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. |
