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]. |
