Constants (scipy.constants)

Physical and mathematical constants and units.

Mathematical constants

pi Pi
golden Golden ratio

Physical constants

c speed of light in vacuum
mu_0 the magnetic constant \(\mu_0\)
epsilon_0 the electric constant (vacuum permittivity), \(\epsilon_0\)
h the Planck constant \(h\)
hbar \(\hbar = h/(2\pi)\)
G Newtonian constant of gravitation
g standard acceleration of gravity
e elementary charge
R molar gas constant
alpha fine-structure constant
N_A Avogadro constant
k Boltzmann constant
sigma Stefan-Boltzmann constant \(\sigma\)
Wien Wien displacement law constant
Rydberg Rydberg constant
m_e electron mass
m_p proton mass
m_n neutron mass

Constants database

In addition to the above variables, scipy.constants also contains the 2010 CODATA recommended values [CODATA2010] database containing more physical constants.

value(key) Value in physical_constants indexed by key
unit(key) Unit in physical_constants indexed by key
precision(key) Relative precision in physical_constants indexed by key
find([sub, disp]) Return list of codata.physical_constant keys containing a given string.
ConstantWarning Accessing a constant no longer in current CODATA data set

Dictionary of physical constants, of the format physical_constants[name] = (value, unit, uncertainty).

Available constants:

alpha particle mass 6.64465675e-27 kg
alpha particle mass energy equivalent 5.97191967e-10 J
alpha particle mass energy equivalent in MeV 3727.37924 MeV
alpha particle mass in u 4.00150617913 u
alpha particle molar mass 0.00400150617912 kg mol^-1
alpha particle-electron mass ratio 7294.2995361
alpha particle-proton mass ratio 3.97259968933
Angstrom star 1.00001495e-10 m
atomic mass constant 1.660538921e-27 kg
atomic mass constant energy equivalent 1.492417954e-10 J
atomic mass constant energy equivalent in MeV 931.494061 MeV
atomic mass unit-electron volt relationship 931494061.0 eV
atomic mass unit-hartree relationship 34231776.845 E_h
atomic mass unit-hertz relationship 2.2523427168e+23 Hz
atomic mass unit-inverse meter relationship 7.5130066042e+14 m^-1
atomic mass unit-joule relationship 1.492417954e-10 J
atomic mass unit-kelvin relationship 1.08095408e+13 K
atomic mass unit-kilogram relationship 1.660538921e-27 kg
atomic unit of 1st hyperpolarizability 3.206361449e-53 C^3 m^3 J^-2
atomic unit of 2nd hyperpolarizability 6.23538054e-65 C^4 m^4 J^-3
atomic unit of action 1.054571726e-34 J s
atomic unit of charge 1.602176565e-19 C
atomic unit of charge density 1.081202338e+12 C m^-3
atomic unit of current 0.00662361795 A
atomic unit of electric dipole mom. 8.47835326e-30 C m
atomic unit of electric field 5.14220652e+11 V m^-1
atomic unit of electric field gradient 9.717362e+21 V m^-2
atomic unit of electric polarizability 1.6487772754e-41 C^2 m^2 J^-1
atomic unit of electric potential 27.21138505 V
atomic unit of electric quadrupole mom. 4.486551331e-40 C m^2
atomic unit of energy 4.35974434e-18 J
atomic unit of force 8.23872278e-08 N
atomic unit of length 5.2917721092e-11 m
atomic unit of mag. dipole mom. 1.854801936e-23 J T^-1
atomic unit of mag. flux density 235051.7464 T
atomic unit of magnetizability 7.891036607e-29 J T^-2
atomic unit of mass 9.10938291e-31 kg
atomic unit of 1.99285174e-24 kg m s^-1
atomic unit of permittivity 1.11265005605e-10 F m^-1
atomic unit of time 2.4188843265e-17 s
atomic unit of velocity 2187691.26379 m s^-1
Avogadro constant 6.02214129e+23 mol^-1
Bohr magneton 9.27400968e-24 J T^-1
Bohr magneton in eV/T 5.7883818066e-05 eV T^-1
Bohr magneton in Hz/T 13996245550.0 Hz T^-1
Bohr magneton in inverse meters per tesla 46.6864498 m^-1 T^-1
Bohr magneton in K/T 0.67171388 K T^-1
Bohr radius 5.2917721092e-11 m
Boltzmann constant 1.3806488e-23 J K^-1
Boltzmann constant in eV/K 8.6173324e-05 eV K^-1
Boltzmann constant in Hz/K 20836618000.0 Hz K^-1
Boltzmann constant in inverse meters per kelvin 69.503476 m^-1 K^-1
characteristic impedance of vacuum 376.730313462 ohm
classical electron radius 2.8179403267e-15 m
Compton wavelength 2.4263102389e-12 m
Compton wavelength over 2 pi 3.86159268e-13 m
conductance quantum 7.7480917346e-05 S
conventional value of Josephson constant 4.835979e+14 Hz V^-1
conventional value of von Klitzing constant 25812.807 ohm
Cu x unit 1.00207697e-13 m
deuteron g factor 0.8574382308
deuteron mag. mom. 4.33073489e-27 J T^-1
deuteron mag. mom. to Bohr magneton ratio 0.0004669754556
deuteron mag. mom. to nuclear magneton ratio 0.8574382308
deuteron mass 3.34358348e-27 kg
deuteron mass energy equivalent 3.00506297e-10 J
deuteron mass energy equivalent in MeV 1875.612859 MeV
deuteron mass in u 2.01355321271 u
deuteron molar mass 0.00201355321271 kg mol^-1
deuteron rms charge radius 2.1424e-15 m
deuteron-electron mag. mom. ratio -0.0004664345537
deuteron-electron mass ratio 3670.4829652
deuteron-neutron mag. mom. ratio -0.44820652
deuteron-proton mag. mom. ratio 0.307012207
deuteron-proton mass ratio 1.99900750097
electric constant 8.85418781762e-12 F m^-1
electron charge to mass quotient -1.758820088e+11 C kg^-1
electron g factor -2.00231930436
electron gyromag. ratio 1.760859708e+11 s^-1 T^-1
electron gyromag. ratio over 2 pi 28024.95266 MHz T^-1
electron mag. mom. -9.2847643e-24 J T^-1
electron mag. mom. anomaly 0.00115965218076
electron mag. mom. to Bohr magneton ratio -1.00115965218
electron mag. mom. to nuclear magneton ratio -1838.2819709
electron mass 9.10938291e-31 kg
electron mass energy equivalent 8.18710506e-14 J
electron mass energy equivalent in MeV 0.510998928 MeV
electron mass in u 0.00054857990946 u
electron molar mass 5.4857990946e-07 kg mol^-1
electron to alpha particle mass ratio 0.000137093355578
electron to shielded helion mag. mom. ratio 864.058257
electron to shielded proton mag. mom. ratio -658.2275971
electron volt 1.602176565e-19 J
electron volt-atomic mass unit relationship 1.07354415e-09 u
electron volt-hartree relationship 0.03674932379 E_h
electron volt-hertz relationship 2.417989348e+14 Hz
electron volt-inverse meter relationship 806554.429 m^-1
electron volt-joule relationship 1.602176565e-19 J
electron volt-kelvin relationship 11604.519 K
electron volt-kilogram relationship 1.782661845e-36 kg
electron-deuteron mag. mom. ratio -2143.923498
electron-deuteron mass ratio 0.00027244371095
electron-helion mass ratio 0.00018195430761
electron-muon mag. mom. ratio 206.7669896
electron-muon mass ratio 0.00483633166
electron-neutron mag. mom. ratio 960.9205
electron-neutron mass ratio 0.00054386734461
electron-proton mag. mom. ratio -658.2106848
electron-proton mass ratio 0.00054461702178
electron-tau mass ratio 0.000287592
electron-triton mass ratio 0.00018192000653
elementary charge 1.602176565e-19 C
elementary charge over h 2.417989348e+14 A J^-1
Faraday constant 96485.3365 C mol^-1
Faraday constant for conventional electric current 96485.3321 C_90 mol^-1
Fermi coupling constant 1.166364e-05 GeV^-2
fine-structure constant 0.0072973525698
first radiation constant 3.74177153e-16 W m^2
first radiation constant for spectral radiance 1.191042869e-16 W m^2 sr^-1
Hartree energy 4.35974434e-18 J
Hartree energy in eV 27.21138505 eV
hartree-atomic mass unit relationship 2.9212623246e-08 u
hartree-electron volt relationship 27.21138505 eV
hartree-hertz relationship 6.57968392073e+15 Hz
hartree-inverse meter relationship 21947463.1371 m^-1
hartree-joule relationship 4.35974434e-18 J
hartree-kelvin relationship 315775.04 K
hartree-kilogram relationship 4.85086979e-35 kg
helion g factor -4.255250613
helion mag. mom. -1.074617486e-26 J T^-1
helion mag. mom. to Bohr magneton ratio -0.001158740958
helion mag. mom. to nuclear magneton ratio -2.127625306
helion mass 5.00641234e-27 kg
helion mass energy equivalent 4.49953902e-10 J
helion mass energy equivalent in MeV 2808.391482 MeV
helion mass in u 3.0149322468 u
helion molar mass 0.0030149322468 kg mol^-1
helion-electron mass ratio 5495.8852754
helion-proton mass ratio 2.9931526707
hertz-atomic mass unit relationship 4.4398216689e-24 u
hertz-electron volt relationship 4.135667516e-15 eV
hertz-hartree relationship 1.519829846e-16 E_h
hertz-inverse meter relationship 3.33564095198e-09 m^-1
hertz-joule relationship 6.62606957e-34 J
hertz-kelvin relationship 4.7992434e-11 K
hertz-kilogram relationship 7.37249668e-51 kg
inverse fine-structure constant 137.035999074
inverse meter-atomic mass unit relationship 1.3310250512e-15 u
inverse meter-electron volt relationship 1.23984193e-06 eV
inverse meter-hartree relationship 4.55633525276e-08 E_h
inverse meter-hertz relationship 299792458.0 Hz
inverse meter-joule relationship 1.986445684e-25 J
inverse meter-kelvin relationship 0.01438777 K
inverse meter-kilogram relationship 2.210218902e-42 kg
inverse of conductance quantum 12906.4037217 ohm
Josephson constant 4.8359787e+14 Hz V^-1
joule-atomic mass unit relationship 6700535850.0 u
joule-electron volt relationship 6.24150934e+18 eV
joule-hartree relationship 2.29371248e+17 E_h
joule-hertz relationship 1.509190311e+33 Hz
joule-inverse meter relationship 5.03411701e+24 m^-1
joule-kelvin relationship 7.2429716e+22 K
joule-kilogram relationship 1.11265005605e-17 kg
kelvin-atomic mass unit relationship 9.2510868e-14 u
kelvin-electron volt relationship 8.6173324e-05 eV
kelvin-hartree relationship 3.1668114e-06 E_h
kelvin-hertz relationship 20836618000.0 Hz
kelvin-inverse meter relationship 69.503476 m^-1
kelvin-joule relationship 1.3806488e-23 J
kelvin-kilogram relationship 1.536179e-40 kg
kilogram-atomic mass unit relationship 6.02214129e+26 u
kilogram-electron volt relationship 5.60958885e+35 eV
kilogram-hartree relationship 2.061485968e+34 E_h
kilogram-hertz relationship 1.356392608e+50 Hz
kilogram-inverse meter relationship 4.52443873e+41 m^-1
kilogram-joule relationship 8.98755178737e+16 J
kilogram-kelvin relationship 6.5096582e+39 K
lattice parameter of silicon 5.431020504e-10 m
Loschmidt constant (273.15 K, 100 kPa) 2.6516462e+25 m^-3
Loschmidt constant (273.15 K, 101.325 kPa) 2.6867805e+25 m^-3
mag. constant 1.25663706144e-06 N A^-2
mag. flux quantum 2.067833758e-15 Wb
Mo x unit 1.00209952e-13 m
molar gas constant 8.3144621 J mol^-1 K^-1
molar mass constant 0.001 kg mol^-1
molar mass of carbon-12 0.012 kg mol^-1
molar Planck constant 3.9903127176e-10 J s mol^-1
molar Planck constant times c 0.119626565779 J m mol^-1
molar volume of ideal gas (273.15 K, 100 kPa) 0.022710953 m^3 mol^-1
molar volume of ideal gas (273.15 K, 101.325 kPa) 0.022413968 m^3 mol^-1
molar volume of silicon 1.205883301e-05 m^3 mol^-1
muon Compton wavelength 1.173444103e-14 m
muon Compton wavelength over 2 pi 1.867594294e-15 m
muon g factor -2.0023318418
muon mag. mom. -4.49044807e-26 J T^-1
muon mag. mom. anomaly 0.00116592091
muon mag. mom. to Bohr magneton ratio -0.00484197044
muon mag. mom. to nuclear magneton ratio -8.89059697
muon mass 1.883531475e-28 kg
muon mass energy equivalent 1.692833667e-11 J
muon mass energy equivalent in MeV 105.6583715 MeV
muon mass in u 0.1134289267 u
muon molar mass 0.0001134289267 kg mol^-1
muon-electron mass ratio 206.7682843
muon-neutron mass ratio 0.1124545177
muon-proton mag. mom. ratio -3.183345107
muon-proton mass ratio 0.1126095272
muon-tau mass ratio 0.0594649
natural unit of action 1.054571726e-34 J s
natural unit of action in eV s 6.58211928e-16 eV s
natural unit of energy 8.18710506e-14 J
natural unit of energy in MeV 0.510998928 MeV
natural unit of length 3.86159268e-13 m
natural unit of mass 9.10938291e-31 kg
natural unit of 2.73092429e-22 kg m s^-1
natural unit of in MeV/c 0.510998928 MeV/c
natural unit of time 1.28808866833e-21 s
natural unit of velocity 299792458.0 m s^-1
neutron Compton wavelength 1.3195909068e-15 m
neutron Compton wavelength over 2 pi 2.1001941568e-16 m
neutron g factor -3.82608545
neutron gyromag. ratio 183247179.0 s^-1 T^-1
neutron gyromag. ratio over 2 pi 29.1646943 MHz T^-1
neutron mag. mom. -9.6623647e-27 J T^-1
neutron mag. mom. to Bohr magneton ratio -0.00104187563
neutron mag. mom. to nuclear magneton ratio -1.91304272
neutron mass 1.674927351e-27 kg
neutron mass energy equivalent 1.505349631e-10 J
neutron mass energy equivalent in MeV 939.565379 MeV
neutron mass in u 1.008664916 u
neutron molar mass 0.001008664916 kg mol^-1
neutron to shielded proton mag. mom. ratio -0.68499694
neutron-electron mag. mom. ratio 0.00104066882
neutron-electron mass ratio 1838.6836605
neutron-muon mass ratio 8.892484
neutron-proton mag. mom. ratio -0.68497934
neutron-proton mass difference 2.30557392e-30
neutron-proton mass difference energy equivalent 2.0721465e-13
neutron-proton mass difference energy equivalent in MeV 1.29333217
neutron-proton mass difference in u 0.00138844919
neutron-proton mass ratio 1.00137841917
neutron-tau mass ratio 0.52879
Newtonian constant of gravitation 6.67384e-11 m^3 kg^-1 s^-2
Newtonian constant of gravitation over h-bar c 6.70837e-39 (GeV/c^2)^-2
nuclear magneton 5.05078353e-27 J T^-1
nuclear magneton in eV/T 3.1524512605e-08 eV T^-1
nuclear magneton in inverse meters per tesla 0.02542623527 m^-1 T^-1
nuclear magneton in K/T 0.00036582682 K T^-1
nuclear magneton in MHz/T 7.62259357 MHz T^-1
Planck constant 6.62606957e-34 J s
Planck constant in eV s 4.135667516e-15 eV s
Planck constant over 2 pi 1.054571726e-34 J s
Planck constant over 2 pi in eV s 6.58211928e-16 eV s
Planck constant over 2 pi times c in MeV fm 197.3269718 MeV fm
Planck length 1.616199e-35 m
Planck mass 2.17651e-08 kg
Planck mass energy equivalent in GeV 1.220932e+19 GeV
Planck temperature 1.416833e+32 K
Planck time 5.39106e-44 s
proton charge to mass quotient 95788335.8 C kg^-1
proton Compton wavelength 1.32140985623e-15 m
proton Compton wavelength over 2 pi 2.1030891047e-16 m
proton g factor 5.585694713
proton gyromag. ratio 267522200.5 s^-1 T^-1
proton gyromag. ratio over 2 pi 42.5774806 MHz T^-1
proton mag. mom. 1.410606743e-26 J T^-1
proton mag. mom. to Bohr magneton ratio 0.00152103221
proton mag. mom. to nuclear magneton ratio 2.792847356
proton mag. shielding correction 2.5694e-05
proton mass 1.672621777e-27 kg
proton mass energy equivalent 1.503277484e-10 J
proton mass energy equivalent in MeV 938.272046 MeV
proton mass in u 1.00727646681 u
proton molar mass 0.00100727646681 kg mol^-1
proton rms charge radius 8.775e-16 m
proton-electron mass ratio 1836.15267245
proton-muon mass ratio 8.88024331
proton-neutron mag. mom. ratio -1.45989806
proton-neutron mass ratio 0.99862347826
proton-tau mass ratio 0.528063
quantum of circulation 0.0003636947552 m^2 s^-1
quantum of circulation times 2 0.0007273895104 m^2 s^-1
Rydberg constant 10973731.5685 m^-1
Rydberg constant times c in Hz 3.28984196036e+15 Hz
Rydberg constant times hc in eV 13.60569253 eV
Rydberg constant times hc in J 2.179872171e-18 J
Sackur-Tetrode constant (1 K, 100 kPa) -1.1517078
Sackur-Tetrode constant (1 K, 101.325 kPa) -1.1648708
second radiation constant 0.01438777 m K
shielded helion gyromag. ratio 203789465.9 s^-1 T^-1
shielded helion gyromag. ratio over 2 pi 32.43410084 MHz T^-1
shielded helion mag. mom. -1.074553044e-26 J T^-1
shielded helion mag. mom. to Bohr magneton ratio -0.001158671471
shielded helion mag. mom. to nuclear magneton ratio -2.127497718
shielded helion to proton mag. mom. ratio -0.761766558
shielded helion to shielded proton mag. mom. ratio -0.7617861313
shielded proton gyromag. ratio 267515326.8 s^-1 T^-1
shielded proton gyromag. ratio over 2 pi 42.5763866 MHz T^-1
shielded proton mag. mom. 1.410570499e-26 J T^-1
shielded proton mag. mom. to Bohr magneton ratio 0.001520993128
shielded proton mag. mom. to nuclear magneton ratio 2.792775598
speed of light in vacuum 299792458.0 m s^-1
standard acceleration of gravity 9.80665 m s^-2
standard atmosphere 101325.0 Pa
standard-state pressure 100000.0 Pa
Stefan-Boltzmann constant 5.670373e-08 W m^-2 K^-4
tau Compton wavelength 6.97787e-16 m
tau Compton wavelength over 2 pi 1.11056e-16 m
tau mass 3.16747e-27 kg
tau mass energy equivalent 2.84678e-10 J
tau mass energy equivalent in MeV 1776.82 MeV
tau mass in u 1.90749 u
tau molar mass 0.00190749 kg mol^-1
tau-electron mass ratio 3477.15
tau-muon mass ratio 16.8167
tau-neutron mass ratio 1.89111
tau-proton mass ratio 1.89372
Thomson cross section 6.652458734e-29 m^2
triton g factor 5.957924896
triton mag. mom. 1.504609447e-26 J T^-1
triton mag. mom. to Bohr magneton ratio 0.001622393657
triton mag. mom. to nuclear magneton ratio 2.978962448
triton mass 5.0073563e-27 kg
triton mass energy equivalent 4.50038741e-10 J
triton mass energy equivalent in MeV 2808.921005 MeV
triton mass in u 3.0155007134 u
triton molar mass 0.0030155007134 kg mol^-1
triton-electron mass ratio 5496.9215267
triton-proton mass ratio 2.9937170308
unified atomic mass unit 1.660538921e-27 kg
von Klitzing constant 25812.8074434 ohm
weak mixing angle 0.2223
Wien frequency displacement law constant 58789254000.0 Hz K^-1
Wien wavelength displacement law constant 0.0028977721 m K
{220} lattice spacing of silicon 1.920155714e-10 m


SI prefixes

yotta \(10^{24}\)
zetta \(10^{21}\)
exa \(10^{18}\)
peta \(10^{15}\)
tera \(10^{12}\)
giga \(10^{9}\)
mega \(10^{6}\)
kilo \(10^{3}\)
hecto \(10^{2}\)
deka \(10^{1}\)
deci \(10^{-1}\)
centi \(10^{-2}\)
milli \(10^{-3}\)
micro \(10^{-6}\)
nano \(10^{-9}\)
pico \(10^{-12}\)
femto \(10^{-15}\)
atto \(10^{-18}\)
zepto \(10^{-21}\)

Binary prefixes

kibi \(2^{10}\)
mebi \(2^{20}\)
gibi \(2^{30}\)
tebi \(2^{40}\)
pebi \(2^{50}\)
exbi \(2^{60}\)
zebi \(2^{70}\)
yobi \(2^{80}\)


gram \(10^{-3}\) kg
metric_ton \(10^{3}\) kg
grain one grain in kg
lb one pound (avoirdupous) in kg
oz one ounce in kg
stone one stone in kg
grain one grain in kg
long_ton one long ton in kg
short_ton one short ton in kg
troy_ounce one Troy ounce in kg
troy_pound one Troy pound in kg
carat one carat in kg
m_u atomic mass constant (in kg)


degree degree in radians
arcmin arc minute in radians
arcsec arc second in radians


minute one minute in seconds
hour one hour in seconds
day one day in seconds
week one week in seconds
year one year (365 days) in seconds
Julian_year one Julian year (365.25 days) in seconds


inch one inch in meters
foot one foot in meters
yard one yard in meters
mile one mile in meters
mil one mil in meters
pt one point in meters
survey_foot one survey foot in meters
survey_mile one survey mile in meters
nautical_mile one nautical mile in meters
fermi one Fermi in meters
angstrom one Angstrom in meters
micron one micron in meters
au one astronomical unit in meters
light_year one light year in meters
parsec one parsec in meters


atm standard atmosphere in pascals
bar one bar in pascals
torr one torr (mmHg) in pascals
psi one psi in pascals


hectare one hectare in square meters
acre one acre in square meters


liter one liter in cubic meters
gallon one gallon (US) in cubic meters
gallon_imp one gallon (UK) in cubic meters
fluid_ounce one fluid ounce (US) in cubic meters
fluid_ounce_imp one fluid ounce (UK) in cubic meters
bbl one barrel in cubic meters


kmh kilometers per hour in meters per second
mph miles per hour in meters per second
mach one Mach (approx., at 15 C, 1 atm) in meters per second
knot one knot in meters per second


zero_Celsius zero of Celsius scale in Kelvin
degree_Fahrenheit one Fahrenheit (only differences) in Kelvins
C2K(C) Convert Celsius to Kelvin
K2C(K) Convert Kelvin to Celsius
F2C(F) Convert Fahrenheit to Celsius
C2F(C) Convert Celsius to Fahrenheit
F2K(F) Convert Fahrenheit to Kelvin
K2F(K) Convert Kelvin to Fahrenheit


eV one electron volt in Joules
calorie one calorie (thermochemical) in Joules
calorie_IT one calorie (International Steam Table calorie, 1956) in Joules
erg one erg in Joules
Btu one British thermal unit (International Steam Table) in Joules
Btu_th one British thermal unit (thermochemical) in Joules
ton_TNT one ton of TNT in Joules


hp one horsepower in watts


dyn one dyne in newtons
lbf one pound force in newtons
kgf one kilogram force in newtons


lambda2nu(lambda_) Convert wavelength to optical frequency
nu2lambda(nu) Convert optical frequency to wavelength.



CODATA Recommended Values of the Fundamental Physical Constants 2010.