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definitions.units.patched
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#
# This file is the units database for use with GNU units, a units conversion
# program by Adrian Mariano adrianm@gnu.org
#
# October 2018 Version 2.44
#
# Copyright (C) 1996-2002, 2004-2018
# Free Software Foundation, Inc
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor,
# Boston, MA 02110-1301 USA
#
############################################################################
#
# Improvements and corrections are welcome.
#
# Fundamental constants in this file are the 2014 CODATA recommended values.
#
# Most units data was drawn from
# 1. NIST Special Publication 811, Guide for the
# Use of the International System of Units (SI).
# Barry N. Taylor. 1995
# 2. CRC Handbook of Chemistry and Physics 70th edition
# 3. Oxford English Dictionary
# 4. Websters New Universal Unabridged Dictionary
# 5. Units of Measure by Stephen Dresner
# 6. A Dictionary of English Weights and Measures by Ronald Zupko
# 7. British Weights and Measures by Ronald Zupko
# 8. Realm of Measure by Isaac Asimov
# 9. United States standards of weights and measures, their
# creation and creators by Arthur H. Frazier.
# 10. French weights and measures before the Revolution: a
# dictionary of provincial and local units by Ronald Zupko
# 11. Weights and Measures: their ancient origins and their
# development in Great Britain up to AD 1855 by FG Skinner
# 12. The World of Measurements by H. Arthur Klein
# 13. For Good Measure by William Johnstone
# 14. NTC's Encyclopedia of International Weights and Measures
# by William Johnstone
# 15. Sizes by John Lord
# 16. Sizesaurus by Stephen Strauss
# 17. CODATA Recommended Values of Physical Constants available at
# http://physics.nist.gov/cuu/Constants/index.html
# 18. How Many? A Dictionary of Units of Measurement. Available at
# http://www.unc.edu/~rowlett/units/index.html
# 19. Numericana. http://www.numericana.com
# 20. UK history of measurement
# http://www.ukmetrication.com/history.htm
# 21. NIST Handbook 44, Specifications, Tolerances, and
# Other Technical Requirements for Weighing and Measuring
# Devices. 2011
# 22. NIST Special Publication 447, Weights and Measures Standards
# of the the United States: a brief history. Lewis V. Judson.
# 1963; rev. 1976
# 23. CRC Handbook of Chemistry and Physics, 96th edition
# 24. Dictionary of Scientific Units, 6th ed. H.G. Jerrard and D.B.
# McNeill. 1992
#
# Thanks to Jeff Conrad for assistance in ferreting out unit definitions.
#
###########################################################################
#
# If units you use are missing or defined incorrectly, please contact me.
# If your country's local units are missing and you are willing to supply
# them, please send me a list.
#
###########################################################################
###########################################################################
#
# Brief Philosophy of this file
#
# Most unit definitions are made in terms of integers or simple fractions of
# other definitions. The typical exceptions are when converting between two
# different unit systems, or the values of measured physical constants. In
# this file definitions are given in the most natural and revealing way in
# terms of integer factors.
#
# If you make changes be sure to run 'units --check' to check your work.
#
# The file is USA-centric, but there is some modest effort to support other
# countries. This file is now coded in UTF-8. To support environments where
# UTF-8 is not available, definitions that require this character set are
# wrapped in !utf8 directives.
#
# When a unit name is used in different countries with the different meanings
# the system should be as follows:
#
# Suppose countries ABC and XYZ both use the "foo". Then globally define
#
# ABCfoo <some value>
# XYZfoo <different value>
#
# Then, using the !locale directive, define the "foo" appropriately for each of
# the two countries with a definition like
#
# !locale ABC
# foo ABCfoo
# !endlocale
#
###########################################################################
!locale en_US
! set UNITS_ENGLISH US
!endlocale
!locale en_GB
! set UNITS_ENGLISH GB
!endlocale
!set UNITS_ENGLISH US # Default setting for English units
!set UNITS_SYSTEM default # Set a default value
!varnot UNITS_SYSTEM si emu esu gaussian gauss default
!message Unknown unit system given with -u or UNITS_SYSTEM environment variable
!message Valid systems: si, emu, esu, gauss[ian]
!message Using SI
!prompt (SI)
!endvar
!var UNITS_SYSTEM si
!message SI units selected
!prompt (SI)
!endvar
###########################################################################
# #
# Primitive units. Any unit defined to contain a '!' character is a #
# primitive unit which will not be reduced any further. All units should #
# reduce to primitive units. #
# #
###########################################################################
#
# SI units
#
kg ! # Mass of the international prototype
kilogram kg
s ! # Duration of 9192631770 periods of the radiation
second s # corresponding to the transition between the two hyperfine
# levels of the ground state of the cesium-133 atom
m ! # Length of the path traveled by light in a vacuum
meter m # during 1|299792458 seconds. Originally meant to be
# 1e-7 of the length along a meridian from the equator
# to a pole.
A ! # The current which produces a force of 2e-7 N/m between two
ampere A # infinitely long wires that are 1 meter apart
amp ampere
cd ! # Luminous intensity in a given direction of a source which
candela cd # emits monochromatic radiation at 540e12 Hz with radiant
# intensity 1|683 W/steradian. (This differs from radiant
# intensity (W/sr) in that it is adjusted for human
# perceptual dependence on wavelength. The frequency of
# 540e12 Hz (yellow) is where human perception is most
# efficient.)
mol ! # The amount of substance of a system which contains as many
mole mol # elementary entities as there are atoms in 0.012 kg of
# carbon 12. The elementary entities must be specified and
# may be atoms, molecules, ions, electrons, or other
# particles or groups of particles. It is understood that
# unbound atoms of carbon 12, at rest and in the ground
# state, are referred to.
K ! # 1|273.16 of the thermodynamic temperature of the triple
kelvin K # point of water
#
# The radian and steradian are defined as dimensionless primitive units.
# The radian is equal to m/m and the steradian to m^2/m^2 so these units are
# dimensionless. Retaining them as named units is useful because it allows
# clarity in expressions and makes the meaning of unit definitions more clear.
# These units will reduce to 1 in conversions but not for sums of units or for
# arguments to functions.
#
radian !dimensionless # The angle subtended at the center of a circle by
# an arc equal in length to the radius of the
# circle
sr !dimensionless # Solid angle which cuts off an area of the surface
steradian sr # of the sphere equal to that of a square with
# sides of length equal to the radius of the
# sphere
#
# Nephelometric Turbidity Units
# A dimensionless unit measuring turbidity
#
NTU !dimensionless
#
# A primitive non-SI unit
#
B !
byte B
bit 1|8 B # Basic unit of information (entropy). The entropy in bits
# of a random variable over a finite alphabet is defined
# to be the sum of -p(i)*log2(p(i)) over the alphabet where
# p(i) is the probability that the random variable takes
# on the value i.
#
# Currency: the primitive unit of currency is defined in currency.units.
# It is usually the US$ or the euro, but it is user selectable.
#
###########################################################################
# #
# Prefixes (longer names must come first) #
# #
###########################################################################
yotta- 1e24 # Greek or Latin octo, "eight"
zetta- 1e21 # Latin septem, "seven"
exa- 1e18 # Greek hex, "six"
peta- 1e15 # Greek pente, "five"
tera- 1e12 # Greek teras, "monster"
giga- 1e9 # Greek gigas, "giant"
mega- 1e6 # Greek megas, "large"
myria- 1e4 # Not an official SI prefix
kilo- 1e3 # Greek chilioi, "thousand"
hecto- 1e2 # Greek hekaton, "hundred"
deca- 1e1 # Greek deka, "ten"
deka- deca
deci- 1e-1 # Latin decimus, "tenth"
centi- 1e-2 # Latin centum, "hundred"
milli- 1e-3 # Latin mille, "thousand"
micro- 1e-6 # Latin micro or Greek mikros, "small"
nano- 1e-9 # Latin nanus or Greek nanos, "dwarf"
pico- 1e-12 # Spanish pico, "a bit"
femto- 1e-15 # Danish-Norwegian femten, "fifteen"
atto- 1e-18 # Danish-Norwegian atten, "eighteen"
zepto- 1e-21 # Latin septem, "seven"
yocto- 1e-24 # Greek or Latin octo, "eight"
quarter- 1|4
semi- 0.5
demi- 0.5
hemi- 0.5
half- 0.5
double- 2
triple- 3
treble- 3
kibi- 2^10 # In response to the convention of illegally
mebi- 2^20 # and confusingly using metric prefixes for
gibi- 2^30 # powers of two, the International
tebi- 2^40 # Electrotechnical Commission aproved these
pebi- 2^50 # binary prefixes for use in 1998. If you
exbi- 2^60 # want to refer to "megabytes" using the
zebi- 2^70
yobi- 2^80
Ki- kibi # binary definition, use these prefixes.
Mi- mebi
Gi- gibi
Ti- tebi
Pi- pebi
Ei- exbi
Zi- zebi
Yi- yobi
Y- yotta
Z- zetta
E- exa
P- peta
T- tera
G- giga
M- mega
k- kilo
h- hecto
da- deka
d- deci
c- centi
m- milli
u- micro # it should be a mu but u is easy to type
mu- micro
n- nano
p- pico
f- femto
a- atto
z- zepto
y- yocto
#
# Names of some numbers
#
one 1
two 2
double 2
couple 2
three 3
triple 3
four 4
quadruple 4
five 5
quintuple 5
six 6
seven 7
eight 8
nine 9
ten 10
eleven 11
twelve 12
thirteen 13
fourteen 14
fifteen 15
sixteen 16
seventeen 17
eighteen 18
nineteen 19
twenty 20
thirty 30
forty 40
fifty 50
sixty 60
seventy 70
eighty 80
ninety 90
hundred 100
thousand 1000
million 1e6
twoscore two score
threescore three score
fourscore four score
fivescore five score
sixscore six score
sevenscore seven score
eightscore eight score
ninescore nine score
tenscore ten score
twelvescore twelve score
# These number terms were described by N. Chuquet and De la Roche in the 16th
# century as being successive powers of a million. These definitions are still
# used in most European countries. The current US definitions for these
# numbers arose in the 17th century and don't make nearly as much sense. These
# numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric
# W. Weisstein.
shortbillion 1e9
shorttrillion 1e12
shortquadrillion 1e15
shortquintillion 1e18
shortsextillion 1e21
shortseptillion 1e24
shortoctillion 1e27
shortnonillion 1e30
shortnoventillion shortnonillion
shortdecillion 1e33
shortundecillion 1e36
shortduodecillion 1e39
shorttredecillion 1e42
shortquattuordecillion 1e45
shortquindecillion 1e48
shortsexdecillion 1e51
shortseptendecillion 1e54
shortoctodecillion 1e57
shortnovemdecillion 1e60
shortvigintillion 1e63
centillion 1e303
googol 1e100
longbillion million^2
longtrillion million^3
longquadrillion million^4
longquintillion million^5
longsextillion million^6
longseptillion million^7
longoctillion million^8
longnonillion million^9
longnoventillion longnonillion
longdecillion million^10
longundecillion million^11
longduodecillion million^12
longtredecillion million^13
longquattuordecillion million^14
longquindecillion million^15
longsexdecillion million^16
longseptdecillion million^17
longoctodecillion million^18
longnovemdecillion million^19
longvigintillion million^20
# These numbers fill the gaps left by the long system above.
milliard 1000 million
billiard 1000 million^2
trilliard 1000 million^3
quadrilliard 1000 million^4
quintilliard 1000 million^5
sextilliard 1000 million^6
septilliard 1000 million^7
octilliard 1000 million^8
nonilliard 1000 million^9
noventilliard nonilliard
decilliard 1000 million^10
# For consistency
longmilliard milliard
longbilliard billiard
longtrilliard trilliard
longquadrilliard quadrilliard
longquintilliard quintilliard
longsextilliard sextilliard
longseptilliard septilliard
longoctilliard octilliard
longnonilliard nonilliard
longnoventilliard noventilliard
longdecilliard decilliard
# The long centillion would be 1e600. The googolplex is another
# familiar large number equal to 10^googol. These numbers give overflows.
#
# The short system prevails in English speaking countries
#
billion shortbillion
trillion shorttrillion
quadrillion shortquadrillion
quintillion shortquintillion
sextillion shortsextillion
septillion shortseptillion
octillion shortoctillion
nonillion shortnonillion
noventillion shortnoventillion
decillion shortdecillion
undecillion shortundecillion
duodecillion shortduodecillion
tredecillion shorttredecillion
quattuordecillion shortquattuordecillion
quindecillion shortquindecillion
sexdecillion shortsexdecillion
septendecillion shortseptendecillion
octodecillion shortoctodecillion
novemdecillion shortnovemdecillion
vigintillion shortvigintillion
#
# Numbers used in India
#
lakh 1e5
crore 1e7
arab 1e9
kharab 1e11
neel 1e13
padm 1e15
shankh 1e17
#############################################################################
# #
# Derived units which can be reduced to the primitive units #
# #
#############################################################################
#
# Named SI derived units (officially accepted)
#
newton kg m / s^2 # force
N newton
pascal N/m^2 # pressure or stress
Pa pascal
joule N m # energy
J joule
watt J/s # power
W watt
coulomb A s # charge
C coulomb
volt W/A # potential difference
V volt
ohm V/A # electrical resistance
siemens A/V # electrical conductance
S siemens
farad C/V # capacitance
F farad
weber V s # magnetic flux
Wb weber
henry V s / A # inductance
H henry
tesla Wb/m^2 # magnetic flux density
T tesla
hertz /s # frequency
Hz hertz
#
# Dimensions. These are here to help with dimensional analysis and
# because they will appear in the list produced by hitting '?' at the
# "You want:" prompt to tell the user the dimension of the unit.
#
LENGTH meter
AREA LENGTH^2
VOLUME LENGTH^3
MASS kilogram
AMOUNT mole
ANGLE radian
SOLID_ANGLE steradian
MONEY US$
FORCE newton
PRESSURE FORCE / AREA
STRESS FORCE / AREA
FREQUENCY hertz
VELOCITY LENGTH / TIME
ACCELERATION VELOCITY / TIME
DENSITY MASS / VOLUME
LINEAR_DENSITY MASS / LENGTH
VISCOSITY FORCE TIME / AREA
KINEMATIC_VISCOSITY VISCOSITY / DENSITY
CURRENT ampere
CHARGE coulomb
CAPACITANCE farad
RESISTANCE ohm
CONDUCTANCE siemens
INDUCTANCE henry
E_FIELD ELECTRIC_POTENTIAL / LENGTH
B_FIELD tesla
# The D and H fields are related to the E and B fields by factors of epsilon
# and mu respectively, so their units can be found by multiplying/dividing by
# the epsilon0 and mu0, but then it is necessary to remove the constant factors
# to get the correct scaling. Defining the units this way allows conversion to
# CGS units to work correctly.
D_FIELD E_FIELD epsilon0 (c/(m/s))^2 4 pi 1e-7
H_FIELD B_FIELD / mu0 * 4 pi 1e-7
ELECTRIC_DIPOLE_MOMENT C m
MAGNETIC_DIPOLE_MOMENT J / T
POLARIZATION ELECTRIC_DIPOLE_MOMENT / VOLUME
MAGNETIZATION MAGNETIC_DIPOLE_MOMENT / VOLUME
ELECTRIC_POTENTIAL volt
VOLTAGE ELECTRIC_POTENTIAL
E_FLUX E_FIELD AREA
D_FLUX D_FIELD AREA
B_FLUX B_FIELD AREA
H_FLUX H_FIELD AREA
#
# units derived easily from SI units
#
gram millikg
gm gram
g gram
tonne 1000 kg
t tonne
metricton tonne
sthene tonne m / s^2
funal sthene
pieze sthene / m^2
quintal 100 kg
bar 1e5 Pa # About 1 atm
b bar
vac millibar
micron micrometer # One millionth of a meter
bicron picometer # One brbillionth of a meter
cc cm^3
are 100 m^2
a are
liter 1000 cc # The liter was defined in 1901 as the
oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at
L liter # the temperature of its maximum density
l liter # under a pressure of 1 atm. This was
# supposed to be 1000 cubic cm, but it
# was discovered that the original
# measurement was off. In 1964, the
# liter was redefined to be exactly 1000
# cubic centimeters.
mho siemens # Inverse of ohm, hence ohm spelled backward
galvat ampere # Named after Luigi Galvani
angstrom 1e-10 m # Convenient for describing molecular sizes
xunit xunit_cu # Used for measuring x-ray wavelengths.
siegbahn xunit # Originally defined to be 1|3029.45 of
xunit_cu 1.00207697e-13 m # the spacing of calcite planes at 18
xunit_mo 1.00209952e-13 m # degC. It was intended to be exactly
# 1e-13 m, but was later found to be
# slightly off. Current usage is with
# reference to common x-ray lines, either
# the K-alpha 1 line of copper or the
# same line of molybdenum.
angstromstar 1.00001495 angstrom # Defined by JA Bearden in 1965
fermi 1e-15 m # Convenient for describing nuclear sizes
# Nuclear radius is from 1 to 10 fermis
barn 1e-28 m^2 # Used to measure cross section for
# particle physics collision, said to
# have originated in the phrase "big as
# a barn".
shed 1e-24 barn # Defined to be a smaller companion to the
# barn, but it's too small to be of
# much use.
brewster micron^2/N # measures stress-optical coef
diopter /m # measures reciprocal of lens focal length
fresnel 1e12 Hz # occasionally used in spectroscopy
shake 1e-8 sec
svedberg 1e-13 s # Used for measuring the sedimentation
# coefficient for centrifuging.
gamma microgram # Also used for 1e-9 tesla
lambda microliter
spat 1e12 m # Rarely used for astronomical measurements
preece 1e13 ohm m # resistivity
planck J s # action of one joule over one second
sturgeon /henry # magnetic reluctance
daraf 1/farad # elastance (farad spelled backwards)
leo 10 m/s^2
poiseuille N s / m^2 # viscosity
mayer J/g K # specific heat
mired / microK # reciprocal color temperature. The name
# abbreviates micro reciprocal degree.
crocodile megavolt # used informally in UK physics labs
metricounce 25 g
mounce metricounce
finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light
# with wavelength 296.7 nm.
fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure
# the energy incident on the receiving
# body across a specified frequency
# bandwidth. [12]
jansky fluxunit # K. G. Jansky identified radio waves coming
Jy jansky # from outer space in 1931.
flick W / cm^2 sr micrometer # Spectral radiance or irradiance
pfu / cm^2 sr s # particle flux unit -- Used to measure
# rate at which particles are received by
# a spacecraft as particles per solid
# angle per detector area per second. [18]
pyron cal_IT / cm^2 min # Measures heat flow from solar radiation,
# from Greek work "pyr" for fire.
katal mol/sec # Measure of the amount of a catalyst. One
kat katal # katal of catalyst enables the reaction
# to consume or produce on mol/sec.
solarluminosity 382.8e24 W # A common yardstick for comparing the
# output of different stars.
# http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
# at mean earth-sun distance
solarirradiance solarluminosity / (4 pi sundist^2)
solarconstant solarirradiance
TSI solarirradiance # total solar irradiance
#
# time
#
sec s
minute 60 s
min minute
hour 60 min
h hour
hr hour
day 24 hr
d day
da day
week 7 day
wk week
sennight 7 day
fortnight 14 day
blink 1e-5 day # Actual human blink takes 1|3 second
ce 1e-2 day
cron 1e6 years
watch 4 hours # time a sentry stands watch or a ship's
# crew is on duty.
bell 1|8 watch # Bell would be sounded every 30 minutes.
# French Revolutionary Time or Decimal Time. It was Proposed during
# the French Revolution. A few clocks were made, but it never caught
# on. In 1998 Swatch defined a time measurement called ".beat" and
# sold some watches that displayed time in this unit.
decimalhour 1|10 day
decimalminute 1|100 decimalhour
decimalsecond 1|100 decimalminute
beat decimalminute # Swatch Internet Time
#
# angular measure
#
circle 2 pi radian
degree 1|360 circle
deg degree
arcdeg degree
arcmin 1|60 degree
arcminute arcmin
' arcmin
arcsec 1|60 arcmin
arcsecond arcsec
" arcsec
'' "
rightangle 90 degrees
quadrant 1|4 circle
quintant 1|5 circle
sextant 1|6 circle
sign 1|12 circle # Angular extent of one sign of the zodiac
turn circle
revolution turn
rev turn
pulsatance radian / sec
gon 1|100 rightangle # measure of grade
grade gon
centesimalminute 1|100 grade
centesimalsecond 1|100 centesimalminute
milangle 1|6400 circle # Official NIST definition.
# Another choice is 1e-3 radian.
pointangle 1|32 circle # Used for reporting compass readings
centrad 0.01 radian # Used for angular deviation of light
# through a prism.
mas milliarcsec # Used by astronomers
seclongitude circle (seconds/day) # Astronomers measure longitude
# (which they call right ascension) in
# time units by dividing the equator into
# 24 hours instead of 360 degrees.
#
# Some geometric formulas
#
circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \
cuberoot(spherevolume/4|3 pi)
spherevol() spherevolume
square(x) range=[0,) x^2 ; sqrt(square)
#
# Solid angle measure
#
sphere 4 pi sr
squaredegree 1|180^2 pi^2 sr
squareminute 1|60^2 squaredegree
squaresecond 1|60^2 squareminute
squarearcmin squareminute
squarearcsec squaresecond
sphericalrightangle 0.5 pi sr
octant 0.5 pi sr
#
# Concentration measures
#
percent 0.01
% percent
mill 0.001 # Originally established by Congress in 1791
# as a unit of money equal to 0.001 dollars,
# it has come to refer to 0.001 in general.
# Used by some towns to set their property
# tax rate, and written with a symbol similar
# to the % symbol but with two 0's in the
# denominator. [18]
proof 1|200 # Alcohol content measured by volume at
# 60 degrees Fahrenheit. This is a USA
# measure. In Europe proof=percent.
ppm 1e-6
partspermillion ppm
ppb 1e-9
partsperbillion ppb # USA billion
ppt 1e-12
partspertrillion ppt # USA trillion
karat 1|24 # measure of gold purity
caratgold karat
gammil mg/l
basispoint 0.01 % # Used in finance
fine 1|1000 # Measure of gold purity
# The pH scale is used to measure the concentration of hydronium (H3O+) ions in
# a solution. A neutral solution has a pH of 7 as a result of dissociated
# water molecules.
pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol))
#
# Temperature
#
# Two types of units are defined: units for converting temperature differences
# and functions for converting absolute temperatures. Conversions for
# differences start with "deg" and conversions for absolute temperature start
# with "temp".
#
TEMPERATURE kelvin
TEMPERATURE_DIFFERENCE kelvin
# In 1741 Anders Celsius introduced a temperature scale with water boiling at
# 0 degrees and freezing at 100 degrees at standard pressure. After his death
# the fixed points were reversed and the scale was called the centigrade
# scale. Due to the difficulty of accurately measuring the temperature of
# melting ice at standard pressure, the centigrade scale was replaced in 1954
# by the Celsius scale which is defined by subtracting 273.15 from the
# temperature in Kelvins. This definition differed slightly from the old
# centigrade definition, but the Kelvin scale depends on the triple point of
# water rather than a melting point, so it can be measured accurately.
tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \
x K + stdtemp ; (tempC +(-stdtemp))/K
tempcelsius() tempC
degcelsius K
degC K
# Fahrenheit defined his temperature scale by setting 0 to the coldest
# temperature he could produce in his lab with a salt water solution and by
# setting 96 degrees to body heat. In Fahrenheit's words:
#
# Placing the thermometer in a mixture of sal ammoniac or sea
# salt, ice, and water a point on the scale will be found which
# is denoted as zero. A second point is obtained if the same
# mixture is used without salt. Denote this position as 30. A
# third point, designated as 96, is obtained if the thermometer
# is placed in the mouth so as to acquire the heat of a healthy
# man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724)
tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
(x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
tempfahrenheit() tempF
degfahrenheit 5|9 * degC
degF 5|9 * degC
degreesrankine degF # The Rankine scale has the
degrankine degreesrankine # Fahrenheit degree, but its zero
degreerankine degF # is at absolute zero.
degR degrankine
tempR degrankine
temprankine degrankine
tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \
x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur
degreaumur 10|8 * degC # The Reaumur scale was used in Europe and
# particularly in France. It is defined
# to be 0 at the freezing point of water
# and 80 at the boiling point. Reaumur
# apparently selected 80 because it is
# divisible by many numbers.
degK K # "Degrees Kelvin" is forbidden usage.
tempK K # For consistency
# Gas mark is implemented below but in a terribly ugly way. There is
# a simple formula, but it requires a conditional which is not
# presently supported.
#
# The formula to convert to degrees Fahrenheit is:
#
# 25 log2(gasmark) + k_f gasmark<=1
# 25 (gasmark-1) + k_f gasmark>=1
#
# k_f = 275
#
gasmark[degR] \
.0625 634.67 \
.125 659.67 \
.25 684.67 \
.5 709.67 \
1 734.67 \
2 759.67 \
3 784.67 \
4 809.67 \
5 834.67 \
6 859.67 \
7 884.67 \
8 909.67 \
9 934.67 \
10 959.67
# Units cannot handle wind chill or heat index because they are two variable
# functions, but they are included here for your edification. Clearly these
# equations are the result of a model fitting operation.
#
# wind chill index (WCI) a measurement of the combined cooling effect of low
# air temperature and wind on the human body. The index was first defined
# by the American Antarctic explorer Paul Siple in 1939. As currently used
# by U.S. meteorologists, the wind chill index is computed from the
# temperature T (in °F) and wind speed V (in mi/hr) using the formula:
# WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4.
# For very low wind speeds, below 4 mi/hr, the WCI is actually higher than
# the air temperature, but for higher wind speeds it is lower than the air
# temperature.
#
# heat index (HI or HX) a measure of the combined effect of heat and
# humidity on the human body. U.S. meteorologists compute the index
# from the temperature T (in °F) and the relative humidity H (as a
# value from 0 to 1).
# HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH
# - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2
# - 0.0199 T^2 H^2.
#
# Physical constants
#
# Basic constants
pi 3.14159265358979323846
π pi
c 2.99792458e8 m/s # speed of light in vacuum (exact)
light c
mu0 4 pi 1e-7 H/m # permeability of vacuum (exact)
epsilon0 1/mu0 c^2 # permittivity of vacuum (exact)
energy c^2 # convert mass to energy
e 1.6021766208e-19 C # electron charge
eV e V # Energy acquired by a particle with charge e
electronvolt eV # when it is accelerated through 1 V
hplanck 4.135667662e-15 eV s # Planck constant
hbar hplanck / 2 pi
spin hbar
G 6.67408e-11 N m^2 / kg^2 # Newtonian gravitational constant
# This is the NIST 2006 value.
# The relative uncertainty on this
# is 1e-4.
coulombconst 1/4 pi epsilon0 # listed as "k" sometimes
# Physico-chemical constants
atomicmassunit 1.660539040e-27 kg # atomic mass unit (defined to be
u atomicmassunit # 1|12 of the mass of carbon 12)
amu atomicmassunit
amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of
# the 3 naturally occuring neutral
# isotopes of oxygen
amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral
# oxygen 16 atom
dalton u # Maybe this should be amu_chem?
avogadro grams/amu mol # size of a mole
N_A avogadro
gasconstant k N_A # molar gas constant
R gasconstant
boltzmann 1.38064852e-23 J/K # Boltzmann constant
k boltzmann
kboltzmann boltzmann
molarvolume mol R stdtemp / atm # Volume occupied by one mole of an
# ideal gas at STP.
loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an
# ideal gas at STP. Loschmidt did
# work similar to Avogadro.
stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a
sigma stefanboltzmann # blackbody at temperature T is
# given by sigma T^4.
wiendisplacement 2.8977729e-3 m K # Wien's Displacement Law gives the
# frequency at which the the Planck
# spectrum has maximum intensity.
# The relation is lambda T = b where
# lambda is wavelength, T is
# temperature and b is the Wien
# displacement. This relation is
# used to determine the temperature
# of stars.
K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until
K_J 483597.8525 GHz/V # recently, laboratories kept Weston cadmium cells as
# a reference, but they could drift. In 1987 the
# CGPM officially recommended the use of the
# Josephson effect as a laboratory representation of
# the volt. The Josephson effect occurs when two
# superconductors are separated by a thin insulating
# layer. A "supercurrent" flows across the insulator
# with a frequency that depends on the potential
# applied across the superconductors. This frequency
# can be very accurately measured. The Josephson
# constant K_J, which is equal to 2e/h, relates the
# measured frequency to the potential. Two values
# given, the conventional (exact) value from 1990 and
# the current CODATA measured value.
R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties.
R_K 25812.8074555 ohm # The old approach involved maintaining resistances
# that were subject to drift. The new standard is
# based on the Hall effect. When a current carrying
# ribbon is placed in a magnetic field, a potential
# difference develops across the ribbon. The ratio
# of the potential difference to the current is
# called the Hall resistance. Klaus von Klitzing
# discovered in 1980 that the Hall resistance varies
# in discrete jumps when the magnetic field is very
# large and the temperature very low. This enables
# accurate realization of the resistance h/e^2 in the
# lab. Two values given, the conventional (exact)
# value from 1990 and the current CODATA measured
# value.
# Various conventional values