11 oldpoint
5116 pica 12 oldpoint
5117 english 14 oldpoint
5118 columbian 16 oldpoint
5119 greatprimer 18 oldpoint
5120 paragon 20 oldpoint
5121 meridian 44 oldpoint
5122 canon 48 oldpoint
5123
5124 # German type sizes
5125
5126 nonplusultra 2 didotpoint
5127 brillant 3 didotpoint
5128 diamant 4 didotpoint
5129 perl 5 didotpoint
5130 nonpareille 6 didotpoint
5131 kolonel 7 didotpoint
5132 petit 8 didotpoint
5133 borgis 9 didotpoint
5134 korpus 10 didotpoint
5135 corpus korpus
5136 garamond korpus
5137 mittel 14 didotpoint
5138 tertia 16 didotpoint
5139 text 18 didotpoint
5140 kleine_kanon 32 didotpoint
5141 kanon 36 didotpoint
5142 grobe_kanon 42 didotpoint
5143 missal 48 didotpoint
5144 kleine_sabon 72 didotpoint
5145 grobe_sabon 84 didotpoint
5146
5147 #
5148 # Information theory units. Note that the name "entropy" is used both
5149 # to measure information and as a physical quantity.
5150 #
5151
5152 INFORMATION bit
5153
5154 nat (1/ln(2)) bits # Entropy measured base e
5155 hartley log2(10) bits # Entropy of a uniformly
5156 ban hartley # distributed random variable
5157 # over 10 symbols.
5158 dit hartley # from Decimal digIT
5159
5160 #
5161 # Computer
5162 #
5163
5164 bps bit/sec # Sometimes the term "baud" is
5165 # incorrectly used to refer to
5166 # bits per second. Baud refers
5167 # to symbols per second. Modern
5168 # modems transmit several bits
5169 # per symbol.
5170 byte 8 bit # Not all machines had 8 bit
5171 B byte # bytes, but these days most of
5172 # them do. But beware: for
5173 # transmission over modems, a
5174 # few extra bits are used so
5175 # there are actually 10 bits per
5176 # byte.
5177 octet 8 bits # The octet is always 8 bits
5178 nybble 4 bits # Half of a byte. Sometimes
5179 # equal to different lengths
5180 # such as 3 bits.
5181 nibble nybble
5182 nyp 2 bits # Donald Knuth asks in an exercise
5183 # for a name for a 2 bit
5184 # quantity and gives the "nyp"
5185 # as a solution due to Gregor
5186 # Purdy. Not in common use.
5187 meg megabyte # Some people consider these
5188 # units along with the kilobyte
5189 gig gigabyte # to be defined according to
5190 # powers of 2 with the kilobyte
5191 # equal to 2^10 bytes, the
5192 # megabyte equal to 2^20 bytes and
5193 # the gigabyte equal to 2^30 bytes
5194 # but these usages are forbidden
5195 # by SI. Binary prefixes have
5196 # been defined by IEC to replace
5197 # the SI prefixes. Use them to
5198 # get the binary values: KiB, MiB,
5199 # and GiB.
5200 jiffy 0.01 sec # This is defined in the Jargon File
5201 jiffies jiffy # (http://www.jargon.org) as being the
5202 # duration of a clock tick for measuring
5203 # wall-clock time. Supposedly the value
5204 # used to be 1|60 sec or 1|50 sec
5205 # depending on the frequency of AC power,
5206 # but then 1|100 sec became more common.
5207 # On linux systems, this term is used and
5208 # for the Intel based chips, it does have
5209 # the value of .01 sec. The Jargon File
5210 # also lists two other definitions:
5211 # millisecond, and the time taken for
5212 # light to travel one foot.
5213 cdaudiospeed 44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2
5214 # samples of sixteen bits each.
5215 cdromspeed 75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read
5216 # each second with 2048 bytes per sector.
5217 # Audio CDs do not have sectors, but
5218 # people sometimes divide the bit rate by
5219 # 75 and claim a sector length of 2352.
5220 # Data CDs have a lower rate due to
5221 # increased error correction overhead.
5222 # There is a rarely used mode (mode2) with
5223 # 2336 bytes per sector that has fewer
5224 # error correction bits than mode1.
5225 dvdspeed 1385 kB/s # This is the "1x" speed of a DVD using
5226 # constant linear velocity (CLV) mode.
5227 # Modern DVDs may vary the linear velocity
5228 # as they go from the inside to the
5229 # outside of the disc.
5230 # See http://www.osta.org/technology/dvdqa/dvdqa4.htm
5231
5232 FIT / 1e9 hour # Failures In Time, number of failures per billion hours
5233
5234 #
5235 # The IP address space is divided into subnets. The number of hosts
5236 # in a subnet depends on the length of the subnet prefix. This is
5237 # often written as /N where N is the number of bits in the prefix.
5238 #
5239 # https://en.wikipedia.org/wiki/Subnetwork
5240 #
5241 # These definitions gives the number of hosts for a subnet whose
5242 # prefix has the specified length in bits.
5243 #
5244
5245 ipv4subnetsize(prefix_len) units=[1;1] domain=[0,32] range=[1,4294967296] \
5246 2^(32-prefix_len) ; 32-log2(ipv4subnetsize)
5247 ipv4classA ipv4subnetsize(8)
5248 ipv4classB ipv4subnetsize(16)
5249 ipv4classC ipv4subnetsize(24)
5250
5251 ipv6subnetsize(prefix_len) units=[1;1] domain=[0,128] \
5252 range=[1,340282366920938463463374607431768211456] \
5253 2^(128-prefix_len) ; 128-log2(ipv6subnetsize)
5254
5255 #
5256 # Musical measures. Musical intervals expressed as ratios. Multiply
5257 # two intervals together to get the sum of the interval. The function
5258 # musicalcent can be used to convert ratios to cents.
5259 #
5260
5261 # Perfect intervals
5262
5263 octave 2
5264 majorsecond musicalfifth^2 / octave
5265 majorthird 5|4
5266 minorthird 6|5
5267 musicalfourth 4|3
5268 musicalfifth 3|2
5269 majorsixth musicalfourth majorthird
5270 minorsixth musicalfourth minorthird
5271 majorseventh musicalfifth majorthird
5272 minorseventh musicalfifth minorthird
5273
5274 pythagoreanthird majorsecond musicalfifth^2 / octave
5275 syntoniccomma pythagoreanthird / majorthird
5276 pythagoreancomma musicalfifth^12 / octave^7
5277
5278 # Equal tempered definitions
5279
5280 semitone octave^(1|12)
5281 musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \
5282 100 log(musicalcent)/log(semitone)
5283
5284 #
5285 # Musical note lengths.
5286 #
5287
5288 wholenote !
5289 MUSICAL_NOTE_LENGTH wholenote
5290 halfnote 1|2 wholenote
5291 quarternote 1|4 wholenote
5292 eighthnote 1|8 wholenote
5293 sixteenthnote 1|16 wholenote
5294 thirtysecondnote 1|32 wholenote
5295 sixtyfourthnote 1|64 wholenote
5296 dotted 3|2
5297 doubledotted 7|4
5298 breve doublewholenote
5299 semibreve wholenote
5300 minimnote halfnote
5301 crotchet quarternote
5302 quaver eighthnote
5303 semiquaver sixteenthnote
5304 demisemiquaver thirtysecondnote
5305 hemidemisemiquaver sixtyfourthnote
5306 semidemisemiquaver hemidemisemiquaver
5307
5308 #
5309 # yarn and cloth measures
5310 #
5311
5312 # yarn linear density
5313
5314 woolyarnrun 1600 yard/pound # 1600 yds of "number 1 yarn" weighs
5315 # a pound.
5316 yarncut 300 yard/pound # Less common system used in
5317 # Pennsylvania for wool yarn
5318 cottonyarncount 840 yard/pound
5319 linenyarncount 300 yard/pound # Also used for hemp and ramie
5320 worstedyarncount 1680 ft/pound
5321 metricyarncount meter/gram
5322 denier 1|9 tex # used for silk and rayon
5323 manchesteryarnnumber drams/1000 yards # old system used for silk
5324 pli lb/in
5325 typp 1000 yd/lb # abbreviation for Thousand Yard Per Pound
5326 asbestoscut 100 yd/lb # used for glass and asbestos yarn
5327
5328 tex gram / km # rational metric yarn measure, meant
5329 drex 0.1 tex # to be used for any kind of yarn
5330 poumar lb / 1e6 yard
5331
5332 # yarn and cloth length
5333
5334 skeincotton 80*54 inch # 80 turns of thread on a reel with a
5335 # 54 in circumference (varies for other
5336 # kinds of thread)
5337 cottonbolt 120 ft # cloth measurement
5338 woolbolt 210 ft
5339 bolt cottonbolt
5340 heer 600 yards
5341 cut 300 yards # used for wet-spun linen yarn
5342 lea 300 yards
5343
5344 sailmakersyard 28.5 in
5345 sailmakersounce oz / sailmakersyard 36 inch
5346
5347 silkmomme momme / 25 yards 1.49 inch # Traditional silk weight
5348 silkmm silkmomme # But it is also defined as
5349 # lb/100 yd 45 inch. The two
5350 # definitions are slightly different
5351 # and neither one seems likely to be
5352 # the true source definition.
5353
5354 #
5355 # drug dosage
5356 #
5357
5358 mcg microgram # Frequently used for vitamins
5359 iudiptheria 62.8 microgram # IU is for international unit
5360 iupenicillin 0.6 microgram
5361 iuinsulin 41.67 microgram
5362 drop 1|20 ml # The drop was an old "unit" that was
5363 # replaced by the minim. But I was
5364 # told by a pharmacist that in his
5365 # profession, the conversion of 20
5366 # drops per ml is actually used.
5367 bloodunit 450 ml # For whole blood. For blood
5368 # components, a blood unit is the
5369 # quanity of the component found in a
5370 # blood unit of whole blood. The
5371 # human body contains about 12 blood
5372 # units of whole blood.
5373
5374 #
5375 # misc medical measure
5376 #
5377
5378 frenchcathetersize 1|3 mm # measure used for the outer diameter
5379 # of a catheter
5380 charriere frenchcathetersize
5381
5382
5383 #
5384 # fixup units for times when prefix handling doesn't do the job
5385 #
5386
5387 hectare hectoare
5388 megohm megaohm
5389 kilohm kiloohm
5390 microhm microohm
5391 megalerg megaerg # 'L' added to make it pronounceable [18].
5392
5393 #
5394 # Money
5395 #
5396 # Note that US$ is the primitive unit so other currencies are
5397 # generally given in US$.
5398 #
5399
5400 unitedstatesdollar US$
5401 usdollar US$
5402 $ dollar
5403 mark germanymark
5404 #bolivar venezuelabolivar # Not all databases are
5405 #venezuelabolivarfuerte 1e-5 bolivar # supplying these
5406 #bolivarfuerte 1e-5 bolivar # The currency was revalued
5407 #oldbolivar 1|1000 bolivarfuerte # twice
5408 peseta spainpeseta
5409 rand southafricarand
5410 escudo portugalescudo
5411 guilder netherlandsguilder
5412 hollandguilder netherlandsguilder
5413 peso mexicopeso
5414 yen japanyen
5415 lira italylira
5416 rupee indiarupee
5417 drachma greecedrachma
5418 franc francefranc
5419 markka finlandmarkka
5420 britainpound unitedkingdompound
5421 greatbritainpound unitedkingdompound
5422 unitedkingdompound ukpound
5423 poundsterling britainpound
5424 yuan chinayuan
5425
5426 # Unicode Currency Names
5427
5428 !utf8
5429 icelandkróna icelandkrona
5430 polandzłoty polandzloty
5431 tongapa’anga tongapa'anga
5432 #venezuelabolívar venezuelabolivar
5433 vietnamđồng vietnamdong
5434 mongoliatögrög mongoliatugrik
5435 sãotomé&príncipedobra saotome&principedobra
5436 !endutf8
5437
5438 UKP GBP # Not an ISO code, but looks like one, and
5439 # sometimes used on usenet.
5440
5441 !include currency.units
5442
5443 # Money on the gold standard, used in the late 19th century and early
5444 # 20th century.
5445
5446 olddollargold 23.22 grains goldprice # Used until 1934
5447 newdollargold 96|7 grains goldprice # After Jan 31, 1934
5448 dollargold newdollargold
5449 poundgold 113 grains goldprice # British pound
5450
5451 # Precious metals
5452
5453 goldounce goldprice troyounce
5454 silverounce silverprice troyounce
5455 platinumounce platinumprice troyounce
5456 XAU goldounce
5457 XPT platinumounce
5458 XAG silverounce
5459
5460 # Nominal masses of US coins. Note that dimes, quarters and half dollars
5461 # have weight proportional to value. Before 1965 it was $40 / kg.
5462
5463 USpennyweight 2.5 grams # Since 1982, 48 grains before
5464 USnickelweight 5 grams
5465 USdimeweight US$ 0.10 / (20 US$ / lb) # Since 1965
5466 USquarterweight US$ 0.25 / (20 US$ / lb) # Since 1965
5467 UShalfdollarweight US$ 0.50 / (20 US$ / lb) # Since 1971
5468 USdollarweight 8.1 grams # Weight of Susan B. Anthony and
5469 # Sacagawea dollar coins
5470
5471 # British currency
5472
5473 quid britainpound # Slang names
5474 fiver 5 quid
5475 tenner 10 quid
5476 monkey 500 quid
5477 brgrand 1000 quid
5478 bob shilling
5479
5480 shilling 1|20 britainpound # Before decimalisation, there
5481 oldpence 1|12 shilling # were 20 shillings to a pound,
5482 farthing 1|4 oldpence # each of twelve old pence
5483 guinea 21 shilling # Still used in horse racing
5484 crown 5 shilling
5485 florin 2 shilling
5486 groat 4 oldpence
5487 tanner 6 oldpence
5488 brpenny 0.01 britainpound
5489 pence brpenny
5490 tuppence 2 pence
5491 tuppenny tuppence
5492 ha'penny halfbrpenny
5493 hapenny ha'penny
5494 oldpenny oldpence
5495 oldtuppence 2 oldpence
5496 oldtuppenny oldtuppence
5497 threepence 3 oldpence # threepence never refers to new money
5498 threepenny threepence
5499 oldthreepence threepence
5500 oldthreepenny threepence
5501 oldhalfpenny halfoldpenny
5502 oldha'penny oldhalfpenny
5503 oldhapenny oldha'penny
5504 brpony 25 britainpound
5505
5506 # Canadian currency
5507
5508 loony 1 canadadollar # This coin depicts a loon
5509 toony 2 canadadollar
5510
5511 # Cryptocurrency
5512
5513 satoshi 1e-8 bitcoin
5514 XBT bitcoin # nonstandard code
5515
5516 #
5517 # Units used for measuring volume of wood
5518 #
5519
5520 cord 4*4*8 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood
5521 facecord 1|2 cord
5522 cordfoot 1|8 cord # One foot long section of a cord
5523 cordfeet cordfoot
5524 housecord 1|3 cord # Used to sell firewood for residences,
5525 # often confusingly called a "cord"
5526 boardfoot ft^2 inch # Usually 1 inch thick wood
5527 boardfeet boardfoot
5528 fbm boardfoot # feet board measure
5529 stack 4 yard^3 # British, used for firewood and coal [18]
5530 rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly
5531 # sometimes called a face cord, but this
5532 # value is equal to 1|3 cord. Name
5533 # comes from an old Norse word for a
5534 # stack of wood.
5535 stere m^3
5536 timberfoot ft^3 # Used for measuring solid blocks of wood
5537 standard 120 12 ft 11 in 1.5 in # This is the St Petersburg or
5538 # Pittsburg standard. Apparently the
5539 # term is short for "standard hundred"
5540 # which was meant to refer to 100 pieces
5541 # of wood (deals). However, this
5542 # particular standard is equal to 120
5543 # deals which are 12 ft by 11 in by 1.5
5544 # inches (not the standard deal).
5545 hoppusfoot (4/pi) ft^3 # Volume calculation suggested in 1736
5546 hoppusboardfoot 1|12 hoppusfoot # forestry manual by Edward Hoppus, for
5547 hoppuston 50 hoppusfoot # estimating the usable volume of a log.
5548 # It results from computing the volume
5549 # of a cylindrical log of length, L, and
5550 # girth (circumference), G, by V=L(G/4)^2.
5551 # The hoppus ton is apparently still in
5552 # use for shipments from Southeast Asia.
5553
5554 # In Britain, the deal is apparently any piece of wood over 6 feet long, over
5555 # 7 wide and 2.5 inches thick. The OED doesn't give a standard size. A piece
5556 # of wood less than 7 inches wide is called a "batten". This unit is now used
5557 # exclusively for fir and pine.
5558
5559 deal 12 ft 11 in 2.5 in # The standard North American deal [OED]
5560 wholedeal 12 ft 11 in 1.25 in # If it's half as thick as the standard
5561 # deal it's called a "whole deal"!
5562 splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal.
5563
5564
5565 # Used for shellac mixing rate
5566
5567 poundcut pound / gallon
5568 lbcut poundcut
5569
5570 #
5571 # Gas and Liquid flow units
5572 #
5573
5574 FLUID_FLOW VOLUME / TIME
5575
5576 # Some obvious volumetric gas flow units (cu is short for cubic)
5577
5578 cumec m^3/s
5579 cusec ft^3/s
5580
5581 # Conventional abbreviations for fluid flow units
5582
5583 gph gal/hr
5584 gpm gal/min
5585 mgd megagal/day
5586 cfs ft^3/s
5587 cfh ft^3/hour
5588 cfm ft^3/min
5589 lpm liter/min
5590 lfm ft/min # Used to report air flow produced by fans.
5591 # Multiply by cross sectional area to get a
5592 # flow in cfm.
5593
5594 pru mmHg / (ml/min) # peripheral resistance unit, used in
5595 # medicine to assess blood flow in
5596 # the capillaries.
5597
5598 # Miner's inch: This is an old historic unit used in the Western United
5599 # States. It is generally defined as the rate of flow through a one square
5600 # inch hole at a specified depth such as 4 inches. In the late 19th century,
5601 # volume of water was sometimes measured in the "24 hour inch". Values for the
5602 # miner's inch were fixed by state statues. (This information is from a web
5603 # site operated by the Nevada Division of Water Planning: The Water Words
5604 # Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.)
5605
5606 minersinchAZ 1.5 ft^3/min
5607 minersinchCA 1.5 ft^3/min
5608 minersinchMT 1.5 ft^3/min
5609 minersinchNV 1.5 ft^3/min
5610 minersinchOR 1.5 ft^3/min
5611 minersinchID 1.2 ft^3/min
5612 minersinchKS 1.2 ft^3/min
5613 minersinchNE 1.2 ft^3/min
5614 minersinchNM 1.2 ft^3/min
5615 minersinchND 1.2 ft^3/min
5616 minersinchSD 1.2 ft^3/min
5617 minersinchUT 1.2 ft^3/min
5618 minersinchCO 1 ft^3/sec / 38.4 # 38.4 miner's inches = 1 ft^3/sec
5619 minersinchBC 1.68 ft^3/min # British Columbia
5620
5621 # Oceanographic flow
5622
5623 sverdrup 1e6 m^3 / sec # Used to express flow of ocean
5624 # currents. Named after Norwegian
5625 # oceanographer H. Sverdrup.
5626
5627 # In vacuum science and some other applications, gas flow is measured
5628 # as the product of volumetric flow and pressure. This is useful
5629 # because it makes it easy to compare with the flow at standard
5630 # pressure (one atmosphere). It also directly relates to the number
5631 # of gas molecules per unit time, and hence to the mass flow if the
5632 # molecular mass is known.
5633
5634 GAS_FLOW PRESSURE FLUID_FLOW
5635
5636 sccm atm cc/min # 's' is for "standard" to indicate
5637 sccs atm cc/sec # flow at standard pressure
5638 scfh atm ft^3/hour #
5639 scfm atm ft^3/min
5640 slpm atm liter/min
5641 slph atm liter/hour
5642 lusec liter micron Hg / s # Used in vacuum science
5643
5644 # US Standard Atmosphere (1976)
5645 # Atmospheric temperature and pressure vs. geometric height above sea level
5646 # This definition covers only the troposphere (the lowest atmospheric
5647 # layer, up to 11 km), and assumes the layer is polytropic.
5648 # A polytropic process is one for which PV^k = const, where P is the
5649 # pressure, V is the volume, and k is the polytropic exponent. The
5650 # polytropic index is n = 1 / (k - 1). As noted in the Wikipedia article
5651 # https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse
5652 # the definitions of "exponent" and "index." The functions below assume
5653 # the following parameters:
5654
5655 # temperature lapse rate, -dT/dz, in troposphere
5656
5657 lapserate 6.5 K/km # US Std Atm (1976)
5658
5659 # air molecular weight, including constituent mol wt, given
5660 # in Table 3, p. 3
5661
5662 air_1976 78.084 % 28.0134 \
5663 + 20.9476 % 31.9988 \
5664 + 9340 ppm 39.948 \
5665 + 314 ppm 44.00995 \
5666 + 18.18 ppm 20.183 \
5667 + 5.24 ppm 4.0026 \
5668 + 2 ppm 16.04303 \
5669 + 1.14 ppm 83.80 \
5670 + 0.55 ppm 2.01594 \
5671 + 0.087 ppm 131.30
5672
5673 # universal gas constant
5674 R_1976 8.31432e3 N m/(kmol K)
5675
5676 # polytropic index n
5677 polyndx_1976 air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1
5678
5679 # If desired, redefine using current values for air mol wt and R
5680
5681 polyndx polyndx_1976
5682 # polyndx air (kg/kmol) gravity/(R lapserate) - 1
5683
5684 # for comparison with various references
5685
5686 polyexpnt (polyndx + 1) / polyndx
5687
5688 # The model assumes the following reference values:
5689 # sea-level temperature and pressure
5690
5691 stdatmT0 288.15 K
5692 stdatmP0 atm
5693
5694 # "effective radius" for relation of geometric to geopotential height,
5695 # at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no
5696 # relation to actual radius
5697
5698 earthradUSAtm 6356766 m
5699
5700 # Temperature vs. geopotential height h
5701 # Assumes 15 degC at sea level
5702 # Based on approx 45 deg latitude
5703 # Lower limits of domain and upper limits of range are those of the
5704 # tables in US Standard Atmosphere (NASA 1976)
5705
5706 stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \
5707 stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate
5708
5709 # Temperature vs. geometric height z; based on approx 45 deg latitude
5710 stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \
5711 stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT))
5712
5713 # Pressure vs. geopotential height h
5714 # Assumes 15 degC and 101325 Pa at sea level
5715 # Based on approx 45 deg latitude
5716 # Lower limits of domain and upper limits of range are those of the
5717 # tables in US Standard Atmosphere (NASA 1976)
5718
5719 stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
5720 atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \
5721 (stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1))))
5722
5723 # Pressure vs. geometric height z; based on approx 45 deg latitude
5724 stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
5725 stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP))
5726
5727 # Geopotential height from geometric height
5728 # Based on approx 45 deg latitude
5729 # Lower limits of domain and range are somewhat arbitrary; they
5730 # correspond to the limits in the US Std Atm tables
5731
5732 geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \
5733 (earthradUSAtm z) / (earthradUSAtm + z) ; \
5734 (earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht))
5735
5736 # The standard value for the sea-level acceleration due to gravity is
5737 # 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949)
5738 # R_eff = 2 g_phi / denom
5739 # g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2)
5740 # or
5741 # g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2)
5742 # denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?)
5743 # There is no inverse function; the standard value applies at a latitude
5744 # of about 45.543 deg
5745
5746 g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror \
5747 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2
5748
5749 # effective Earth radius for relation of geometric height to
5750 # geopotential height, as function of latitude (Harrison 1949)
5751
5752 earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \
5753 m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \
5754 (3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat))
5755
5756 # References
5757 # Harrison, L.P. 1949. Relation Between Geopotential and Geometric
5758 # Height. In Smithsonian Meteorological Tables. List, Robert J., ed.
5759 # 6th ed., 4th reprint, 1968. Washington, DC: Smithsonian Institution.
5760 # NASA. US National Aeronautics and Space Administration. 1976.
5761 # US Standard Atmosphere 1976. Washington, DC: US Government Printing Office.
5762
5763 # Gauge pressure functions
5764 #
5765 # Gauge pressure is measured relative to atmospheric pressure. In the English
5766 # system, where pressure is often given in pounds per square inch, gauge
5767 # pressure is often indicated by 'psig' to distinguish it from absolute
5768 # pressure, often indicated by 'psia'. At the standard atmospheric pressure
5769 # of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696
5770 # psia; an automobile tire inflated to 31 psig has an absolute pressure of
5771 # 45.696 psia.
5772 #
5773 # With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5
5774 # bar)); with psig(), the units are taken as psi, so the example above of tire
5775 # pressure could be given as psig(31).
5776 #
5777 # If the normal elevation is significantly different from sea level, change
5778 # Patm appropriately, and adjust the lower domain limit on the gaugepressure
5779 # definition.
5780
5781 Patm atm
5782
5783 gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \
5784 x + Patm ; gaugepressure+(-Patm)
5785
5786 psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \
5787 gaugepressure(x psi) ; ~gaugepressure(psig) / psi
5788
5789
5790 # Pressure for underwater diving
5791
5792 seawater 0.1 bar / meter
5793 msw meter seawater
5794 fsw foot seawater
5795
5796 #
5797 # Wire Gauge
5798 #
5799 # This area is a nightmare with huge charts of wire gauge diameters
5800 # that usually have no clear origin. There are at least 5 competing wire gauge
5801 # systems to add to the confusion. The use of wire gauge is related to the
5802 # manufacturing method: a metal rod is heated and drawn through a hole. The
5803 # size change can't be too big. To get smaller wires, the process is repeated
5804 # with a series of smaller holes. Generally larger gauges mean smaller wires.
5805 # The gauges often have values such as "00" and "000" which are larger sizes
5806 # than simply "0" gauge. In the tables that appear below, these gauges must be
5807 # specified as negative numbers (e.g. "00" is -1, "000" is -2, etc).
5808 # Alternatively, you can use the following units:
5809 #
5810
5811 g00 (-1)
5812 g000 (-2)
5813 g0000 (-3)
5814 g00000 (-4)
5815 g000000 (-5)
5816 g0000000 (-6)
5817
5818 # American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most
5819 # important gauge. ASTM B-258 specifies that this gauge is based on geometric
5820 # interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36
5821 # which is 0.005 inches exactly. Therefore, the diameter in inches of a wire
5822 # is given by the formula 1|200 92^((36-g)/39). Note that 92^(1/39) is close
5823 # to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the
5824 # repeated zero values, use negative numbers in the formula. The same document
5825 # also specifies rounding rules which seem to be ignored by makers of tables.
5826 # Gauges up to 44 are to be specified with up to 4 significant figures, but no
5827 # closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the
5828 # nearest 0.00001 inch.
5829 #
5830 # In addition to being used to measure wire thickness, this gauge is used to
5831 # measure the thickness of sheets of aluminum, copper, and most metals other
5832 # than steel, iron and zinc.
5833
5834 wiregauge(g) units=[1;m] range=(0,) \
5835 1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92)
5836 awg() wiregauge
5837
5838 # Next we have the SWG, the Imperial or British Standard Wire Gauge. This one
5839 # is piecewise linear. It was used for aluminum sheets.
5840
5841 brwiregauge[in] \
5842 -6 0.5 \
5843 -5 0.464 \
5844 -3 0.4 \
5845 -2 0.372 \
5846 3 0.252 \
5847 6 0.192 \
5848 10 0.128 \
5849 14 0.08 \
5850 19 0.04 \
5851 23 0.024 \
5852 26 0.018 \
5853 28 0.0148 \
5854 30 0.0124 \
5855 39 0.0052 \
5856 49 0.0012 \
5857 50 0.001
5858
5859 # The following is from the Appendix to ASTM B 258
5860 #
5861 # For example, in U.S. gage, the standard for sheet metal is based on the
5862 # weight of the metal, not on the thickness. 16-gage is listed as
5863 # approximately .0625 inch thick and 40 ounces per square foot (the original
5864 # standard was based on wrought iron at .2778 pounds per cubic inch; steel
5865 # has almost entirely superseded wrought iron for sheet use, at .2833 pounds
5866 # per cubic inch). Smaller numbers refer to greater thickness. There is no
5867 # formula for converting gage to thickness or weight.
5868 #
5869 # It's rather unclear from the passage above whether the plate gauge values are
5870 # therefore wrong if steel is being used. Reference [15] states that steel is
5871 # in fact measured using this gauge (under the name Manufacturers' Standard
5872 # Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel.
5873 # But this doesn't seem to be the correct density of steel (.2833 lb/in3 is
5874 # closer).
5875 #
5876 # This gauge was established in 1893 for purposes of taxation.
5877
5878 # Old plate gauge for iron
5879
5880 plategauge[(oz/ft^2)/(480*lb/ft^3)] \
5881 -5 300 \
5882 1 180 \
5883 14 50 \
5884 16 40 \
5885 17 36 \
5886 20 24 \
5887 26 12 \
5888 31 7 \
5889 36 4.5 \
5890 38 4
5891
5892 # Manufacturers Standard Gage
5893
5894 stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \
5895 -5 300 \
5896 1 180 \
5897 14 50 \
5898 16 40 \
5899 17 36 \
5900 20 24 \
5901 26 12 \
5902 31 7 \
5903 36 4.5 \
5904 38 4
5905
5906 # A special gauge is used for zinc sheet metal. Notice that larger gauges
5907 # indicate thicker sheets.
5908
5909 zincgauge[in] \
5910 1 0.002 \
5911 10 0.02 \
5912 15 0.04 \
5913 19 0.06 \
5914 23 0.1 \
5915 24 0.125 \
5916 27 0.5 \
5917 28 1
5918
5919 #
5920 # Imperial drill bit sizes are reported in inches or in a numerical or
5921 # letter gauge.
5922 #
5923
5924 drillgauge[in] \
5925 1 0.2280 \
5926 2 0.2210 \
5927 3 0.2130 \
5928 4 0.2090 \
5929 5 0.2055 \
5930 6 0.2040 \
5931 7 0.2010 \
5932 8 0.1990 \
5933 9 0.1960 \
5934 10 0.1935 \
5935 11 0.1910 \
5936 12 0.1890 \
5937 13 0.1850 \
5938 14 0.1820 \
5939 15 0.1800 \
5940 16 0.1770 \
5941 17 0.1730 \
5942 18 0.1695 \
5943 19 0.1660 \
5944 20 0.1610 \
5945 22 0.1570 \
5946 23 0.1540 \
5947 24 0.1520 \
5948 25 0.1495 \
5949 26 0.1470 \
5950 27 0.1440 \
5951 28 0.1405 \
5952 29 0.1360 \
5953 30 0.1285 \
5954 31 0.1200 \
5955 32 0.1160 \
5956 33 0.1130 \
5957 34 0.1110 \
5958 35 0.1100 \
5959 36 0.1065 \
5960 38 0.1015 \
5961 39 0.0995 \
5962 40 0.0980 \
5963 41 0.0960 \
5964 42 0.0935 \
5965 43 0.0890 \
5966 44 0.0860 \
5967 45 0.0820 \
5968 46 0.0810 \
5969 48 0.0760 \
5970 51 0.0670 \
5971 52 0.0635 \
5972 53 0.0595 \
5973 54 0.0550 \
5974 55 0.0520 \
5975 56 0.0465 \
5976 57 0.0430 \
5977 65 0.0350 \
5978 66 0.0330 \
5979 68 0.0310 \
5980 69 0.0292 \
5981 70 0.0280 \
5982 71 0.0260 \
5983 73 0.0240 \
5984 74 0.0225 \
5985 75 0.0210 \
5986 76 0.0200 \
5987 78 0.0160 \
5988 79 0.0145 \
5989 80 0.0135 \
5990 88 0.0095 \
5991 104 0.0031
5992
5993 drillA 0.234 in
5994 drillB 0.238 in
5995 drillC 0.242 in
5996 drillD 0.246 in
5997 drillE 0.250 in
5998 drillF 0.257 in
5999 drillG 0.261 in
6000 drillH 0.266 in
6001 drillI 0.272 in
6002 drillJ 0.277 in
6003 drillK 0.281 in
6004 drillL 0.290 in
6005 drillM 0.295 in
6006 drillN 0.302 in
6007 drillO 0.316 in
6008 drillP 0.323 in
6009 drillQ 0.332 in
6010 drillR 0.339 in
6011 drillS 0.348 in
6012 drillT 0.358 in
6013 drillU 0.368 in
6014 drillV 0.377 in
6015 drillW 0.386 in
6016 drillX 0.397 in
6017 drillY 0.404 in
6018 drillZ 0.413 in
6019
6020 #
6021 # Screw sizes
6022 #
6023 # In the USA, screw diameters for both wood screws and machine screws
6024 # are reported using a gauge number. Metric machine screws are
6025 # reported as Mxx where xx is the diameter in mm.
6026 #
6027
6028 screwgauge(g) units=[1;m] range=[0,) \
6029 (.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013
6030
6031 #
6032 # Abrasive grit size
6033 #
6034 # Standards governing abrasive grit sizes are complicated, specifying
6035 # fractions of particles that are passed or retained by different mesh
6036 # sizes. As a result, it is not possible to make precise comparisons
6037 # of different grit standards. The tables below allow the
6038 # determination of rough equivlants by using median particle size.
6039 #
6040 # Standards in the USA are determined by the Unified Abrasives
6041 # Manufacturers' Association (UAMA), which resulted from the merger of
6042 # several previous organizations. One of the old organizations was
6043 # CAMI (Coated Abrasives Manufacturers' Institute).
6044 #
6045 # UAMA has a web page with plots showing abrasive particle ranges for
6046 # various different grits and comparisons between standards.
6047 #
6048 # http://www.uama.org/Abrasives101/101Standards.html
6049 #
6050 # Abrasives are grouped into "bonded" abrasives for use with grinding
6051 # wheels and "coated" abrasives for sandpapers and abrasive films.
6052 # The industry uses different grit standards for these two
6053 # categories.
6054 #
6055 # Another division is between "macrogrits", grits below 240 and
6056 # "microgrits", which are above 240. Standards differ, as do methods
6057 # for determining particle size. In the USA, ANSI B74.12 is the
6058 # standard governing macrogrits. ANSI B74.10 covers bonded microgrit
6059 # abrasives, and ANSI B74.18 covers coated microgrit abrasives. It
6060 # appears that the coated standard is identical to the bonded standard
6061 # for grits up through 600 but then diverges significantly.
6062 #
6063 # European grit sizes are determined by the Federation of European
6064 # Producers of Abrasives. http://www.fepa-abrasives.org
6065 #
6066 # They give two standards, the "F" grit for bonded abrasives and the
6067 # "P" grit for coated abrasives. This data is taken directly from
6068 # their web page.
6069
6070 # FEPA P grit for coated abrasives is commonly seen on sandpaper in
6071 # the USA where the paper will be marked P600, for example. FEPA P
6072 # grits are said to be more tightly constrained than comparable ANSI
6073 # grits so that the particles are more uniform in size and hence give
6074 # a better finish.
6075
6076 grit_P[micron] \
6077 12 1815 \
6078 16 1324 \
6079 20 1000 \
6080 24 764 \
6081 30 642 \
6082 36 538 \
6083 40 425 \
6084 50 336 \
6085 60 269 \
6086 80 201 \
6087 100 162 \
6088 120 125 \
6089 150 100 \
6090 180 82 \
6091 220 68 \
6092 240 58.5 \
6093 280 52.2 \
6094 320 46.2 \
6095 360 40.5 \
6096 400 35 \
6097 500 30.2 \
6098 600 25.8 \
6099 800 21.8 \
6100 1000 18.3 \
6101 1200 15.3 \
6102 1500 12.6 \
6103 2000 10.3 \
6104 2500 8.4
6105
6106 # The F grit is the European standard for bonded abrasives such as
6107 # grinding wheels
6108
6109 grit_F[micron] \
6110 4 4890 \
6111 5 4125 \
6112 6 3460 \
6113 7 2900 \
6114 8 2460 \
6115 10 2085 \
6116 12 1765 \
6117 14 1470 \
6118 16 1230 \
6119 20 1040 \
6120 22 885 \
6121 24 745 \
6122 30 625 \
6123 36 525 \
6124 40 438 \
6125 46 370 \
6126 54 310 \
6127 60 260 \
6128 70 218 \
6129 80 185 \
6130 90 154 \
6131 100 129 \
6132 120 109 \
6133 150 82 \
6134 180 69 \
6135 220 58 \
6136 230 53 \
6137 240 44.5 \
6138 280 36.5 \
6139 320 29.2 \
6140 360 22.8 \
6141 400 17.3 \
6142 500 12.8 \
6143 600 9.3 \
6144 800 6.5 \
6145 1000 4.5 \
6146 1200 3 \
6147 1500 2.0 \
6148 2000 1.2
6149
6150 # According to the UAMA web page, the ANSI bonded and ANSI coated standards
6151 # are identical to FEPA F in the macrogrit range (under 240 grit), so these
6152 # values are taken from the FEPA F table. The values for 240 and above are
6153 # from the UAMA web site and represent the average of the "d50" range
6154 # endpoints listed there.
6155
6156 ansibonded[micron] \
6157 4 4890 \
6158 5 4125 \
6159 6 3460 \
6160 7 2900 \
6161 8 2460 \
6162 10 2085 \
6163 12 1765 \
6164 14 1470 \
6165 16 1230 \
6166 20 1040 \
6167 22 885 \
6168 24 745 \
6169 30 625 \
6170 36 525 \
6171 40 438 \
6172 46 370 \
6173 54 310 \
6174 60 260 \
6175 70 218 \
6176 80 185 \
6177 90 154 \
6178 100 129 \
6179 120 109 \
6180 150 82 \
6181 180 69 \
6182 220 58 \
6183 240 50 \
6184 280 39.5 \
6185 320 29.5 \
6186 360 23 \
6187 400 18.25 \
6188 500 13.9 \
6189 600 10.55 \
6190 800 7.65 \
6191 1000 5.8 \
6192 1200 3.8
6193
6194 grit_ansibonded() ansibonded
6195
6196 # Like the bonded grit, the coated macrogrits below 240 are taken from the
6197 # FEPA F table. Data above this is from the UAMA site. Note that the coated
6198 # and bonded standards are evidently the same from 240 up to 600 grit, but
6199 # starting at 800 grit, the coated standard diverges. The data from UAMA show
6200 # that 800 grit coated has an average size slightly larger than the average
6201 # size of 600 grit coated/bonded. However, the 800 grit has a significantly
6202 # smaller particle size variation.
6203 #
6204 # Because of this non-monotonicity from 600 grit to 800 grit this definition
6205 # produces a warning about the lack of a unique inverse.
6206
6207 ansicoated[micron] noerror \
6208 4 4890 \
6209 5 4125 \
6210 6 3460 \
6211 7 2900 \
6212 8 2460 \
6213 10 2085 \
6214 12 1765 \
6215 14 1470 \
6216 16 1230 \
6217 20 1040 \
6218 22 885 \
6219 24 745 \
6220 30 625 \
6221 36 525 \
6222 40 438 \
6223 46 370 \
6224 54 310 \
6225 60 260 \
6226 70 218 \
6227 80 185 \
6228 90 154 \
6229 100 129 \
6230 120 109 \
6231 150 82 \
6232 180 69 \
6233 220 58 \
6234 240 50 \
6235 280 39.5 \
6236 320 29.5 \
6237 360 23 \
6238 400 18.25 \
6239 500 13.9 \
6240 600 10.55 \
6241 800 11.5 \
6242 1000 9.5 \
6243 2000 7.2 \
6244 2500 5.5 \
6245 3000 4 \
6246 4000 3 \
6247 6000 2 \
6248 8000 1.2
6249
6250 grit_ansicoated() ansicoated
6251
6252
6253 #
6254 # Is this correct? This is the JIS Japanese standard used on waterstones
6255 #
6256 jisgrit[micron] \
6257 150 75 \
6258 180 63 \
6259 220 53 \
6260 280 48 \
6261 320 40 \
6262 360 35 \
6263 400 30 \
6264 600 20 \
6265 700 17 \
6266 800 14 \
6267 1000 11.5 \
6268 1200 9.5 \
6269 1500 8 \
6270 2000 6.7 \
6271 2500 5.5 \
6272 3000 4 \
6273 4000 3 \
6274 6000 2 \
6275 8000 1.2
6276
6277 # The "Finishing Scale" marked with an A (e.g. A75). This information
6278 # is from the web page of the sand paper manufacturer Klingspor
6279 # http://www.klingspor.com/gritgradingsystems.htm
6280 #
6281 # I have no information about what this scale is used for.
6282
6283 grit_A[micron]\
6284 16 15.3 \
6285 25 21.8 \
6286 30 23.6 \
6287 35 25.75 \
6288 45 35 \
6289 60 46.2 \
6290 65 53.5 \
6291 75 58.5 \
6292 90 65 \
6293 110 78 \
6294 130 93 \
6295 160 127 \
6296 200 156
6297 #
6298 # Grits for DMT brand diamond sharpening stones from
6299 # http://dmtsharp.com/products/colorcode.htm
6300 #
6301
6302 dmtxxcoarse 120 micron # 120 mesh
6303 dmtsilver dmtxxcoarse
6304 dmtxx dmtxxcoarse
6305 dmtxcoarse 60 micron # 220 mesh
6306 dmtx dmtxcoarse
6307 dmtblack dmtxcoarse
6308 dmtcoarse 45 micron # 325 mesh
6309 dmtc dmtcoarse
6310 dmtblue dmtcoarse
6311 dmtfine 25 micron # 600 mesh
6312 dmtred dmtfine
6313 dmtf dmtfine
6314 dmtefine 9 micron # 1200 mesh
6315 dmte dmtefine
6316 dmtgreen dmtefine
6317 dmtceramic 7 micron # 2200 mesh
6318 dmtcer dmtceramic
6319 dmtwhite dmtceramic
6320 dmteefine 3 micron # 8000 mesh
6321 dmttan dmteefine
6322 dmtee dmteefine
6323
6324 #
6325 # The following values come from a page in the Norton Stones catalog,
6326 # available at their web page, http://www.nortonstones.com.
6327 #
6328
6329 hardtranslucentarkansas 6 micron # Natural novaculite (silicon quartz)
6330 softarkansas 22 micron # stones
6331
6332 extrafineindia 22 micron # India stones are Norton's manufactured
6333 fineindia 35 micron # aluminum oxide product
6334 mediumindia 53.5 micron
6335 coarseindia 97 micron
6336
6337 finecrystolon 45 micron # Crystolon stones are Norton's
6338 mediumcrystalon 78 micron # manufactured silicon carbide product
6339 coarsecrystalon 127 micron
6340
6341 # The following are not from the Norton catalog
6342 hardblackarkansas 6 micron
6343 hardwhitearkansas 11 micron
6344 washita 35 micron
6345
6346 #
6347 # Mesh systems for measuring particle sizes by sifting through a wire
6348 # mesh or sieve
6349 #
6350
6351 # The Tyler system and US Sieve system are based on four steps for
6352 # each factor of 2 change in the size, so each size is 2^1|4 different
6353 # from the adjacent sizes. Unfortunately, the mesh numbers are
6354 # arbitrary, so the sizes cannot be expressed with a functional form.
6355 # Various references round the values differently. The mesh numbers
6356 # are supposed to correspond to the number of holes per inch, but this
6357 # correspondence is only approximate because it doesn't include the
6358 # wire size of the mesh.
6359
6360 # The Tyler Mesh system was apparently introduced by the WS Tyler
6361 # company, but it appears that they no longer use it. They follow the
6362 # ASTM E11 standard.
6363
6364 meshtyler[micron] \
6365 2.5 8000 \
6366 3 6727 \
6367 3.5 5657 \
6368 4 4757 \
6369 5 4000 \
6370 6 3364 \
6371 7 2828 \
6372 8 2378 \
6373 9 2000 \
6374 10 1682 \
6375 12 1414 \
6376 14 1189 \
6377 16 1000 \
6378 20 841 \
6379 24 707 \
6380 28 595 \
6381 32 500 \
6382 35 420 \
6383 42 354 \
6384 48 297 \
6385 60 250 \
6386 65 210 \
6387 80 177 \
6388 100 149 \
6389 115 125 \
6390 150 105 \
6391 170 88 \
6392 200 74 \
6393 250 63 \
6394 270 53 \
6395 325 44 \
6396 400 37
6397
6398 # US Sieve size, ASTM E11
6399 #
6400 # The WS Tyler company prints the list from ASTM E11 in their catalog,
6401 # http://wstyler.com/wp-content/uploads/2015/11/Product-Catalog-2.pdf
6402
6403 sieve[micron] \
6404 3.5 5600 \
6405 4 4750 \
6406 5 4000 \
6407 6 3350 \
6408 7 2800 \
6409 8 2360 \
6410 10 2000 \
6411 12 1700 \
6412 14 1400 \
6413 16 1180 \
6414 18 1000 \
6415 20 850 \
6416 25 710 \
6417 30 600 \
6418 35 500 \
6419 40 425 \
6420 45 355 \
6421 50 300 \
6422 60 250 \
6423 70 212 \
6424 80 180 \
6425 100 150 \
6426 120 125 \
6427 140 106 \
6428 170 90 \
6429 200 75 \
6430 230 63 \
6431 270 53 \
6432 325 45 \
6433 400 38 \
6434 450 32 \
6435 500 25 \
6436 625 20 # These last two values are not in the standard series
6437 # but were included in the ASTM standard because they
6438 meshUS() sieve # were in common usage.
6439
6440 # British Mesh size, BS 410: 1986
6441 # This system appears to correspond to the Tyler and US system, but
6442 # with different mesh numbers.
6443 #
6444 # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
6445 #
6446
6447 meshbritish[micron] \
6448 3 5657 \
6449 3.5 4757 \
6450 4 4000 \
6451 5 3364 \
6452 6 2828 \
6453 7 2378 \
6454 8 2000 \
6455 10 1682 \
6456 12 1414 \
6457 14 1189 \
6458 16 1000 \
6459 18 841 \
6460 22 707 \
6461 25 595 \
6462 30 500 \
6463 36 420 \
6464 44 354 \
6465 52 297 \
6466 60 250 \
6467 72 210 \
6468 85 177 \
6469 100 149 \
6470 120 125 \
6471 150 105 \
6472 170 88 \
6473 200 74 \
6474 240 63 \
6475 300 53 \
6476 350 44 \
6477 400 37
6478
6479 # French system, AFNOR NFX11-501: 1970
6480 # The system appears to be based on size doubling every 3 mesh
6481 # numbers, though the values have been agressively rounded.
6482 # It's not clear if the unrounded values would be considered
6483 # incorrect, so this is given as a table rather than a function.
6484 # Functional form:
6485 # meshtamis(mesh) units=[1;m] 5000 2^(1|3 (mesh-38)) micron
6486 #
6487 # http://www.panadyne.com/technical/panadyne_international_sieve_chart.pdf
6488
6489 meshtamis[micron] \
6490 17 40 \
6491 18 50 \
6492 19 63 \
6493 20 80 \
6494 21 100 \
6495 22 125 \
6496 23 160 \
6497 24 200 \
6498 25 250 \
6499 26 315 \
6500 27 400 \
6501 28 500 \
6502 29 630 \
6503 30 800 \
6504 31 1000 \
6505 32 1250 \
6506 33 1600 \
6507 34 2000 \
6508 35 2500 \
6509 36 3150 \
6510 37 4000 \
6511 38 5000
6512
6513 #
6514 # Ring size. All ring sizes are given as the circumference of the ring.
6515 #
6516
6517 # USA ring sizes. Several slightly different definitions seem to be in
6518 # circulation. According to [15], the interior diameter of size n ring in
6519 # inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The
6520 # size 2 ring is inconsistently 0.538in and no 2.5 size is listed.
6521 #
6522 # However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the
6523 # diameter and list no special case for size 2. (Or alternatively they are
6524 # 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One
6525 # reference claimed that the original system was that each size was 1|10 inch
6526 # circumference, but that source doesn't have an explanation for the modern
6527 # system which is somewhat different.
6528
6529 ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \
6530 (1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018
6531
6532 # Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes
6533 # specified alphabetically and based on the ring inside diameter in steps of
6534 # 1|64 inch. This system was replaced in 1987 by British Standard 6820 which
6535 # specifies sizes based on circumference. Each size is 1.25 mm different from
6536 # the preceding size. The baseline is size C which is 40 mm circumference.
6537 # The new sizes are close to the old ones. Sometimes it's necessary to go
6538 # beyond size Z to Z+1, Z+2, etc.
6539
6540 sizeAring 37.50 mm
6541 sizeBring 38.75 mm
6542 sizeCring 40.00 mm
6543 sizeDring 41.25 mm
6544 sizeEring 42.50 mm
6545 sizeFring 43.75 mm
6546 sizeGring 45.00 mm
6547 sizeHring 46.25 mm
6548 sizeIring 47.50 mm
6549 sizeJring 48.75 mm
6550 sizeKring 50.00 mm
6551 sizeLring 51.25 mm
6552 sizeMring 52.50 mm
6553 sizeNring 53.75 mm
6554 sizeOring 55.00 mm
6555 sizePring 56.25 mm
6556 sizeQring 57.50 mm
6557 sizeRring 58.75 mm
6558 sizeSring 60.00 mm
6559 sizeTring 61.25 mm
6560 sizeUring 62.50 mm
6561 sizeVring 63.75 mm
6562 sizeWring 65.00 mm
6563 sizeXring 66.25 mm
6564 sizeYring 67.50 mm
6565 sizeZring 68.75 mm
6566
6567 # Japanese sizes start with size 1 at a 13mm inside diameter and each size is
6568 # 1|3 mm larger in diameter than the previous one. They are multiplied by pi
6569 # to give circumference.
6570
6571 jpringsize(n) units=[1;mm] domain=[1,) range=[0.040840704,) \
6572 (38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38)
6573
6574 # The European ring sizes are the length of the circumference in mm minus 40.
6575
6576 euringsize(n) units=[1;mm] (n+40) mm ; euringsize/mm + (-40)
6577
6578 #
6579 # Abbreviations
6580 #
6581
6582 mph mile/hr
6583 mpg mile/gal
6584 kph km/hr
6585 fL footlambert
6586 fpm ft/min
6587 fps ft/s
6588 rpm rev/min
6589 rps rev/sec
6590 mi mile
6591 smi mile
6592 nmi nauticalmile
6593 mbh 1e3 btu/hour
6594 mcm 1e3 circularmil
6595 ipy inch/year # used for corrosion rates
6596 ccf 100 ft^3 # used for selling water [18]
6597 Mcf 1000 ft^3 # not million cubic feet [18]
6598 kp kilopond
6599 kpm kp meter
6600 Wh W hour
6601 hph hp hour
6602 plf lb / foot # pounds per linear foot
6603
6604 #
6605 # Compatibility units with Unix version
6606 #
6607
6608 pa Pa
6609 ev eV
6610 hg Hg
6611 oe Oe
6612 mh mH
6613 rd rod
6614 pf pF
6615 gr grain
6616 nt N
6617 hz Hz
6618 hd hogshead
6619 dry drygallon/gallon
6620 nmile nauticalmile
6621 beV GeV
6622 bev beV
6623 coul C
6624
6625 #
6626 # Radioactivity units
6627 #
6628
6629 becquerel /s # Activity of radioactive source
6630 Bq becquerel #
6631 curie 3.7e10 Bq # Defined in 1910 as the radioactivity
6632 Ci curie # emitted by the amount of radon that is
6633 # in equilibrium with 1 gram of radium.
6634 rutherford 1e6 Bq #
6635
6636 RADIATION_DOSE gray
6637 gray J/kg # Absorbed dose of radiation
6638 Gy gray #
6639 rad 1e-2 Gy # From Radiation Absorbed Dose
6640 rep 8.38 mGy # Roentgen Equivalent Physical, the amount
6641 # of radiation which , absorbed in the
6642 # body, would liberate the same amount
6643 # of energy as 1 roentgen of X rays
6644 # would, or 97 ergs.
6645
6646 sievert J/kg # Dose equivalent: dosage that has the
6647 Sv sievert # same effect on human tissues as 200
6648 rem 1e-2 Sv # keV X-rays. Different types of
6649 # radiation are weighted by the
6650 # Relative Biological Effectiveness
6651 # (RBE).
6652 #
6653 # Radiation type RBE
6654 # X-ray, gamma ray 1
6655 # beta rays, > 1 MeV 1
6656 # beta rays, < 1 MeV 1.08
6657 # neutrons, < 1 MeV 4-5
6658 # neutrons, 1-10 MeV 10
6659 # protons, 1 MeV 8.5
6660 # protons, .1 MeV 10
6661 # alpha, 5 MeV 15
6662 # alpha, 1 MeV 20
6663 #
6664 # The energies are the kinetic energy
6665 # of the particles. Slower particles
6666 # interact more, so they are more
6667 # effective ionizers, and hence have
6668 # higher RBE values.
6669 #
6670 # rem stands for Roentgen Equivalent
6671 # Mammal
6672 banana_dose 0.1e-6 sievert # Informal measure of the dose due to
6673 # eating one average sized banana
6674 roentgen 2.58e-4 C / kg # Ionizing radiation that produces
6675 # 1 statcoulomb of charge in 1 cc of
6676 # dry air at stp.
6677 rontgen roentgen # Sometimes it appears spelled this way
6678 sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one
6679 # hour at a distance of 1 cm from a
6680 # point source of 1 mg of radium
6681 # enclosed in platinum .5 mm thick.
6682
6683 eman 1e-7 Ci/m^3 # radioactive concentration
6684 mache 3.7e-7 Ci/m^3
6685
6686 #
6687 # Atomic weights. The atomic weight of an element is the ratio of the mass of
6688 # a mole of the element to 1|12 of a mole of Carbon 12. The Standard Atomic
6689 # Weights apply to the elements as they occur naturally on earth. Elements
6690 # which do not occur naturally or which occur with wide isotopic variability do
6691 # not have Standard Atomic Weights. For these elements, the atomic weight is
6692 # based on the longest lived isotope, as marked in the comments. In some
6693 # cases, the comment for these entries also gives a number which is an atomic
6694 # weight for a different isotope that may be of more interest than the longest
6695 # lived isotope.
6696 #
6697
6698 actinium 227.0278
6699 aluminum 26.981539
6700 americium 243.0614 # Longest lived. 241.06
6701 antimony 121.760
6702 argon 39.948
6703 arsenic 74.92159
6704 astatine 209.9871 # Longest lived
6705 barium 137.327
6706 berkelium 247.0703 # Longest lived. 249.08
6707 beryllium 9.012182
6708 bismuth 208.98037
6709 boron 10.811
6710 bromine 79.904
6711 cadmium 112.411
6712 calcium 40.078
6713 californium 251.0796 # Longest lived. 252.08
6714 carbon 12.011
6715 cerium 140.115
6716 cesium 132.90543
6717 chlorine 35.4527
6718 chromium 51.9961
6719 cobalt 58.93320
6720 copper 63.546
6721 curium 247.0703
6722 deuterium 2.0141017778
6723 dysprosium 162.50
6724 einsteinium 252.083 # Longest lived
6725 erbium 167.26
6726 europium 151.965
6727 fermium 257.0951 # Longest lived
6728 fluorine 18.9984032
6729 francium 223.0197 # Longest lived
6730 gadolinium 157.25
6731 gallium 69.723
6732 germanium 72.61
6733 gold 196.96654
6734 hafnium 178.49
6735 helium 4.002602
6736 holmium 164.93032
6737 hydrogen 1.00794
6738 indium 114.818
6739 iodine 126.90447
6740 iridium 192.217
6741 iron 55.845
6742 krypton 83.80
6743 lanthanum 138.9055
6744 lawrencium 262.11 # Longest lived
6745 lead 207.2
6746 lithium 6.941
6747 lutetium 174.967
6748 magnesium 24.3050
6749 manganese 54.93805
6750 mendelevium 258.10 # Longest lived
6751 mercury 200.59
6752 molybdenum 95.94
6753 neodymium 144.24
6754 neon 20.1797
6755 neptunium 237.0482
6756 nickel 58.6934
6757 niobium 92.90638
6758 nitrogen 14.00674
6759 nobelium 259.1009 # Longest lived
6760 osmium 190.23
6761 oxygen 15.9994
6762 palladium 106.42
6763 phosphorus 30.973762
6764 platinum 195.08
6765 plutonium 244.0642 # Longest lived. 239.05
6766 polonium 208.9824 # Longest lived. 209.98
6767 potassium 39.0983
6768 praseodymium 140.90765
6769 promethium 144.9127 # Longest lived. 146.92
6770 protactinium 231.03588
6771 radium 226.0254
6772 radon 222.0176 # Longest lived
6773 rhenium 186.207
6774 rhodium 102.90550
6775 rubidium 85.4678
6776 ruthenium 101.07
6777 samarium 150.36
6778 scandium 44.955910
6779 selenium 78.96
6780 silicon 28.0855
6781 silver 107.8682
6782 sodium 22.989768
6783 strontium 87.62
6784 sulfur 32.066
6785 tantalum 180.9479
6786 technetium 97.9072 # Longest lived. 98.906
6787 tellurium 127.60
6788 terbium 158.92534
6789 thallium 204.3833
6790 thorium 232.0381
6791 thullium 168.93421
6792 tin 118.710
6793 titanium 47.867
6794 tungsten 183.84
6795 uranium 238.0289
6796 vanadium 50.9415
6797 xenon 131.29
6798 ytterbium 173.04
6799 yttrium 88.90585
6800 zinc 65.39
6801 zirconium 91.224
6802
6803 # Average molecular weight of air
6804 #
6805 # The atmospheric composition listed is from NASA Earth Fact Sheet (accessed
6806 # 28 August 2015)
6807 # http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
6808 # Numbers do not add up to exactly 100% due to roundoff and uncertainty Water
6809 # is highly variable, typically makes up about 1%
6810
6811 air 78.08% nitrogen 2 \
6812 + 20.95% oxygen 2 \
6813 + 9340 ppm argon \
6814 + 400 ppm (carbon + oxygen 2) \
6815 + 18.18 ppm neon \
6816 + 5.24 ppm helium \
6817 + 1.7 ppm (carbon + 4 hydrogen) \
6818 + 1.14 ppm krypton \
6819 + 0.55 ppm hydrogen 2
6820
6821
6822 # Density of the elements
6823 #
6824 # Note some elements occur in multiple forms (allotropes) with different
6825 # densities, and they are accordingly listed multiple times.
6826
6827 # Density of gas phase elements at STP
6828
6829 hydrogendensity 0.08988 g/l
6830 heliumdensity 0.1786 g/l
6831 neondensity 0.9002 g/l
6832 nitrogendensity 1.2506 g/l
6833 oxygendensity 1.429 g/l
6834 fluorinedensity 1.696 g/l
6835 argondensity 1.784 g/l
6836 chlorinedensity 3.2 g/l
6837 kryptondensity 3.749 g/l
6838 xenondensity 5.894 g/l
6839 radondensity 9.73 g/l
6840
6841 # Density of liquid phase elements near room temperature
6842
6843 brominedensity 3.1028 g/cm^3
6844 mercurydensity 13.534 g/cm^3
6845
6846 # Density of solid elements near room temperature
6847
6848 lithiumdensity 0.534 g/cm^3
6849 potassiumdensity 0.862 g/cm^3
6850 sodiumdensity 0.968 g/cm^3
6851 rubidiumdensity 1.532 g/cm^3
6852 calciumdensity 1.55 g/cm^3
6853 magnesiumdensity 1.738 g/cm^3
6854 phosphorus_white_density 1.823 g/cm^3
6855 berylliumdensity 1.85 g/cm^3
6856 sulfur_gamma_density 1.92 g/cm^3
6857 cesiumdensity 1.93 g/cm^3
6858 carbon_amorphous_density 1.95 g/cm^3 # average value
6859 sulfur_betadensity 1.96 g/cm^3
6860 sulfur_alpha_density 2.07 g/cm^3
6861 carbon_graphite_density 2.267 g/cm^3
6862 phosphorus_red_density 2.27 g/cm^3 # average value
6863 silicondensity 2.3290 g/cm^3
6864 phosphorus_violet_density 2.36 g/cm^3
6865 borondensity 2.37 g/cm^3
6866 strontiumdensity 2.64 g/cm^3
6867 phosphorus_black_density 2.69 g/cm^3
6868 aluminumdensity 2.7 g/cm^3
6869 bariumdensity 3.51 g/cm^3
6870 carbon_diamond_density 3.515 g/cm^3
6871 scandiumdensity 3.985 g/cm^3
6872 selenium_vitreous_density 4.28 g/cm^3
6873 selenium_alpha_density 4.39 g/cm^3
6874 titaniumdensity 4.406 g/cm^3
6875 yttriumdensity 4.472 g/cm^3
6876 selenium_gray_density 4.81 g/cm^3
6877 iodinedensity 4.933 g/cm^3
6878 europiumdensity 5.264 g/cm^3
6879 germaniumdensity 5.323 g/cm^3
6880 radiumdensity 5.5 g/cm^3
6881 arsenicdensity 5.727 g/cm^3
6882 tin_alpha_density 5.769 g/cm^3
6883 galliumdensity 5.91 g/cm^3
6884 vanadiumdensity 6.11 g/cm^3
6885 lanthanumdensity 6.162 g/cm^3
6886 telluriumdensity 6.24 g/cm^3
6887 zirconiumdensity 6.52 g/cm^3
6888 antimonydensity 6.697 g/cm^3
6889 ceriumdensity 6.77 g/cm^3
6890 praseodymiumdensity 6.77 g/cm^3
6891 ytterbiumdensity 6.9 g/cm^3
6892 neodymiumdensity 7.01 g/cm^3
6893 zincdensity 7.14 g/cm^3
6894 chromiumdensity 7.19 g/cm^3
6895 manganesedensity 7.21 g/cm^3
6896 promethiumdensity 7.26 g/cm^3
6897 tin_beta_density 7.265 g/cm^3
6898 indiumdensity 7.31 g/cm^3
6899 samariumdensity 7.52 g/cm^3
6900 irondensity 7.874 g/cm^3
6901 gadoliniumdensity 7.9 g/cm^3
6902 terbiumdensity 8.23 g/cm^3
6903 dysprosiumdensity 8.54 g/cm^3
6904 niobiumdensity 8.57 g/cm^3
6905 cadmiumdensity 8.65 g/cm^3
6906 holmiumdensity 8.79 g/cm^3
6907 cobaltdensity 8.9 g/cm^3
6908 nickeldensity 8.908 g/cm^3
6909 erbiumdensity 9.066 g/cm^3
6910 polonium_alpha_density 9.196 g/cm^3
6911 thuliumdensity 9.32 g/cm^3
6912 polonium_beta_density 9.398 g/cm^3
6913 bismuthdensity 9.78 g/cm^3
6914 lutetiumdensity 9.841 g/cm^3
6915 actiniumdensity 10 g/cm^3
6916 molybdenumdensity 10.28 g/cm^3
6917 silverdensity 10.49 g/cm^3
6918 technetiumdensity 11 g/cm^3
6919 leaddensity 11.34 g/cm^3
6920 thoriumdensity 11.7 g/cm^3
6921 thalliumdensity 11.85 g/cm^3
6922 americiumdensity 12 g/cm^3
6923 palladiumdensity 12.023 g/cm^3
6924 rhodiumdensity 12.41 g/cm^3
6925 rutheniumdensity 12.45 g/cm^3
6926 berkelium_beta_density 13.25 g/cm^3
6927 hafniumdensity 13.31 g/cm^3
6928 curiumdensity 13.51 g/cm^3
6929 berkelium_alphadensity 14.78 g/cm^3
6930 californiumdensity 15.1 g/cm^3
6931 protactiniumdensity 15.37 g/cm^3
6932 tantalumdensity 16.69 g/cm^3
6933 uraniumdensity 19.1 g/cm^3
6934 tungstendensity 19.3 g/cm^3
6935 golddensity 19.30 g/cm^3
6936 plutoniumdensity 19.816 g/cm^3
6937 neptuniumdensity 20.45 g/cm^3 # alpha form, only one at room temp
6938 rheniumdensity 21.02 g/cm^3
6939 platinumdensity 21.45 g/cm^3
6940 iridiumdensity 22.56 g/cm^3
6941 osmiumdensity 22.59 g/cm^3
6942
6943 # A few alternate names
6944
6945 tin_gray tin_alpha_density
6946 tin_white tin_beta_density
6947 graphitedensity carbon_graphite_density
6948 diamonddensity carbon_diamond_density
6949
6950 # Predicted density of elements that have not been made in sufficient
6951 # quantities for measurement.
6952
6953 franciumdensity 2.48 g/cm^3 # liquid, predicted melting point 8 degC
6954 astatinedensity 6.35 g/cm^3
6955 einsteiniumdensity 8.84 g/cm^3
6956 fermiumdensity 9.7 g/cm^3
6957 nobeliumdensity 9.9 g/cm^3
6958 mendeleviumdensity 10.3 g/cm^3
6959 lawrenciumdensity 16 g/cm^3
6960 rutherfordiumdensity 23.2 g/cm^3
6961 roentgeniumdensity 28.7 g/cm^3
6962 dubniumdensity 29.3 g/cm^3
6963 darmstadtiumdensity 34.8 g/cm^3
6964 seaborgiumdensity 35 g/cm^3
6965 bohriumdensity 37.1 g/cm^3
6966 meitneriumdensity 37.4 g/cm^3
6967 hassiumdensity 41 g/cm^3
6968
6969 #
6970 # population units
6971 #
6972
6973 people 1
6974 person people
6975 death people
6976 capita people
6977 percapita per capita
6978
6979 # TGM dozen based unit system listed on the "dozenal" forum
6980 # http://www.dozenalsociety.org.uk/apps/tgm.htm. These units are
6981 # proposed as an allegedly more rational alternative to the SI system.
6982
6983 Tim 12^-4 hour # Time
6984 Grafut gravity Tim^2 # Length based on gravity
6985 Surf Grafut^2 # area
6986 Volm Grafut^3 # volume
6987 Vlos Grafut/Tim # speed
6988 Denz Maz/Volm # density
6989 Mag Maz gravity # force
6990 Maz Volm kg / oldliter # mass based on water
6991
6992 Tm Tim # Abbreviations
6993 Gf Grafut
6994 Sf Surf
6995 Vm Volm
6996 Vl Vlos
6997 Mz Maz
6998 Dz Denz
6999
7000 # Dozen based unit prefixes
7001
7002 Zena- 12
7003 Duna- 12^2
7004 Trina- 12^3
7005 Quedra- 12^4
7006 Quena- 12^5
7007 Hesa- 12^6
7008 Seva- 12^7
7009 Aka- 12^8
7010 Neena- 12^9
7011 Dexa- 12^10
7012 Lefa- 12^11
7013 Zennila- 12^12
7014
7015 Zeni- 12^-1
7016 Duni- 12^-2
7017 Trini- 12^-3
7018 Quedri- 12^-4
7019 Queni- 12^-5
7020 Hesi- 12^-6
7021 Sevi- 12^-7
7022 Aki- 12^-8
7023 Neeni- 12^-9
7024 Dexi- 12^-10
7025 Lefi- 12^-11
7026 Zennili- 12^-12
7027
7028 #
7029 # Traditional Japanese units (shakkanhou)
7030 #
7031 # The traditional system of weights and measures is called shakkanhou from the
7032 # shaku and the ken. Japan accepted SI units in 1891 and legalized conversions
7033 # to the traditional system. In 1909 the inch-pound system was also legalized,
7034 # so Japan had three legally approved systems. A change to the metric system
7035 # started in 1921 but there was a lot of resistance. The Measurement Law of
7036 # October 1999 prohibits sales in anything but SI units. However, the old
7037 # units still live on in construction and as the basis for paper sizes of books
7038 # and tools used for handicrafts.
7039 #
7040 # Note that units below use the Hepburn romanization system. Some other
7041 # systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho".
7042 #
7043 #
7044 # http://hiramatu-hifuka.com/onyak/onyindx.html
7045
7046 # Japanese Proportions. These are still in everyday use. They also
7047 # get used as units to represent the proportion of the standard unit.
7048
7049 wari_proportion 1|10
7050 wari wari_proportion
7051 bu_proportion 1|100 # The character bu can also be read fun or bun
7052 # but usually "bu" is used for units.
7053 rin_proportion 1|1000
7054 mou_proportion 1|10000
7055
7056
7057 # Japanese Length Measures
7058 #
7059 # The length system is called kanejaku or
7060 # square and originated in China. It was
7061 # adopted as Japan's official measure in 701
7062 # by the Taiho Code. This system is still in
7063 # common use in architecture and clothing.
7064
7065 shaku 1|3.3 m
7066 mou 1|10000 shaku
7067 rin 1|1000 shaku
7068 bu_distance 1|100 shaku
7069 sun 1|10 shaku
7070 jou_distance 10 shaku
7071 jou jou_distance
7072
7073 kanejakusun sun # Alias to emphasize architectural name
7074 kanejaku shaku
7075 kanejakujou jou
7076
7077 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
7078 taichi shaku # http://zh.wikipedia.org/wiki/台尺
7079 taicun sun # http://zh.wikipedia.org/wiki/台制
7080 !utf8
7081 台尺 taichi # via Hanyu Pinyin romanizations
7082 台寸 taicun
7083 !endutf8
7084
7085 # In context of clothing, shaku is different from architecture
7086 # http://www.scinet.co.jp/sci/sanwa/kakizaki-essay54.html
7087
7088 kujirajaku 10|8 shaku
7089 kujirajakusun 1|10 kujirajaku
7090 kujirajakubu 1|100 kujirajaku
7091 kujirajakujou 10 kujirajaku
7092 tan_distance 3 kujirajakujou
7093
7094 ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6
7095 # http://www.homarewood.co.jp/syakusun.htm
7096
7097 # mostly unused
7098 chou_distance 60 ken
7099 chou chou_distance
7100 ri 36 chou
7101
7102 # Japanese Area Measures
7103
7104 # Tsubo is still used for land size, though the others are more
7105 # recognized by their homonyms in the other measurements.
7106
7107 gou_area 1|10 tsubo
7108 tsubo 36 shaku^2 # Size of two tatami = ken^2 ??
7109 se 30 tsubo
7110 tan_area 10 se
7111 chou_area 10 tan_area
7112
7113 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
7114 ping tsubo # http://zh.wikipedia.org/wiki/坪
7115 jia 2934 ping # http://zh.wikipedia.org/wiki/甲_(单位)
7116 fen 1|10 jia # http://zh.wikipedia.org/wiki/分
7117 fen_area 1|10 jia # Protection against future collisions
7118 !utf8
7119 坪 ping # via Hanyu Pinyin romanizations
7120 甲 jia
7121 分 fen
7122 分地 fen_area # Protection against future collisions
7123 !endutf8
7124
7125 # Japanese architecture is based on a "standard" size of tatami mat.
7126 # Room sizes today are given in number of tatami, and this number
7127 # determines the spacing between colums and hence sizes of sliding
7128 # doors and paper screens. However, every region has its own slightly
7129 # different tatami size. Edoma, used in and around Tokyo and
7130 # Hokkaido, is becoming a nationwide standard. Kyouma is used around
7131 # Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya.
7132 # Note that the tatami all have the aspect ratio 2:1 so that the mats
7133 # can tile the room with some of them turned 90 degrees.
7134 #
7135 # http://www.moon2.net/tatami/infotatami/structure.html
7136
7137 edoma (5.8*2.9) shaku^2
7138 kyouma (6.3*3.15) shaku^2
7139 chuukyouma (6*3) shaku^2
7140 jou_area edoma
7141 tatami jou_area
7142
7143 # Japanese Volume Measures
7144
7145 # The "shou" is still used for such things as alcohol and seasonings.
7146 # Large quantities of paint are still purchased in terms of "to".
7147
7148 shaku_volume 1|10 gou_volume
7149 gou_volume 1|10 shou
7150 gou gou_volume
7151 shou (4.9*4.9*2.7) sun^3 # The character shou which is
7152 # the same as masu refers to a
7153 # rectangular wooden cup used to
7154 # measure liquids and cereal.
7155 # Sake is sometimes served in a masu
7156 # Note that it happens to be
7157 # EXACTLY 7^4/11^3 liters.
7158 to 10 shou
7159 koku 10 to # No longer used; historically a measure of rice
7160
7161 # Japanese Weight Measures
7162 #
7163 # http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html
7164
7165 # Not really used anymore.
7166
7167 rin_weight 1|10 bu_weight
7168 bu_weight 1|10 monme
7169 fun 1|10 monme
7170 monme momme
7171 kin 160 monme
7172 kan 1000 monme
7173 kwan kan # This was the old pronounciation of the unit.
7174 # The old spelling persisted a few centuries
7175 # longer and was not changed until around
7176 # 1950.
7177
7178 # http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
7179 # says: "Volume measure in Taiwan is largely metric".
7180 taijin kin # http://zh.wikipedia.org/wiki/台斤
7181 tailiang 10 monme # http://zh.wikipedia.org/wiki/台斤
7182 taiqian monme # http://zh.wikipedia.org/wiki/台制
7183 !utf8
7184 台斤 taijin # via Hanyu Pinyin romanizations
7185 台兩 tailiang
7186 台錢 taiqian
7187 !endutf8
7188
7189 #
7190 # Australian unit
7191 #
7192
7193 australiasquare (10 ft)^2 # Used for house area
7194
7195
7196 #
7197 # A few German units as currently in use.
7198 #
7199
7200 zentner 50 kg
7201 doppelzentner 2 zentner
7202 pfund 500 g
7203
7204 # The klafter, which was used in central Europe, was derived from the span of
7205 # outstretched arms.
7206 #
7207 # https://en.wikipedia.org/wiki/Obsolete_Austrian_units_of_measurement
7208 # https://www.llv.li/files/abi/klafter-m2-en.pdf
7209
7210 austriaklafter 1.89648384 m # Exact definition, 23 July 1871
7211 austriafoot 1|6 austriaklafter
7212 prussiaklafter 1.88 m
7213 prussiafoot 1|6 prussiaklafter
7214 bavariaklafter 1.751155 m
7215 bavariafoot 1|6 bavariaklafter
7216 hesseklafter 2.5 m
7217 hessefoot 1|6 hesseklafter
7218 switzerlandklafter metricklafter
7219 switzerlandfoot 1|6 switzerlandklafter
7220 swissklafter switzerlandklafter
7221 swissfoot 1|6 swissklafter
7222 metricklafter 1.8 m
7223
7224 austriayoke 8 austriaklafter * 200 austriaklafter
7225
7226 liechtensteinsquareklafter 3.596652 m^2 # Used until 2017 to measure land area
7227 liechtensteinklafter sqrt(liechtensteinsquareklafter)
7228
7229 # The klafter was also used to measure volume of wood, generally being a stack
7230 # of wood one klafter wide, one klafter long, with logs 3 feet (half a klafter)
7231 # in length
7232
7233 prussiawoodklafter 0.5 prussiaklafter^3
7234 austriawoodklafter 0.5 austriaklafter^3
7235 festmeter m^3 # modern measure of wood, solid cube
7236 raummeter 0.7 festmeter # Air space between the logs, stacked
7237 schuettraummeter 0.65 raummeter # A cubic meter volume of split and cut
7238 schüttraummeter schuettraummeter# firewood in a loose, unordered
7239 # pile, not stacked. This is called
7240 # "tipped".
7241
7242
7243 #
7244 # Swedish (Sweden) pre-metric units of 1739.
7245 # The metric system was adopted in 1878.
7246 # https://sv.wikipedia.org/wiki/Verkm%C3%A5tt
7247 #
7248
7249 verklinje 2.0618125 mm
7250 verktum 12 verklinje
7251 kvarter 6 verktum
7252 fot 2 kvarter
7253 aln 2 fot
7254 famn 3 aln
7255
7256 #
7257 # Some traditional Russian measures
7258 #
7259 # If you would like to help expand this section and understand
7260 # cyrillic transliteration, let me know. These measures are meant to
7261 # reflect common usage, e.g. in translated literature.
7262 #
7263
7264 dessiatine 2400 sazhen^2 # Land measure
7265 dessjatine dessiatine
7266
7267 funt 409.51718 grams # similar to pound
7268 zolotnik 1|96 funt # used for precious metal measure
7269 pood 40 funt # common in agricultural measure
7270
7271 arshin (2 + 1|3) feet
7272 sazhen 3 arshin # analogous to fathom
7273 verst 500 sazhen # of similar use to mile
7274 versta verst
7275 borderverst 1000 sazhen
7276 russianmile 7 verst
7277
7278
7279
7280
7281 #
7282 # Old French distance measures, from French Weights and Measures
7283 # Before the Revolution by Zupko
7284 #
7285
7286 frenchfoot 144|443.296 m # pied de roi, the standard of Paris.
7287 pied frenchfoot # Half of the hashimicubit,
7288 frenchfeet frenchfoot # instituted by Charlemagne.
7289 frenchinch 1|12 frenchfoot # This exact definition comes from
7290 frenchthumb frenchinch # a law passed on 10 Dec 1799 which
7291 pouce frenchthumb # fixed the meter at
7292 # 3 frenchfeet + 11.296 lignes.
7293 frenchline 1|12 frenchinch # This is supposed to be the size
7294 ligne frenchline # of the average barleycorn
7295 frenchpoint 1|12 frenchline
7296 toise 6 frenchfeet
7297 arpent 180^2 pied^2 # The arpent is 100 square perches,
7298 # but the perche seems to vary a lot
7299 # and can be 18 feet, 20 feet, or 22
7300 # feet. This measure was described
7301 # as being in common use in Canada in
7302 # 1934 (Websters 2nd). The value
7303 # given here is the Paris standard
7304 # arpent.
7305 frenchgrain 1|18827.15 kg # Weight of a wheat grain, hence
7306 # smaller than the British grain.
7307 frenchpound 9216 frenchgrain
7308
7309 #
7310 # Before the Imperial Weights and Measures Act of 1824, various different
7311 # weights and measures were in use in different places.
7312 #
7313
7314 # Scots linear measure
7315
7316 scotsinch 1.00540054 UKinch
7317 scotslink 1|100 scotschain
7318 scotsfoot 12 scotsinch
7319 scotsfeet scotsfoot
7320 scotsell 37 scotsinch
7321 scotsfall 6 scotsell
7322 scotschain 4 scotsfall
7323 scotsfurlong 10 scotschain
7324 scotsmile 8 scotsfurlong
7325
7326 # Scots area measure
7327
7328 scotsrood 40 scotsfall^2
7329 scotsacre 4 scotsrood
7330
7331 # Irish linear measure
7332
7333 irishinch UKinch
7334 irishpalm 3 irishinch
7335 irishspan 3 irishpalm
7336 irishfoot 12 irishinch
7337 irishfeet irishfoot
7338 irishcubit 18 irishinch
7339 irishyard 3 irishfeet
7340 irishpace 5 irishfeet
7341 irishfathom 6 irishfeet
7342 irishpole 7 irishyard # Only these values
7343 irishperch irishpole # are different from
7344 irishchain 4 irishperch # the British Imperial
7345 irishlink 1|100 irishchain # or English values for
7346 irishfurlong 10 irishchain # these lengths.
7347 irishmile 8 irishfurlong #
7348
7349 # Irish area measure
7350
7351 irishrood 40 irishpole^2
7352 irishacre 4 irishrood
7353
7354 # English wine capacity measures (Winchester measures)
7355
7356 winepint 1|2 winequart
7357 winequart 1|4 winegallon
7358 winegallon 231 UKinch^3 # Sometimes called the Winchester Wine Gallon,
7359 # it was legalized in 1707 by Queen Anne, and
7360 # given the definition of 231 cubic inches. It
7361 # had been in use for a while as 8 pounds of wine
7362 # using a merchant's pound, but the definition of
7363 # the merchant's pound had become uncertain. A
7364 # pound of 15 tower ounces (6750 grains) had been
7365 # common, but then a pound of 15 troy ounces
7366 # (7200 grains) gained popularity. Because of
7367 # the switch in the value of the merchants pound,
7368 # the size of the wine gallon was uncertain in
7369 # the market, hence the official act in 1707.
7370 # The act allowed that a six inch tall cylinder
7371 # with a 7 inch diameter was a lawful wine
7372 # gallon. (This comes out to 230.9 in^3.)
7373 # Note also that in Britain a legal conversion
7374 # was established to the 1824 Imperial gallon
7375 # then taken as 277.274 in^3 so that the wine
7376 # gallon was 0.8331 imperial gallons. This is
7377 # 231.1 cubic inches (using the international
7378 # inch).
7379 winerundlet 18 winegallon
7380 winebarrel 31.5 winegallon
7381 winetierce 42 winegallon
7382 winehogshead 2 winebarrel
7383 winepuncheon 2 winetierce
7384 winebutt 2 winehogshead
7385 winepipe winebutt
7386 winetun 2 winebutt
7387
7388 # English beer and ale measures used 1803-1824 and used for beer before 1688
7389
7390 beerpint 1|2 beerquart
7391 beerquart 1|4 beergallon
7392 beergallon 282 UKinch^3
7393 beerbarrel 36 beergallon
7394 beerhogshead 1.5 beerbarrel
7395
7396 # English ale measures used from 1688-1803 for both ale and beer
7397
7398 alepint 1|2 alequart
7399 alequart 1|4 alegallon
7400 alegallon beergallon
7401 alebarrel 34 alegallon
7402 alehogshead 1.5 alebarrel
7403
7404 # Scots capacity measure
7405
7406 scotsgill 1|4 mutchkin
7407 mutchkin 1|2 choppin
7408 choppin 1|2 scotspint
7409 scotspint 1|2 scotsquart
7410 scotsquart 1|4 scotsgallon
7411 scotsgallon 827.232 UKinch^3
7412 scotsbarrel 8 scotsgallon
7413 jug scotspint
7414
7415 # Scots dry capacity measure
7416
7417 scotswheatlippy 137.333 UKinch^3 # Also used for peas, beans, rye, salt
7418 scotswheatlippies scotswheatlippy
7419 scotswheatpeck 4 scotswheatlippy
7420 scotswheatfirlot 4 scotswheatpeck
7421 scotswheatboll 4 scotswheatfirlot
7422 scotswheatchalder 16 scotswheatboll
7423
7424 scotsoatlippy 200.345 UKinch^3 # Also used for barley and malt
7425 scotsoatlippies scotsoatlippy
7426 scotsoatpeck 4 scotsoatlippy
7427 scotsoatfirlot 4 scotsoatpeck
7428 scotsoatboll 4 scotsoatfirlot
7429 scotsoatchalder 16 scotsoatboll
7430
7431 # Scots Tron weight
7432
7433 trondrop 1|16 tronounce
7434 tronounce 1|20 tronpound
7435 tronpound 9520 grain
7436 tronstone 16 tronpound
7437
7438 # Irish liquid capacity measure
7439
7440 irishnoggin 1|4 irishpint
7441 irishpint 1|2 irishquart
7442 irishquart 1|2 irishpottle
7443 irishpottle 1|2 irishgallon
7444 irishgallon 217.6 UKinch^3
7445 irishrundlet 18 irishgallon
7446 irishbarrel 31.5 irishgallon
7447 irishtierce 42 irishgallon
7448 irishhogshead 2 irishbarrel
7449 irishpuncheon 2 irishtierce
7450 irishpipe 2 irishhogshead
7451 irishtun 2 irishpipe
7452
7453 # Irish dry capacity measure
7454
7455 irishpeck 2 irishgallon
7456 irishbushel 4 irishpeck
7457 irishstrike 2 irishbushel
7458 irishdrybarrel 2 irishstrike
7459 irishquarter 2 irishbarrel
7460
7461 # English Tower weights, abolished in 1528
7462
7463 towerpound 5400 grain
7464 towerounce 1|12 towerpound
7465 towerpennyweight 1|20 towerounce
7466 towergrain 1|32 towerpennyweight
7467
7468 # English Mercantile weights, used since the late 12th century
7469
7470 mercpound 6750 grain
7471 mercounce 1|15 mercpound
7472 mercpennyweight 1|20 mercounce
7473
7474 # English weights for lead
7475
7476 leadstone 12.5 lb
7477 fotmal 70 lb
7478 leadwey 14 leadstone
7479 fothers 12 leadwey
7480
7481 # English Hay measure
7482
7483 newhaytruss 60 lb # New and old here seem to refer to "new"
7484 newhayload 36 newhaytruss # hay and "old" hay rather than a new unit
7485 oldhaytruss 56 lb # and an old unit.
7486 oldhayload 36 oldhaytruss
7487
7488 # English wool measure
7489
7490 woolclove 7 lb
7491 woolstone 2 woolclove
7492 wooltod 2 woolstone
7493 woolwey 13 woolstone
7494 woolsack 2 woolwey
7495 woolsarpler 2 woolsack
7496 woollast 6 woolsarpler
7497
7498 #
7499 # Ancient history units: There tends to be uncertainty in the definitions
7500 # of the units in this section
7501 # These units are from [11]
7502
7503 # Roman measure. The Romans had a well defined distance measure, but their
7504 # measures of weight were poor. They adopted local weights in different
7505 # regions without distinguishing among them so that there are half a dozen
7506 # different Roman "standard" weight systems.
7507
7508 romanfoot 296 mm # There is some uncertainty in this definition
7509 romanfeet romanfoot # from which all the other units are derived.
7510 pes romanfoot # This value appears in numerous sources. In "The
7511 pedes romanfoot # Roman Land Surveyors", Dilke gives 295.7 mm.
7512 romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the
7513 romandigit 1|16 romanfoot # same names as the subdivisions of the pound,
7514 romanpalm 1|4 romanfoot # but we can't have the names for different
7515 romancubit 18 romaninch # units.
7516 romanpace 5 romanfeet # Roman double pace (basic military unit)
7517 passus romanpace
7518 romanperch 10 romanfeet
7519 stade 125 romanpaces
7520 stadia stade
7521 stadium stade
7522 romanmile 8 stadia # 1000 paces
7523 romanleague 1.5 romanmile
7524 schoenus 4 romanmile
7525
7526 # Other values for the Roman foot (from Dilke)
7527
7528 earlyromanfoot 29.73 cm
7529 pesdrusianus 33.3 cm # or 33.35 cm, used in Gaul & Germany in 1st c BC
7530 lateromanfoot 29.42 cm
7531
7532 # Roman areas
7533
7534 actuslength 120 romanfeet # length of a Roman furrow
7535 actus 120*4 romanfeet^2 # area of the furrow
7536 squareactus 120^2 romanfeet^2 # actus quadratus
7537 acnua squareactus
7538 iugerum 2 squareactus
7539 iugera iugerum
7540 jugerum iugerum
7541 jugera iugerum
7542 heredium 2 iugera # heritable plot
7543 heredia heredium
7544 centuria 100 heredia
7545 centurium centuria
7546
7547 # Roman volumes
7548
7549 sextarius 35.4 in^3 # Basic unit of Roman volume. As always,
7550 sextarii sextarius # there is uncertainty. Six large Roman
7551 # measures survive with volumes ranging from
7552 # 34.4 in^3 to 39.55 in^3. Three of them
7553 # cluster around the size given here.
7554 #
7555 # But the values for this unit vary wildly
7556 # in other sources. One reference gives 0.547
7557 # liters, but then says the amphora is a
7558 # cubic Roman foot. This gives a value for the
7559 # sextarius of 0.540 liters. And the
7560 # encyclopedia Britannica lists 0.53 liters for
7561 # this unit. Both [7] and [11], which were
7562 # written by scholars of weights and measures,
7563 # give the value of 35.4 cubic inches.
7564 cochlearia 1|48 sextarius
7565 cyathi 1|12 sextarius
7566 acetabula 1|8 sextarius
7567 quartaria 1|4 sextarius
7568 quartarius quartaria
7569 heminae 1|2 sextarius
7570 hemina heminae
7571 cheonix 1.5 sextarii
7572
7573 # Dry volume measures (usually)
7574
7575 semodius 8 sextarius
7576 semodii semodius
7577 modius 16 sextarius
7578 modii modius
7579
7580 # Liquid volume measures (usually)
7581
7582 congius 12 heminae
7583 congii congius
7584 amphora 8 congii
7585 amphorae amphora # Also a dry volume measure
7586 culleus 20 amphorae
7587 quadrantal amphora
7588
7589 # Roman weights
7590
7591 libra 5052 grain # The Roman pound varied significantly
7592 librae libra # from 4210 grains to 5232 grains. Most of
7593 romanpound libra # the standards were obtained from the weight
7594 uncia 1|12 libra # of particular coins. The one given here is
7595 unciae uncia # based on the Gold Aureus of Augustus which
7596 romanounce uncia # was in use from BC 27 to AD 296.
7597 deunx 11 uncia
7598 dextans 10 uncia
7599 dodrans 9 uncia
7600 bes 8 uncia
7601 seprunx 7 uncia
7602 semis 6 uncia
7603 quincunx 5 uncia
7604 triens 4 uncia
7605 quadrans 3 uncia
7606 sextans 2 uncia
7607 sescuncia 1.5 uncia
7608 semuncia 1|2 uncia
7609 siscilius 1|4 uncia
7610 sextula 1|6 uncia
7611 semisextula 1|12 uncia
7612 scriptulum 1|24 uncia
7613 scrupula scriptulum
7614 romanobol 1|2 scrupula
7615
7616 romanaspound 4210 grain # Old pound based on bronze coinage, the
7617 # earliest money of Rome BC 338 to BC 268.
7618
7619 # Egyptian length measure
7620
7621 egyptianroyalcubit 20.63 in # plus or minus .2 in
7622 egyptianpalm 1|7 egyptianroyalcubit
7623 egyptiandigit 1|4 egyptianpalm
7624 egyptianshortcubit 6 egyptianpalm
7625
7626 doubleremen 29.16 in # Length of the diagonal of a square with
7627 remendigit 1|40 doubleremen # side length of 1 royal egyptian cubit.
7628 # This is divided into 40 digits which are
7629 # not the same size as the digits based on
7630 # the royal cubit.
7631
7632 # Greek length measures
7633
7634 greekfoot 12.45 in # Listed as being derived from the
7635 greekfeet greekfoot # Egyptian Royal cubit in [11]. It is
7636 greekcubit 1.5 greekfoot # said to be 3|5 of a 20.75 in cubit.
7637 pous greekfoot
7638 podes greekfoot
7639 orguia 6 greekfoot
7640 greekfathom orguia
7641 stadion 100 orguia
7642 akaina 10 greekfeet
7643 plethron 10 akaina
7644 greekfinger 1|16 greekfoot
7645 homericcubit 20 greekfingers # Elbow to end of knuckles.
7646 shortgreekcubit 18 greekfingers # Elbow to start of fingers.
7647
7648 ionicfoot 296 mm
7649 doricfoot 326 mm
7650
7651 olympiccubit 25 remendigit # These olympic measures were not as
7652 olympicfoot 2|3 olympiccubit # common as the other greek measures.
7653 olympicfinger 1|16 olympicfoot # They were used in agriculture.
7654 olympicfeet olympicfoot
7655 olympicdakylos olympicfinger
7656 olympicpalm 1|4 olympicfoot
7657 olympicpalestra olympicpalm
7658 olympicspithame 3|4 foot
7659 olympicspan olympicspithame
7660 olympicbema 2.5 olympicfeet
7661 olympicpace olympicbema
7662 olympicorguia 6 olympicfeet
7663 olympicfathom olympicorguia
7664 olympiccord 60 olympicfeet
7665 olympicamma olympiccord
7666 olympicplethron 100 olympicfeet
7667 olympicstadion 600 olympicfeet
7668
7669 # Greek capacity measure
7670
7671 greekkotyle 270 ml # This approximate value is obtained
7672 xestes 2 greekkotyle # from two earthenware vessels that
7673 khous 12 greekkotyle # were reconstructed from fragments.
7674 metretes 12 khous # The kotyle is a day's corn ration
7675 choinix 4 greekkotyle # for one man.
7676 hekteos 8 choinix
7677 medimnos 6 hekteos
7678
7679 # Greek weight. Two weight standards were used, an Aegina standard based
7680 # on the Beqa shekel and an Athens (attic) standard.
7681
7682 aeginastater 192 grain # Varies up to 199 grain
7683 aeginadrachmae 1|2 aeginastater
7684 aeginaobol 1|6 aeginadrachmae
7685 aeginamina 50 aeginastaters
7686 aeginatalent 60 aeginamina # Supposedly the mass of a cubic foot
7687 # of water (whichever foot was in use)
7688
7689 atticstater 135 grain # Varies 134-138 grain
7690 atticdrachmae 1|2 atticstater
7691 atticobol 1|6 atticdrachmae
7692 atticmina 50 atticstaters
7693 attictalent 60 atticmina # Supposedly the mass of a cubic foot
7694 # of water (whichever foot was in use)
7695
7696 # "Northern" cubit and foot. This was used by the pre-Aryan civilization in
7697 # the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China,
7698 # central and Western Europe until modern times when it was displaced by
7699 # the metric system.
7700
7701 northerncubit 26.6 in # plus/minus .2 in
7702 northernfoot 1|2 northerncubit
7703
7704 sumeriancubit 495 mm
7705 kus sumeriancubit
7706 sumerianfoot 2|3 sumeriancubit
7707
7708 assyriancubit 21.6 in
7709 assyrianfoot 1|2 assyriancubit
7710 assyrianpalm 1|3 assyrianfoot
7711 assyriansusi 1|20 assyrianpalm
7712 susi assyriansusi
7713 persianroyalcubit 7 assyrianpalm
7714
7715
7716 # Arabic measures. The arabic standards were meticulously kept. Glass weights
7717 # accurate to .2 grains were made during AD 714-900.
7718
7719 hashimicubit 25.56 in # Standard of linear measure used
7720 # in Persian dominions of the Arabic
7721 # empire 7-8th cent. Is equal to two
7722 # French feet.
7723
7724 blackcubit 21.28 in
7725 arabicfeet 1|2 blackcubit
7726 arabicfoot arabicfeet
7727 arabicinch 1|12 arabicfoot
7728 arabicmile 4000 blackcubit
7729
7730 silverdirhem 45 grain # The weights were derived from these two
7731 tradedirhem 48 grain # units with two identically named systems
7732 # used for silver and used for trade purposes
7733
7734 silverkirat 1|16 silverdirhem
7735 silverwukiyeh 10 silverdirhem
7736 silverrotl 12 silverwukiyeh
7737 arabicsilverpound silverrotl
7738
7739 tradekirat 1|16 tradedirhem
7740 tradewukiyeh 10 tradedirhem
7741 traderotl 12 tradewukiyeh
7742 arabictradepound traderotl
7743
7744 # Miscellaneous ancient units
7745
7746 parasang 3.5 mile # Persian unit of length usually thought
7747 # to be between 3 and 3.5 miles
7748 biblicalcubit 21.8 in
7749 hebrewcubit 17.58 in
7750 li 10|27.8 mile # Chinese unit of length
7751 # 100 li is considered a day's march
7752 liang 11|3 oz # Chinese weight unit
7753
7754
7755 # Medieval time units. According to the OED, these appear in Du Cange
7756 # by Papias.
7757
7758 timepoint 1|5 hour # also given as 1|4
7759 timeminute 1|10 hour
7760 timeostent 1|60 hour
7761 timeounce 1|8 timeostent
7762 timeatom 1|47 timeounce
7763
7764 # Given in [15], these subdivisions of the grain were supposedly used
7765 # by jewelers. The mite may have been used but the blanc could not
7766 # have been accurately measured.
7767
7768 mite 1|20 grain
7769 droit 1|24 mite
7770 periot 1|20 droit
7771 blanc 1|24 periot
7772
7773 #
7774 # Localization
7775 #
7776
7777 !var UNITS_ENGLISH US
7778 hundredweight ushundredweight
7779 ton uston
7780 scruple apscruple
7781 fluidounce usfluidounce
7782 gallon usgallon
7783 bushel usbushel
7784 quarter quarterweight
7785 cup uscup
7786 tablespoon ustablespoon
7787 teaspoon usteaspoon
7788 dollar US$
7789 cent $ 0.01
7790 penny cent
7791 minim minimvolume
7792 pony ponyvolume
7793 grand usgrand
7794 firkin usfirkin
7795 hogshead ushogshead
7796 !endvar
7797
7798 !var UNITS_ENGLISH GB
7799 hundredweight brhundredweight
7800 ton brton
7801 scruple brscruple
7802 fluidounce brfluidounce
7803 gallon brgallon
7804 bushel brbushel
7805 quarter brquarter
7806 chaldron brchaldron
7807 cup brcup
7808 teacup brteacup
7809 tablespoon brtablespoon
7810 teaspoon brteaspoon
7811 dollar US$
7812 cent $ 0.01
7813 penny brpenny
7814 minim minimnote
7815 pony brpony
7816 grand brgrand
7817 firkin brfirkin
7818 hogshead brhogshead
7819 !endvar
7820
7821 !varnot UNITS_ENGLISH GB US
7822 !message Unknown value for environment variable UNITS_ENGLISH. Should be GB or US.
7823 !endvar
7824
7825
7826 !utf8
7827 ⅛- 1|8
7828 ¼- 1|4
7829 ⅜- 3|8
7830 ½- 1|2
7831 ⅝- 5|8
7832 ¾- 3|4
7833 ⅞- 7|8
7834 ⅙- 1|6
7835 ⅓- 1|3
7836 ⅔- 2|3
7837 ⅚- 5|6
7838 ⅕- 1|5
7839 ⅖- 2|5
7840 ⅗- 3|5
7841 ⅘- 4|5
7842 # U+2150- 1|7 For some reason these characters are getting
7843 # U+2151- 1|9 flagged as invalid UTF8.
7844 # U+2152- 1|10
7845 #⅐- 1|7 # fails under MacOS
7846 #⅑- 1|9 # fails under MacOS
7847 #⅒- 1|10 # fails under MacOS
7848 ℯ exp(1) # U+212F, base of natural log
7849 µ- micro # micro sign U+00B5
7850 μ- micro # small mu U+03BC
7851 ångström angstrom
7852 Å angstrom # angstrom symbol U+212B
7853 Å angstrom # A with ring U+00C5
7854 röntgen roentgen
7855 °C degC
7856 °F degF
7857 °K K # °K is incorrect notation
7858 °R degR
7859 ° degree
7860 ℃ degC
7861 ℉ degF
7862 K K # Kelvin symbol, U+212A
7863 ℓ liter # unofficial abbreviation used in some places
7864 Ω ohm # Ohm symbol U+2126
7865 Ω ohm # Greek capital omega U+03A9
7866 ℧ mho
7867 ʒ dram # U+0292
7868 ℈ scruple
7869 ℥ ounce
7870 ℔ lb
7871 ℎ h
7872 ℏ hbar
7873 ‰ 1|1000
7874 ‱ 1|10000
7875 ′ ' # U+2032
7876 ″ " # U+2033
7877
7878 #
7879 # Unicode currency symbols
7880 #
7881
7882 ¢ cent
7883 £ britainpound
7884 ¥ japanyen
7885 € euro
7886 ₩ southkoreawon
7887 ₪ israelnewshekel
7888 ₤ lira
7889 # ₺ turkeylira # fails under MacOS
7890 ₨ rupee # unofficial legacy rupee sign
7891 # ₹ indiarupee # official rupee sign # MacOS fail
7892 #؋ afghanafghani # fails under MacOS
7893 ฿ thailandbaht
7894 ₡ elsalvadorcolon # Also costaricacolon
7895 ₣ francefranc
7896 ₦ nigerianaira
7897 ₧ spainpeseta
7898 ₫ vietnamdong
7899 ₭ laokip
7900 ₮ mongoliatugrik
7901 ₯ greecedrachma
7902 ₱ philippinepeso
7903 # ₲ paraguayguarani # fails under MacOS
7904 #₴ ukrainehryvnia # fails under MacOS
7905 #₵ ghanacedi # fails under MacOS
7906 #₸ kazakhstantenge # fails under MacOS
7907 #₼ azerbaijanmanat # fails under MacOS
7908 #₽ russiaruble # fails under MacOS
7909 #₾ georgialari # fails under MacOS
7910 ﷼ iranrial
7911 ﹩ $
7912 ￠ ¢
7913 ￡ £
7914 ￥ ¥
7915 ￦ ₩
7916
7917 #
7918 # Square Unicode symbols starting at U+3371
7919 #
7920
7921 ㍱ hPa
7922 ㍲ da
7923 ㍳ au
7924 ㍴ bar
7925 # ㍵ oV???
7926 ㍶ pc
7927 #㍷ dm invalid on Mac
7928 #㍸ dm^2 invalid on Mac
7929 #㍹ dm^3 invalid on Mac
7930 ㎀ pA
7931 ㎁ nA
7932 ㎂ µA
7933 ㎃ mA
7934 ㎄ kA
7935 ㎅ kB
7936 ㎆ MB
7937 ㎇ GB
7938 ㎈ cal
7939 ㎉ kcal
7940 ㎊ pF
7941 ㎋ nF
7942 ㎌ µF
7943 ㎍ µg
7944 ㎎ mg
7945 ㎏ kg
7946 ㎐ Hz
7947 ㎑ kHz
7948 ㎒ MHz
7949 ㎓ GHz
7950 ㎔ THz
7951 ㎕ µL
7952 ㎖ mL
7953 ㎗ dL
7954 ㎘ kL
7955 ㎙ fm
7956 ㎚ nm
7957 ㎛ µm
7958 ㎜ mm
7959 ㎝ cm
7960 ㎞ km
7961 ㎟ mm^2
7962 ㎠ cm^2
7963 ㎡ m^2
7964 ㎢ km^2
7965 ㎣ mm^3
7966 ㎤ cm^3
7967 ㎥ m^3
7968 ㎦ km^3
7969 ㎧ m/s
7970 ㎨ m/s^2
7971 ㎩ Pa
7972 ㎪ kPa
7973 ㎫ MPa
7974 ㎬ GPa
7975 ㎭ rad
7976 ㎮ rad/s
7977 ㎯ rad/s^2
7978 ㎰ ps
7979 ㎱ ns
7980 ㎲ µs
7981 ㎳ ms
7982 ㎴ pV
7983 ㎵ nV
7984 ㎶ µV
7985 ㎷ mV
7986 ㎸ kV
7987 ㎹ MV
7988 ㎺ pW
7989 ㎻ nW
7990 ㎼ µW
7991 ㎽ mW
7992 ㎾ kW
7993 ㎿ MW
7994 ㏀ kΩ
7995 ㏁ MΩ
7996 ㏃ Bq
7997 ㏄ cc
7998 ㏅ cd
7999 ㏆ C/kg
8000 ㏈() dB
8001 ㏉ Gy
8002 ㏊ ha
8003 # ㏋ HP??
8004 ㏌ in
8005 # ㏍ KK??
8006 # ㏎ KM???
8007 ㏏ kt
8008 ㏐ lm
8009 # ㏑ ln
8010 # ㏒ log
8011 ㏓ lx
8012 ㏔ mb
8013 ㏕ mil
8014 ㏖ mol
8015 ㏗() pH
8016 ㏙ ppm
8017 # ㏚ PR???
8018 ㏛ sr
8019 ㏜ Sv
8020 ㏝ Wb
8021 #㏞ V/m Invalid on Mac
8022 #㏟ A/m Invalid on Mac
8023 #㏿ gal Invalid on Mac
8024
8025 !endutf8
8026
8027 ############################################################################
8028 #
8029 # Unit list aliases
8030 #
8031 # These provide a shorthand for conversions to unit lists.
8032 #
8033 ############################################################################
8034
8035 !unitlist hms hr;min;sec
8036 !unitlist time year;day;hr;min;sec
8037 !unitlist dms deg;arcmin;arcsec
8038 !unitlist ftin ft;in;1|8 in
8039 !unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in
8040 !unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
8041 tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
8042
8043 ############################################################################
8044 #
8045 # The following units were in the Unix units database but do not appear in
8046 # this file:
8047 #
8048 # wey used for cheese, salt and other goods. Measured mass or
8049 # waymass volume depending on what was measured and where the measuring
8050 # took place. A wey of cheese ranged from 200 to 324 pounds.
8051 #
8052 # sack No precise definition
8053 #
8054 # spindle The length depends on the type of yarn
8055 #
8056 # block Defined variously on different computer systems
8057 #
8058 # erlang A unit of telephone traffic defined variously.
8059 # Omitted because there are no other units for this
8060 # dimension. Is this true? What about CCS = 1/36 erlang?
8061 # Erlang is supposed to be dimensionless. One erlang means
8062 # a single channel occupied for one hour.
8063 #
8064 ############################################################################
8065