BIPM units (BIPM.ini)

The table below lists the contents of the BIPM.ini file. It implements the definitions from [BIPM2006], including the System International (SI) units and some non-SI units.

The definitions depend on the following items:

  • Classes: ScalarUnit
  • Functions: exp(), log(), and log10()
  • Mathematical constants: pi
  • Base constants: R_inf, c, k_J, R_K, k_F, and R
  • Derived units: cyc
Symbol Expression Prefixable Name & notes
—— Mathematical relations ——
rad cyc/(2*pi) True radian
—— Empirical relations ——
m 10973731.568539*cyc/R_inf True metre
s 299792458*m/c True second
Wb 483597.870e9/k_J True weber
S 25812.8074434/(R_K*cyc) True siemens (aka mho)
mol 96485.3365*Wb*cyc*S/k_F True mole
K 8.3144621*(Wb*cyc)**2*S/(s*mol*R) True kelvin
—— Units decoupled from the base constants ——
cd ScalarUnit(1., 'J') True candela (decoupled by the luminosity function)
—— Remaining SI base units (BIPM2006, Table 1) and intermediate units ——
Hz cyc/s True hertz
V Wb*Hz True volt
A V*S True ampere
C A*s True coulomb
J V*C True joule
Gy m**2/s**2 True gray
kg J/Gy False kilogram
g kg/1000 True gram (included for prefixes other than k)
—— Remaining coherent derived SI units (BIPM2006, Table 3) ——
sr rad**2 True steradian
lm cd*sr True lumen
W J/s True watt
N J/m True newton
Pa N/m**2 True pascal
T Wb/m**2 True tesla
lx lm/m**2 True lux
F s*S True farad
ohm S**-1 True ohm
H s/S True henry
kat mol/s True katal
Sv Gy True sievert
Bq s**-1 True becquerel
degC (lambda n: (n + 273.15)*K, lambda T: T/K - 273.15) True degree Celsius
—— Non-SI units accepted for use with SI (BIPM2006, Table 6) ——
min 60*s False minute
hr 60*min False hour
d 24*hr False day
deg cyc/360 False degree (aka degree of arc, arc degree, or arcdegree)
arcmin deg/60 False arcminute
arcsec arcmin/60 False arcsecond
ha hm**2 False hectare
L dm**3 True litre
t Mg False tonne
—— Other non-SI units (BIPM2006, Table 8) ——
g_0 9.80665*m/s**2   standard gravity [1], [2]
cc cm**3 False cubic centimetre [1]
Hg 13.5951*g*g_0/cc   force per volume of mercury under standard gravity [1], [2]
mmHg mm*Hg False millimetre of mercury
bar 100*kPa True bar
b 100*fm**2 False barn
angstrom 0.1*nm False angstrom
nmi 1852*m False nautical mile
kn nmi/hr False knot
Np (exp, log) False neper (in terms of amplitude ratio, not power ratio)
B (lambda n: 10**n, log10) True bel (in terms of power ratio, not amplitude ratio)
dB dB False decibel (explicitly included with prefix)
—— Non-SI units associated with CGS and CGS-Gaussian system of units (BIPM2006, Table 9) ——
cm cm False centimetre [3]
Gal cm/s**2 True gal (unit of acceleration)
dyn g*Gal True dyne (unit of force)
erg dyn*cm True erg (unit of energy)
Ba dyn/cm**2 True barye (aka barad, barrie, bary, baryd, baryed, or barie; unit of pressure) [2]
P Ba*s True poise (unit of dynamic viscosity)
St cm**2/s True stokes (aka stoke; unit of kinematic viscosity)
sb cd/cm**2 True stilb (unit of luminance)
ph sb*sr True phot (unit of illuminance)
abA daA True abampere (aka decaampere or Biot (Bi)) [2]
Mx erg/(abA*cyc) True maxwell (unit of magnetic flux)
Gs Mx/cm**2 True gauss (unit of magnetic flux density)
pole 4*pi*Mx False unit pole [2]
Oe dyn/pole True oersted (unit of the auxiliary magnetic field)

Since angle is explicit, some definitions are different than in [BIPM2006] and [NIST2014]:

  • m ≈ 10973732 cyc R_inf-1 (i.e., R_inf ≈ 10973732 cyc m-1) [4]
  • S ≈ 25813 R_K-1 cyc-1 (i.e., R_K ≈ 25813 ohm cyc-1) [4]
  • Hz = cyc s-1 [5]
  • V = Wb Hz (i.e., Wb = V s cyc-1) [5]
  • H = ohm s = V s A-1 (H ≠ Wb A-1)

Note that frequency can be expressed in Hz or rad s-1 but not s-1. Torque can be expressed in N m rad-1 or J rad-1 but not N m or J. Also note that the steradian (sr), a unit of solid angle, has dimension A2.

deg, arcmin, and arcsec are used as the symbols for the degree, arcminute, and arcsecond since the symbols in Table 6 of [BIPM2006] are not valid Python names. hr is used as the symbol for the hour (instead of h per [BIPM2006]) since h is used for the Planck constant. nmi is used as the symbol for nautical mile (instead of M per [BIPM2006]) since M is used for the unit molar. Gs is used as the symbol for the gauss mile (instead of G per [BIPM2006]) since G is used as the `gravitational constant`_.

In general, prefixes are not included because they are added upon access. However, [BIPM2006] (and BIPM.ini) includes two units with explicit prefixes: kg and dB.

References

[BIPM2006](1, 2, 3, 4, 5, 6, 7, 8, 9) International Bureau of Weights and Measures (BIPM), “The International System of Units (SI),” 8th ed., 2006.
[NIST2014](1, 2) National Institute of Science and Technology, “Fundamental Physical Constants: Complete Listing,” http://physics.nist.gov/constants, accessed 2014.

Footnotes

[1](1, 2, 3) a constant (not a unit), but useful here
[2](1, 2, 3, 4, 5) not defined in [BIPM2006], but useful here
[3]not included in Table 9, but explicitly provided since this is a CGS base unit
[4](1, 2) Traditionally, angle is dropped [NIST2014].
[5](1, 2) Angle is dropped in [BIPM2006].