================================== Constants (:mod:`scipy.constants`) ================================== .. module:: 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 :math:`\mu_0` ``epsilon_0`` the electric constant (vacuum permittivity), :math:`\epsilon_0` ``h`` the Planck constant :math:`h` ``hbar`` :math:`\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 :math:`\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 containing physical constants, :mod:`scipy.constants` also contains a database of additional physical constants. .. autosummary:: :toctree: generated/ value unit precision find .. data:: physical_constants Dictionary of physical constants, of the format ``physical_constants[name] = (value, unit, uncertainty)``. Available constants: ====================================================================== ==== ``alpha particle mass`` ``alpha particle mass energy equivalent`` ``alpha particle mass energy equivalent in MeV`` ``alpha particle mass in u`` ``alpha particle molar mass`` ``alpha particle-electron mass ratio`` ``alpha particle-proton mass ratio`` ``Angstrom star`` ``atomic mass constant`` ``atomic mass constant energy equivalent`` ``atomic mass constant energy equivalent in MeV`` ``atomic mass unit-electron volt relationship`` ``atomic mass unit-hartree relationship`` ``atomic mass unit-hertz relationship`` ``atomic mass unit-inverse meter relationship`` ``atomic mass unit-joule relationship`` ``atomic mass unit-kelvin relationship`` ``atomic mass unit-kilogram relationship`` ``atomic unit of 1st hyperpolarizablity`` ``atomic unit of 2nd hyperpolarizablity`` ``atomic unit of action`` ``atomic unit of charge`` ``atomic unit of charge density`` ``atomic unit of current`` ``atomic unit of electric dipole moment`` ``atomic unit of electric field`` ``atomic unit of electric field gradient`` ``atomic unit of electric polarizablity`` ``atomic unit of electric potential`` ``atomic unit of electric quadrupole moment`` ``atomic unit of energy`` ``atomic unit of force`` ``atomic unit of length`` ``atomic unit of magnetic dipole moment`` ``atomic unit of magnetic flux density`` ``atomic unit of magnetizability`` ``atomic unit of mass`` ``atomic unit of momentum`` ``atomic unit of permittivity`` ``atomic unit of time`` ``atomic unit of velocity`` ``Avogadro constant`` ``Bohr magneton`` ``Bohr magneton in eV/T`` ``Bohr magneton in Hz/T`` ``Bohr magneton in inverse meters per tesla`` ``Bohr magneton in K/T`` ``Bohr radius`` ``Boltzmann constant`` ``Boltzmann constant in eV/K`` ``Boltzmann constant in Hz/K`` ``Boltzmann constant in inverse meters per kelvin`` ``characteristic impedance of vacuum`` ``classical electron radius`` ``Compton wavelength`` ``Compton wavelength over 2 pi`` ``conductance quantum`` ``conventional value of Josephson constant`` ``conventional value of von Klitzing constant`` ``Cu x unit`` ``deuteron magnetic moment`` ``deuteron magnetic moment to Bohr magneton ratio`` ``deuteron magnetic moment to nuclear magneton ratio`` ``deuteron mass`` ``deuteron mass energy equivalent`` ``deuteron mass energy equivalent in MeV`` ``deuteron mass in u`` ``deuteron molar mass`` ``deuteron rms charge radius`` ``deuteron-electron magnetic moment ratio`` ``deuteron-electron mass ratio`` ``deuteron-neutron magnetic moment ratio`` ``deuteron-proton magnetic moment ratio`` ``deuteron-proton mass ratio`` ``electric constant`` ``electron charge to mass quotient`` ``electron g factor`` ``electron gyromagnetic ratio`` ``electron gyromagnetic ratio over 2 pi`` ``electron magnetic moment`` ``electron magnetic moment anomaly`` ``electron magnetic moment to Bohr magneton ratio`` ``electron magnetic moment to nuclear magneton ratio`` ``electron mass`` ``electron mass energy equivalent`` ``electron mass energy equivalent in MeV`` ``electron mass in u`` ``electron molar mass`` ``electron to alpha particle mass ratio`` ``electron to shielded helion magnetic moment ratio`` ``electron to shielded proton magnetic moment ratio`` ``electron volt`` ``electron volt-atomic mass unit relationship`` ``electron volt-hartree relationship`` ``electron volt-hertz relationship`` ``electron volt-inverse meter relationship`` ``electron volt-joule relationship`` ``electron volt-kelvin relationship`` ``electron volt-kilogram relationship`` ``electron-deuteron magnetic moment ratio`` ``electron-deuteron mass ratio`` ``electron-muon magnetic moment ratio`` ``electron-muon mass ratio`` ``electron-neutron magnetic moment ratio`` ``electron-neutron mass ratio`` ``electron-proton magnetic moment ratio`` ``electron-proton mass ratio`` ``electron-tau mass ratio`` ``elementary charge`` ``elementary charge over h`` ``Faraday constant`` ``Faraday constant for conventional electric current`` ``Fermi coupling constant`` ``fine-structure constant`` ``first radiation constant`` ``first radiation constant for spectral radiance`` ``Hartree energy`` ``Hartree energy in eV`` ``hartree-atomic mass unit relationship`` ``hartree-electron volt relationship`` ``hartree-hertz relationship`` ``hartree-inverse meter relationship`` ``hartree-joule relationship`` ``hartree-kelvin relationship`` ``hartree-kilogram relationship`` ``helion mass`` ``helion mass energy equivalent`` ``helion mass energy equivalent in MeV`` ``helion mass in u`` ``helion molar mass`` ``helion-electron mass ratio`` ``helion-proton mass ratio`` ``hertz-atomic mass unit relationship`` ``hertz-electron volt relationship`` ``hertz-hartree relationship`` ``hertz-inverse meter relationship`` ``hertz-joule relationship`` ``hertz-kelvin relationship`` ``hertz-kilogram relationship`` ``inverse fine-structure constant`` ``inverse meter-atomic mass unit relationship`` ``inverse meter-electron volt relationship`` ``inverse meter-hartree relationship`` ``inverse meter-hertz relationship`` ``inverse meter-joule relationship`` ``inverse meter-kelvin relationship`` ``inverse meter-kilogram relationship`` ``inverse of conductance quantum`` ``Josephson constant`` ``joule-atomic mass unit relationship`` ``joule-electron volt relationship`` ``joule-hartree relationship`` ``joule-hertz relationship`` ``joule-inverse meter relationship`` ``joule-kelvin relationship`` ``joule-kilogram relationship`` ``kelvin-atomic mass unit relationship`` ``kelvin-electron volt relationship`` ``kelvin-hartree relationship`` ``kelvin-hertz relationship`` ``kelvin-inverse meter relationship`` ``kelvin-joule relationship`` ``kelvin-kilogram relationship`` ``kilogram-atomic mass unit relationship`` ``kilogram-electron volt relationship`` ``kilogram-hartree relationship`` ``kilogram-hertz relationship`` ``kilogram-inverse meter relationship`` ``kilogram-joule relationship`` ``kilogram-kelvin relationship`` ``lattice parameter of silicon`` ``Loschmidt constant (273.15 K, 101.325 kPa)`` ``magnetic constant`` ``magnetic flux quantum`` ``Mo x unit`` ``molar gas constant`` ``molar mass constant`` ``molar mass of carbon-12`` ``molar Planck constant`` ``molar Planck constant times c`` ``molar volume of ideal gas (273.15 K, 100 kPa)`` ``molar volume of ideal gas (273.15 K, 101.325 kPa)`` ``molar volume of silicon`` ``muon Compton wavelength`` ``muon Compton wavelength over 2 pi`` ``muon g factor`` ``muon magnetic moment`` ``muon magnetic moment anomaly`` ``muon magnetic moment to Bohr magneton ratio`` ``muon magnetic moment to nuclear magneton ratio`` ``muon mass`` ``muon mass energy equivalent`` ``muon mass energy equivalent in MeV`` ``muon mass in u`` ``muon molar mass`` ``muon-electron mass ratio`` ``muon-neutron mass ratio`` ``muon-proton magnetic moment ratio`` ``muon-proton mass ratio`` ``muon-tau mass ratio`` ``natural unit of action`` ``natural unit of action in eV s`` ``natural unit of energy`` ``natural unit of energy in MeV`` ``natural unit of length`` ``natural unit of mass`` ``natural unit of momentum`` ``natural unit of momentum in MeV/c`` ``natural unit of time`` ``natural unit of velocity`` ``neutron Compton wavelength`` ``neutron Compton wavelength over 2 pi`` ``neutron g factor`` ``neutron gyromagnetic ratio`` ``neutron gyromagnetic ratio over 2 pi`` ``neutron magnetic moment`` ``neutron magnetic moment to Bohr magneton ratio`` ``neutron magnetic moment to nuclear magneton ratio`` ``neutron mass`` ``neutron mass energy equivalent`` ``neutron mass energy equivalent in MeV`` ``neutron mass in u`` ``neutron molar mass`` ``neutron to shielded proton magnetic moment ratio`` ``neutron-electron magnetic moment ratio`` ``neutron-electron mass ratio`` ``neutron-muon mass ratio`` ``neutron-proton magnetic moment ratio`` ``neutron-proton mass ratio`` ``neutron-tau mass ratio`` ``Newtonian constant of gravitation`` ``Newtonian constant of gravitation over h-bar c`` ``nuclear magneton`` ``nuclear magneton in eV/T`` ``nuclear magneton in inverse meters per tesla`` ``nuclear magneton in K/T`` ``nuclear magneton in MHz/T`` ``Planck constant`` ``Planck constant in eV s`` ``Planck constant over 2 pi`` ``Planck constant over 2 pi in eV s`` ``Planck constant over 2 pi times c in MeV fm`` ``Planck length`` ``Planck mass`` ``Planck temperature`` ``Planck time`` ``proton charge to mass quotient`` ``proton Compton wavelength`` ``proton Compton wavelength over 2 pi`` ``proton g factor`` ``proton gyromagnetic ratio`` ``proton gyromagnetic ratio over 2 pi`` ``proton magnetic moment`` ``proton magnetic moment to Bohr magneton ratio`` ``proton magnetic moment to nuclear magneton ratio`` ``proton magnetic shielding correction`` ``proton mass`` ``proton mass energy equivalent`` ``proton mass energy equivalent in MeV`` ``proton mass in u`` ``proton molar mass`` ``proton rms charge radius`` ``proton-electron mass ratio`` ``proton-muon mass ratio`` ``proton-neutron magnetic moment ratio`` ``proton-neutron mass ratio`` ``proton-tau mass ratio`` ``quantum of circulation`` ``quantum of circulation times 2`` ``Rydberg constant`` ``Rydberg constant times c in Hz`` ``Rydberg constant times hc in eV`` ``Rydberg constant times hc in J`` ``Sackur-Tetrode constant (1 K, 100 kPa)`` ``Sackur-Tetrode constant (1 K, 101.325 kPa)`` ``second radiation constant`` ``shielded helion gyromagnetic ratio`` ``shielded helion gyromagnetic ratio over 2 pi`` ``shielded helion magnetic moment`` ``shielded helion magnetic moment to Bohr magneton ratio`` ``shielded helion magnetic moment to nuclear magneton ratio`` ``shielded helion to proton magnetic moment ratio`` ``shielded helion to shielded proton magnetic moment ratio`` ``shielded proton gyromagnetic ratio`` ``shielded proton gyromagnetic ratio over 2 pi`` ``shielded proton magnetic moment`` ``shielded proton magnetic moment to Bohr magneton ratio`` ``shielded proton magnetic moment to nuclear magneton ratio`` ``speed of light in vacuum`` ``standard acceleration of gravity`` ``standard atmosphere`` ``Stefan-Boltzmann constant`` ``tau Compton wavelength`` ``tau Compton wavelength over 2 pi`` ``tau mass`` ``tau mass energy equivalent`` ``tau mass energy equivalent in MeV`` ``tau mass in u`` ``tau molar mass`` ``tau-electron mass ratio`` ``tau-muon mass ratio`` ``tau-neutron mass ratio`` ``tau-proton mass ratio`` ``Thomson cross section`` ``unified atomic mass unit`` ``von Klitzing constant`` ``weak mixing angle`` ``Wien displacement law constant`` ``{220} lattice spacing of silicon`` ====================================================================== ==== Unit prefixes ============= SI -- ============ ================================================================= ``yotta`` :math:`10^{24}` ``zetta`` :math:`10^{21}` ``exa`` :math:`10^{18}` ``peta`` :math:`10^{15}` ``tera`` :math:`10^{12}` ``giga`` :math:`10^{9}` ``mega`` :math:`10^{6}` ``kilo`` :math:`10^{3}` ``hecto`` :math:`10^{2}` ``deka`` :math:`10^{1}` ``deci`` :math:`10^{-1}` ``centi`` :math:`10^{-2}` ``milli`` :math:`10^{-3}` ``micro`` :math:`10^{-6}` ``nano`` :math:`10^{-9}` ``pico`` :math:`10^{-12}` ``femto`` :math:`10^{-15}` ``atto`` :math:`10^{-18}` ``zepto`` :math:`10^{-21}` ============ ================================================================= Binary ------ ============ ================================================================= ``kibi`` :math:`2^{10}` ``mebi`` :math:`2^{20}` ``gibi`` :math:`2^{30}` ``tebi`` :math:`2^{40}` ``pebi`` :math:`2^{50}` ``exbi`` :math:`2^{60}` ``zebi`` :math:`2^{70}` ``yobi`` :math:`2^{80}` ============ ================================================================= Units ===== Weight ------ ================= ============================================================ ``gram`` :math:`10^{-3}` kg ``metric_ton`` :math:`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) ================= ============================================================ Angle ----- ================= ============================================================ ``degree`` degree in radians ``arcmin`` arc minute in radians ``arcsec`` arc second in radians ================= ============================================================ Time ---- ================= ============================================================ ``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 ================= ============================================================ Length ------ ================= ============================================================ ``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 Ångström 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 ================= ============================================================ Pressure -------- ================= ============================================================ ``atm`` standard atmosphere in pascals ``bar`` one bar in pascals ``torr`` one torr (mmHg) in pascals ``psi`` one psi in pascals ================= ============================================================ Area ---- ================= ============================================================ ``hectare`` one hectare in square meters ``acre`` one acre in square meters ================= ============================================================ Volume ------ =================== ======================================================== ``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 =================== ======================================================== Speed ----- ================= ========================================================== ``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 ================= ========================================================== Temperature ----------- ===================== ======================================================= ``zero_Celsius`` zero of Celsius scale in Kelvin ``degree_Fahrenheit`` one Fahrenheit (only differences) in Kelvins ===================== ======================================================= .. autosummary:: :toctree: generated/ C2K K2C F2C C2F F2K K2F Energy ------ ==================== ======================================================= ``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 ==================== ======================================================= Power ----- ==================== ======================================================= ``hp`` one horsepower in watts ==================== ======================================================= Force ----- ==================== ======================================================= ``dyn`` one dyne in newtons ``lbf`` one pound force in newtons ``kgf`` one kilogram force in newtons ==================== ======================================================= Optics ------ .. autosummary:: :toctree: generated/ lambda2nu nu2lambda