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==================================
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Constants (:mod:`scipy.constants`)
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==================================
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.. module:: scipy.constants
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Physical and mathematical constants and units.
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Mathematical constants
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======================
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============ =================================================================
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``pi`` Pi
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``golden`` Golden ratio
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============ =================================================================
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Physical constants
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==================
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============= =================================================================
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``c`` speed of light in vacuum
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``mu_0`` the magnetic constant :math:`\mu_0`
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``epsilon_0`` the electric constant (vacuum permittivity), :math:`\epsilon_0`
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``h`` the Planck constant :math:`h`
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``hbar`` :math:`\hbar = h/(2\pi)`
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``G`` Newtonian constant of gravitation
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``g`` standard acceleration of gravity
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``e`` elementary charge
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``R`` molar gas constant
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``alpha`` fine-structure constant
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``N_A`` Avogadro constant
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``k`` Boltzmann constant
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``sigma`` Stefan-Boltzmann constant :math:`\sigma`
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``Wien`` Wien displacement law constant
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``Rydberg`` Rydberg constant
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``m_e`` electron mass
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``m_p`` proton mass
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``m_n`` neutron mass
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============= =================================================================
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Constants database
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==================
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In addition to the above variables containing physical constants,
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:mod:`scipy.constants` also contains a database of additional physical
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constants.
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.. autosummary::
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:toctree: generated/
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value
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unit
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precision
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find
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.. data:: physical_constants
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Dictionary of physical constants, of the format
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``physical_constants[name] = (value, unit, uncertainty)``.
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Available constants:
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====================================================================== ====
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``alpha particle mass``
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``alpha particle mass energy equivalent``
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``alpha particle mass energy equivalent in MeV``
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``alpha particle mass in u``
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``alpha particle molar mass``
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``alpha particle-electron mass ratio``
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``alpha particle-proton mass ratio``
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``Angstrom star``
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``atomic mass constant``
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``atomic mass constant energy equivalent``
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``atomic mass constant energy equivalent in MeV``
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``atomic mass unit-electron volt relationship``
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``atomic mass unit-hartree relationship``
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``atomic mass unit-hertz relationship``
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``atomic mass unit-inverse meter relationship``
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``atomic mass unit-joule relationship``
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``atomic mass unit-kelvin relationship``
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``atomic mass unit-kilogram relationship``
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``atomic unit of 1st hyperpolarizablity``
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``atomic unit of 2nd hyperpolarizablity``
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``atomic unit of action``
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``atomic unit of charge``
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``atomic unit of charge density``
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``atomic unit of current``
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``atomic unit of electric dipole moment``
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``atomic unit of electric field``
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``atomic unit of electric field gradient``
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``atomic unit of electric polarizablity``
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``atomic unit of electric potential``
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``atomic unit of electric quadrupole moment``
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``atomic unit of energy``
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``atomic unit of force``
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``atomic unit of length``
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``atomic unit of magnetic dipole moment``
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``atomic unit of magnetic flux density``
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``atomic unit of magnetizability``
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``atomic unit of mass``
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``atomic unit of momentum``
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``atomic unit of permittivity``
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``atomic unit of time``
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``atomic unit of velocity``
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``Avogadro constant``
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``Bohr magneton``
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``Bohr magneton in eV/T``
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``Bohr magneton in Hz/T``
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``Bohr magneton in inverse meters per tesla``
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``Bohr magneton in K/T``
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``Bohr radius``
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``Boltzmann constant``
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``Boltzmann constant in eV/K``
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``Boltzmann constant in Hz/K``
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``Boltzmann constant in inverse meters per kelvin``
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``characteristic impedance of vacuum``
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``classical electron radius``
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``Compton wavelength``
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``Compton wavelength over 2 pi``
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``conductance quantum``
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``conventional value of Josephson constant``
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``conventional value of von Klitzing constant``
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``Cu x unit``
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``deuteron magnetic moment``
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``deuteron magnetic moment to Bohr magneton ratio``
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``deuteron magnetic moment to nuclear magneton ratio``
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``deuteron mass``
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``deuteron mass energy equivalent``
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``deuteron mass energy equivalent in MeV``
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``deuteron mass in u``
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``deuteron molar mass``
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``deuteron rms charge radius``
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``deuteron-electron magnetic moment ratio``
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``deuteron-electron mass ratio``
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``deuteron-neutron magnetic moment ratio``
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``deuteron-proton magnetic moment ratio``
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``deuteron-proton mass ratio``
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``electric constant``
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``electron charge to mass quotient``
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``electron g factor``
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``electron gyromagnetic ratio``
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``electron gyromagnetic ratio over 2 pi``
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``electron magnetic moment``
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``electron magnetic moment anomaly``
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``electron magnetic moment to Bohr magneton ratio``
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``electron magnetic moment to nuclear magneton ratio``
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``electron mass``
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``electron mass energy equivalent``
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``electron mass energy equivalent in MeV``
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``electron mass in u``
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``electron molar mass``
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``electron to alpha particle mass ratio``
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``electron to shielded helion magnetic moment ratio``
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``electron to shielded proton magnetic moment ratio``
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``electron volt``
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``electron volt-atomic mass unit relationship``
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``electron volt-hartree relationship``
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``electron volt-hertz relationship``
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``electron volt-inverse meter relationship``
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``electron volt-joule relationship``
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``electron volt-kelvin relationship``
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``electron volt-kilogram relationship``
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``electron-deuteron magnetic moment ratio``
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``electron-deuteron mass ratio``
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``electron-muon magnetic moment ratio``
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``electron-muon mass ratio``
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``electron-neutron magnetic moment ratio``
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``electron-neutron mass ratio``
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``electron-proton magnetic moment ratio``
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``electron-proton mass ratio``
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``electron-tau mass ratio``
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``elementary charge``
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``elementary charge over h``
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``Faraday constant``
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``Faraday constant for conventional electric current``
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``Fermi coupling constant``
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``fine-structure constant``
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``first radiation constant``
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``first radiation constant for spectral radiance``
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``Hartree energy``
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``Hartree energy in eV``
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``hartree-atomic mass unit relationship``
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``hartree-electron volt relationship``
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``hartree-hertz relationship``
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``hartree-inverse meter relationship``
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``hartree-joule relationship``
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``hartree-kelvin relationship``
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``hartree-kilogram relationship``
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``helion mass``
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``helion mass energy equivalent``
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``helion mass energy equivalent in MeV``
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``helion mass in u``
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``helion molar mass``
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``helion-electron mass ratio``
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``helion-proton mass ratio``
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``hertz-atomic mass unit relationship``
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``hertz-electron volt relationship``
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``hertz-hartree relationship``
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``hertz-inverse meter relationship``
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``hertz-joule relationship``
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``hertz-kelvin relationship``
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``hertz-kilogram relationship``
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``inverse fine-structure constant``
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``inverse meter-atomic mass unit relationship``
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``inverse meter-electron volt relationship``
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``inverse meter-hartree relationship``
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``inverse meter-hertz relationship``
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``inverse meter-joule relationship``
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``inverse meter-kelvin relationship``
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``inverse meter-kilogram relationship``
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``inverse of conductance quantum``
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``Josephson constant``
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``joule-atomic mass unit relationship``
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``joule-electron volt relationship``
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``joule-hartree relationship``
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``joule-hertz relationship``
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``joule-inverse meter relationship``
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``joule-kelvin relationship``
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``joule-kilogram relationship``
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``kelvin-atomic mass unit relationship``
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``kelvin-electron volt relationship``
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``kelvin-hartree relationship``
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``kelvin-hertz relationship``
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``kelvin-inverse meter relationship``
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``kelvin-joule relationship``
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``kelvin-kilogram relationship``
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``kilogram-atomic mass unit relationship``
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``kilogram-electron volt relationship``
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``kilogram-hartree relationship``
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``kilogram-hertz relationship``
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``kilogram-inverse meter relationship``
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``kilogram-joule relationship``
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``kilogram-kelvin relationship``
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``lattice parameter of silicon``
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``Loschmidt constant (273.15 K, 101.325 kPa)``
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``magnetic constant``
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``magnetic flux quantum``
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``Mo x unit``
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``molar gas constant``
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``molar mass constant``
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``molar mass of carbon-12``
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``molar Planck constant``
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``molar Planck constant times c``
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``molar volume of ideal gas (273.15 K, 100 kPa)``
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``molar volume of ideal gas (273.15 K, 101.325 kPa)``
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``molar volume of silicon``
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``muon Compton wavelength``
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``muon Compton wavelength over 2 pi``
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``muon g factor``
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``muon magnetic moment``
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``muon magnetic moment anomaly``
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``muon magnetic moment to Bohr magneton ratio``
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``muon magnetic moment to nuclear magneton ratio``
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``muon mass``
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``muon mass energy equivalent``
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``muon mass energy equivalent in MeV``
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``muon mass in u``
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``muon molar mass``
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``muon-electron mass ratio``
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``muon-neutron mass ratio``
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``muon-proton magnetic moment ratio``
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``muon-proton mass ratio``
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``muon-tau mass ratio``
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``natural unit of action``
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``natural unit of action in eV s``
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``natural unit of energy``
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``natural unit of energy in MeV``
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``natural unit of length``
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``natural unit of mass``
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``natural unit of momentum``
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``natural unit of momentum in MeV/c``
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``natural unit of time``
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``natural unit of velocity``
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``neutron Compton wavelength``
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``neutron Compton wavelength over 2 pi``
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``neutron g factor``
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``neutron gyromagnetic ratio``
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``neutron gyromagnetic ratio over 2 pi``
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``neutron magnetic moment``
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``neutron magnetic moment to Bohr magneton ratio``
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``neutron magnetic moment to nuclear magneton ratio``
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``neutron mass``
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``neutron mass energy equivalent``
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``neutron mass energy equivalent in MeV``
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``neutron mass in u``
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``neutron molar mass``
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``neutron to shielded proton magnetic moment ratio``
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``neutron-electron magnetic moment ratio``
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``neutron-electron mass ratio``
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``neutron-muon mass ratio``
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``neutron-proton magnetic moment ratio``
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``neutron-proton mass ratio``
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``neutron-tau mass ratio``
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``Newtonian constant of gravitation``
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``Newtonian constant of gravitation over h-bar c``
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``nuclear magneton``
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``nuclear magneton in eV/T``
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``nuclear magneton in inverse meters per tesla``
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``nuclear magneton in K/T``
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``nuclear magneton in MHz/T``
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``Planck constant``
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``Planck constant in eV s``
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``Planck constant over 2 pi``
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``Planck constant over 2 pi in eV s``
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``Planck constant over 2 pi times c in MeV fm``
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``Planck length``
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``Planck mass``
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``Planck temperature``
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``Planck time``
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``proton charge to mass quotient``
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``proton Compton wavelength``
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``proton Compton wavelength over 2 pi``
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``proton g factor``
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``proton gyromagnetic ratio``
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``proton gyromagnetic ratio over 2 pi``
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``proton magnetic moment``
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``proton magnetic moment to Bohr magneton ratio``
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``proton magnetic moment to nuclear magneton ratio``
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``proton magnetic shielding correction``
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``proton mass``
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``proton mass energy equivalent``
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``proton mass energy equivalent in MeV``
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``proton mass in u``
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``proton molar mass``
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``proton rms charge radius``
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``proton-electron mass ratio``
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``proton-muon mass ratio``
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``proton-neutron magnetic moment ratio``
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``proton-neutron mass ratio``
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``proton-tau mass ratio``
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``quantum of circulation``
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``quantum of circulation times 2``
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``Rydberg constant``
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``Rydberg constant times c in Hz``
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``Rydberg constant times hc in eV``
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``Rydberg constant times hc in J``
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``Sackur-Tetrode constant (1 K, 100 kPa)``
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``Sackur-Tetrode constant (1 K, 101.325 kPa)``
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``second radiation constant``
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``shielded helion gyromagnetic ratio``
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``shielded helion gyromagnetic ratio over 2 pi``
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``shielded helion magnetic moment``
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``shielded helion magnetic moment to Bohr magneton ratio``
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``shielded helion magnetic moment to nuclear magneton ratio``
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``shielded helion to proton magnetic moment ratio``
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``shielded helion to shielded proton magnetic moment ratio``
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``shielded proton gyromagnetic ratio``
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``shielded proton gyromagnetic ratio over 2 pi``
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``shielded proton magnetic moment``
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``shielded proton magnetic moment to Bohr magneton ratio``
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``shielded proton magnetic moment to nuclear magneton ratio``
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``speed of light in vacuum``
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``standard acceleration of gravity``
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``standard atmosphere``
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``Stefan-Boltzmann constant``
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``tau Compton wavelength``
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``tau Compton wavelength over 2 pi``
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``tau mass``
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``tau mass energy equivalent``
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``tau mass energy equivalent in MeV``
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``tau mass in u``
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``tau molar mass``
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``tau-electron mass ratio``
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``tau-muon mass ratio``
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``tau-neutron mass ratio``
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``tau-proton mass ratio``
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``Thomson cross section``
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``unified atomic mass unit``
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||
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``von Klitzing constant``
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||
|
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``weak mixing angle``
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||
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``Wien displacement law constant``
|
||
|
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``{220} lattice spacing of silicon``
|
||
|
|
====================================================================== ====
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||
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|
||
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|
|
||
|
|
Unit prefixes
|
||
|
|
=============
|
||
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|
|
||
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|
SI
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||
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|
--
|
||
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|
||
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|
============ =================================================================
|
||
|
|
``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
|