Other constants and units (other.ini)

The table below lists the contents of the other.ini file. It establishes some units besides the SI and non-SI units from [BIPM2006].

The definitions below depend on the following items:

  • Mathematical constants: pi
  • Base constants: c
  • SI and non-SI units from [BIPM2006]
  • Other constants and units: g_0 and cyc
Symbol Expression Prefixable Name & notes
—— Time ——
y 365.25*d False Julian year
—— Length ——
ly c*y True light year
au 149597870700*m False astronomical unit
pc au*648e3/pi False parsec
inch 2.54*cm False inch
ft 12*inch False foot
yd 3*ft False yard
mi 1760*yd False mile
pica inch/6 False pica
point pica/12 False point
—— Mass ——
u g/(N_A*mol) True unified atomic mass unit (aka dalton (Da))
oz 28.349523125*g False avoirdupois ounce
lb 16*oz False pound
ton 2e3*lb False short ton
—— Force ——
lbf lb*g_0 False pound force
kip 1000*lbf False kip
—— Pressure ——
atm 101325*Pa False atmosphere
Pag (lambda n: n*Pa + atm, lambda p: (p - atm)/Pa) True pascal, gauge
psi lbf/inch**2 False pounds per square inch
psig (lambda n: n*psi + atm, lambda p: (p - atm)/psi) False pounds per square inch, gauge
Torr atm/760 False torr
—— Energy ——
BTU 1055.05585262*J True British thermal unit, based on International Steam Table calorie [IT1956]
cal 4.184*J True small calorie (thermochemical)
Cal kcal True large calorie (aka food calorie)
Wh W*hr True watt hour
eV e*V True electron volt
—— Power ——
hp 550*ft*lbf/s False mechanical horsepower
—— Area ——
ac mi**2/640 False acre
—— Volume ——
gal 231*inch**3 False US gallon
qt gal/4 False US quart
pt qt/2 False US pint
cup pt/2 False US cup
fluid_oz cup/8 False US fluid ounce
bbl 42*gal False oil barrel
—— Angle ——
grad cyc/400 False gradian
sign rad/6 False  
sextant cyc/6 False  
quadrant cyc/4 False  
—— Solid angle ——
sp 4*pi*sr False spat
—— Velocity ——
mph mi/hr False miles per hour
kph km/hr False kilometres per hour
—— Frequency/Angular velocity ——
rpm cyc/min False revolution per minute
—— Temperature ——
degR K*5/9 False degree Rankine
degF (lambda n: (n + 459.67)*degR, lambda T: T/degR - 459.67) False degree Fahrenheit
—— Dimensionless ——
pct 0.01 False percent (%)
ppm 1e-6 False parts per million
ppb 1e-9 False parts per billion
ppt 1e-12 False parts per trillion
ppq 1e-15 False parts per quadrillion
—— Remaining EMU and Gaussian units (besides those in [BIPM2006]) ——
abC abA*s True abcoloumb
abV erg/abC True abvolt
abF abC/abV True abfarad
abohm s/abF True abohm
abH abohm*s True abhenry
—— Remaining ESU units (besides those in [BIPM2006]) ——
statC sqrt(g*cc)/s True statcoulomb (aka franklin (Fr) or electrostatic unit (esu) of charge)
statA statC/s True statampere
statV erg/statC True statvolt
statWb statV/Hz True statweber
statT statWb/cm**2 True stattesla
—— Constants related to Ampere’s force law ——
k_A dyn/abA**2   Ampere constant (aka magnetic force constant)
k_C k_A*c**2   Coulomb constant (aka electric force constant or electrostatic constant)
epsilon_0 1/(k_C*(4*pi if rational else 1))   electric constant (aka vacuum permittivity or permittivity of free space)
mu_0 1/(epsilon_0*cyc**2*c**2)   magnetic constant (aka vacuum permeability or permeability of free space)
Z_0 2*k_A*c/rad   characteristic impedance of vacuum
alpha k_A*c/R_K   fine structure constant
a_0 alpha/(2*R_inf)   Bohr radius (aka Hartree length)
lambda_e alpha*a_0/sr   electron Compton wavelength
kappa lambda_e*c/2   quantum of circulation
m_e Phi_0/kappa   electron rest mass per elementary charge
r_e k_A/m_e   classical electron radius per elementary charge (aka Lorentz radius or Thomson scattering length)
mu_B kappa*e*sp/2   Bohr magnetron
M_e m_e*e   mass of an electron (aka Hartree mass or natural unit of mass)
t_H a_0*sqrt(M_e/Ha)   Hartree time
l_n h*rad/(M_e*c)   natural unit of length
t_n l_n/c   natural unit of time
—— Misc. units and constants ——
AT A*cyc False ampere-turn
D cdyn/atm True darcy
M mol/L True molar

Since angle is explicit, it appears in several of the constants and units:

  • mu_0 ≈ 4 pi 10-7 H m-1 cyc-2 [1]
  • Z_0 ≈ 376.730 ohm cyc-1 [1]
  • kappa ≈ 3.637×10-4 m2 s-1 cyc-1 [1]
  • rpm = cyc min-1
  • sp = 4 pi sr
  • AT = A cyc
  • Oe = 5 kA rad m-1 = 0.25 kA cyc pi-1 m-1 = 250 AT pi-1 m-1
  • Mx = erg abA-1 cyc-1 = 10-8 V Hz-1 [2]
  • Gs = Mx cm2 = 10-4 Wb m-2 = 10-4 V Hz-1 m-2 [2]
  • statWb = statV Hz-1 [2]
  • statT = statWb cm2 = statV Hz-1 cm2 [2]

Note that torque can be expressed in lbf ft rad-1 but not lbf ft.

References

[BIPM2006](1, 2, 3, 4) International Bureau of Weights and Measures (BIPM), “The International System of Units (SI),” 8th ed., 2006.
[IT1956]Fifth International Conference on the Properties of Steam, London, July 1956.
[NIST2014]National Institute of Science and Technology, “Fundamental Physical Constants: Complete Listing,” http://physics.nist.gov/constants, accessed 2014.

Footnotes

[1](1, 2, 3) Traditionally, angle is dropped [NIST2014].
[2](1, 2, 3, 4) ... where Hz has dimension of angle per time.