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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. |