List of Physical Constants

Name
Symbol
Value
speed of light in vacuum
\(c_0\)
\(2.99792458 \times 10^8 \left[\frac{\mathrm{m}}{\mathrm{s}}\right]\)
permeability of vacuum
\(\mu_0\)
\(4\pi \times 10^{-7} \left[\frac{\mathrm{H}}{\mathrm{m}}\right]\)
permittivity of vacuum
\(\varepsilon_0 = \frac{1}{\mu_0 c^2}\)
\(8.85418781758 \times 10^{-12} \left[\frac{\mathrm{F}}{\mathrm{m}}\right]\)
characteristic impedance of vacuum
\(Z_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}}\)
\(376.730313461\left[\mathrm{\Omega}\right]\)
Newtonian gravitational constant
\(G\)
\(6.673 \times 10^{-11} \left[\frac{\mathrm{N}\mathrm{}}{\mathrm{kg}^2}\right]\)
Plank's constant
\(h\)
\(6.62606876 \times 10^{-34} \left[\mathrm{Js}\right]\)
\(4.13566727 \times 10^{-15} \left[\mathrm{eVs}\right]\)
Planck's constant (rationalized)
\(\hbar = \frac{h}{2\pi}\)
\(1.054571596 \times 10^{-34} \left[\mathrm{Js}\right]\)
\(6.58211889 \times 10^{-16} \left[\mathrm{eVs}\right]\)
elementary electric charge
\(e\)
\(1.602176462 \times 10^{-19} \left[\mathrm{C}\right]\)
standard acceleration of gravity
\(g_n\)
\(9.80665 \left[\frac{\mathrm{m}}{\mathrm{s}^2}\right]\)
Planck's mass
\(m_p = \sqrt{\frac{\hbar c}{G}}\)
\(2.17671 \times 10^{-8} \left[\mathrm{kg}\right]\)
Planck's length
\(L_p = \frac{\hbar}{m_p c} = \sqrt{\frac{\hbar G}{c^3}}\)
\(1.6160\times 10^{-35} \left[\mathrm{m}\right]\)
Planck's time
\(t_p = \frac{L_p}{c} = \sqrt{\frac{\hbar G}{c^3}}\)
\(5.3906 \times 10^{-44} \left[\mathrm{s}\right]\)
quantum of magnetic flux
\(\Phi_0 = \frac{h}{2e}\)
\(2.067833636 \times 10^{15} \left[\mathrm{Wb}\right]\)
Fermi's coupling constant
\(\frac{G_F}{\hbar^3 c^3}\)
\(1.16639 \left[\mathrm{GeV}^2\right]\)
Subzs sqzared if weak mixing angle
\(\sin^2 \theta_w\)
0.2235
Avogadro's number
\(N_A, L\)
\(6.02214199 \times 10^23 \left[\frac{1}{\mathrm{mol}}\right]\)
atomic mass unit
\(u \) or \(\mathrm{u.m.a}\)
\(1.66053873 \times 10^{-27} \left[\mathrm{kg}\right]\)
\(931.494013 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]\)
Faraday's constant
\(F = N_A \times e\)
\(96485.3415 \left[\frac{\mathrm{C}}{\mathrm{mol}}\right]\)
Boltzmann's constant
\(k = \frac{R}{N_A}\)
\(1.3806503 \times 10^{-23} \left[\frac{\mathrm{J}}{\mathrm{K}}\right]\)
\(8.617342 \times 10^{-5} \left[\frac{\mathrm{eV}}{K}\right]
ideal gas constant
\(R\)
\(8.314472 \left[\frac{J}{\mathrm{Kmol}}\right]\)
molar Planck constant
\(N_Ah\)
\(3.990312689 \times 10^{-10} \left[\frac{\mathrm{Js}}{\mathrm{mol}}\right]\)
standard atmosphere
\(P_0\)
\(101325 \left[\mathrm{Pa}\right]\)
standard mola volume (STP) ideal gas
\(V_0 = \frac{RT_0}{P_0}\)
\(22.413996 \times 10^{-3} \left[\frac{\mathrm{m}^3}{\mathrm{mol}}\right] (273.15 [\mathrm{K}], 1 [\mathrm{atm}])\)
\(22.710981 \times 10^{-3} \left[\frac{\mathrm{m}^3}{\mathrm{mol}}\right] (273.15 [\mathrm{K}], 100 [\mathrm{kPa}])\)
Loschsmidt's constant
\(n_0 = \frac{N_A}{V_m}\)
\(2.6867775 \times 10^{-25} \left[\frac{1}{\mathrm{m}^3}\right]\)
Sackur-Tetrode constant (absolute entropy)
\(\frac{S_0}{R}\)
\(-1.1517048 (T = 1 [\mathrm{K}], P = 100 [\mathrm{kPa}]\)
\(-1.1648678 (T = 1 [\mathrm{K}], P = 101325 [\mathrm{Pa}]\)
Stefan-Boltzmann constant
\(\sigma = \frac{\pi^2}{60} = \frac{k^4}{\hbar^3 c^2}\)
\(5.6704 \times 10^{-8} \left[\frac{\mathrm{W}}{\mathrm{m}^2\mathrm{K}^4}\right]\)
first radiation constant
\(c_1 = 2 \pi h c^2\)
\(3.74177107 \times 10^{16} \left[\frac{\mathrm{W}}{\mathrm{m}^2}\right]\)
second raditiation constant
\(c_2 = \frac{hc}{k}\)
\(0.014387752 [\mathrm{m} \mathrm{K}]\)
Wien displacement law constant
\(b = \frac{c_2}{4.96511423}\)
\(2.8977686 \times 10^{-3} \left[\mathrm{m}\mathrm{K}\right]\)
electron rest mass
\(m_e\)
\(9.10938188 \times 10^{-31} [\mathrm{kg}]\)
\(5.48579911 \times 10^{-4} [\mathrm{u}]\)
Bohr magneton
\(\mu_B = \frac{e\hbar}{2m_e}\)
\(9.27400899 \times 10^{-24} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(5.788381749 \times 10^{-5} \left[\frac{\mathrm{eV}}{\mathrm{T}}\right]\)
fine structure constant
\(\alpha = \frac{\mu_0e^2c}{2h}\)
\(7.297352533 \times 10^{-3}\)
Rydberg constant
\(R_\infty = \frac{E_h}{2hc}\)
\(1.0973731568548 \times 10^7 \left[\frac{1}{\mathrm{m}}\right]\)
Rydberg
\(R_y = R_\infty h c\)
\(2.1798719 \times 10^{-18} [\mathrm{J}]\)
\(13.60569172 [\mathrm{eV}]\)
first Bohr atomic radius
\(a_0 = \frac{4\pi\varepsilon_0\hbar^2}{m_0e^2}\)
\(0.5291772083\times 10^{-10}[\mathrm{m}]\)
quantized Hall resistance (Von Klitzing constant)
\(\frac{h}{e^2} = \frac{\mu_0c}{2\alpha}\)
\(25812.807572 [\mathrm{\Omega}]\)
proton rest mass
\(M_p\)
\(1.67262158 \times 10^{-27} [\mathrm{kg}]\)
nuclear magneton
\(\mu_N = \frac{e\hbar}{2m_p}\)
\(5.05078317 \times 10^{-27} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(3.152451238 \times 10^{-8}\left[\frac{\mathrm{eV}}{\mathrm{T}}\right]\)
Hartree energy
\(E_h = \frac{\hbar^2}{m_0a_0^2}\)
\(4.35974381 \times 10^{-18} [\mathrm{J}]\)
\(27.2113834 [\mathrm{eV}]\)
Josephson constant
\(K_J = \frac{2e}{h}\)
\(4.83597898 \times 10^{14} \left[\frac{\mathrm{Hz}}{\mathrm{V}}\right]\)
quantum of circulation
\(\frac{h}{2m_e}\)
\(3.63694751627 \times 10^{-4} \left[\frac{\mathrm{m}^2}{\mathrm{s}}\right]\)
quantum of magnetic flux
\(\frac{h}{2e} = \Psi_0 \)
\(2.067833636 \times 10^{-15} [\mathrm{Wb}]\)
quantum of conductance
\(G_0 = \frac{2e^2}{h}\)
\(7.748091696 \times 10^{-5} [\mathrm{S}]\)
electron rest mass
\(m_e\)
\(9.10938188 \times 10^{-31} [\mathrm{kg}]\)
\(5.48579911 \times 10^{-4} [\mathrm{u}]\)
\(0.510998902 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]
electron molar mass
\(M_e\)
\(5.48579911 \times 10^{-7} \left[\frac{\mathrm{kg}}{\mathrm{mol}}\right]\)
electron-proton rest mass ratio
\(\frac{m_e}{m_p}\)
\(5.446170232 \times 10^{-4}\)
electron-neutron rest mass ratio
\(\frac{m_e}{m_n}\)
\(5.438673462 \times 10^{-4}\)
electron-muon rest mass ratio
\(\frac{m_e}{m_\mu}\)
\(4.83633210 \times 10^{-3}\)
electron-deutron rest mass ratio
\(\frac{m_e}{m_d}\)
\(2.724437117 \times 10^{-4}\)
electron-helion rest mass ratio
\(\frac{m_e}{m_\alpha}\)
\(1.37093354 \times 10^{-4}\)
electron-tau rest mass ratio
\(\frac{m_e}{m_r}\)
\(2.87555 \times 10^{-4}\)
electron specific charge
\(\frac{e}{m_e}\)
\(-1.758820174 \times 10^{11} \left[\frac{\mathrm{C}}{\mathrm{kg}}\right]\)
electron classic radius
\(r_e = a_0 \alpha^2\)
\(2.817940285 \times 10^{-15} [\mathrm{m}]\)
electron Thomson cross section
\(\sigma_e = \left(\frac{8\pi}{3}\right)r_e^2\)
\(0.665245854 \times 10^{-28} [\mathrm{m}^2]\)
electron Compton wavelength
\(\Lambda_C = \frac{h}{m_0c}\)
\(2.426310215 \times 10^{-12} [\mathrm{m}]\)
electron Compton rationalized wavelength
\(\frac{\hbar}{m_0c}\)
\(3.861592642 \times 10^{-13} [\mathrm{m}]\)
mqgentic moment of electron
\(\mu_e\)
\(9.28476362 \times 10^{-24} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(1.0011596521869 [\mathrm{B}]\)
\(1838.2819660 [\mathrm{N}]\)
electron magnetic moment anomaly
\(a_e = (\frac{\mu_e}{\mu_B})-1\)
\(1.1596521869 \times 10^{-3}\)
electron Lande factor (g-factor)
\(g_e = 2(1+a_e)\)
\(2.0023193043737\)
electron-proton magnetic moment ratio
\(\frac{\mu_e}{\mu_p}\)
\(658.2106875\)
electron-muon magnetic moment ratio
\(\frac{\mu_e}{\mu_n}\)
\(206.7669720\)
electron gyromagnetic ratio
\(\gamma_e = \frac{4\pi\mu_e}{h}\)
\(1.760589794 \times 10^{-11} \left[\frac{1}{\mathrm{s}\mathrm{T}}\right]\)
\(28024.9540 \left[\frac{\mathrm{MHz}}{\mathrm{T}}\right]\)
electron-neutron magnetic moment ratio
\(\frac{\mu_e}{\mu_n}\)
\(960.92050\)
electron-deuteron magnetic moment ratio
\(\frac{\mu_e}{\mu_d}\)
\(-2143.923498\)
electron-shielded proton magnetic moment (H\(_2\)O sphere at 298.15 [K])
\(\frac{\mu_e}{\mu_p}\)
\(-658.2275954\)
electron shielded helion magnetic moment ratio (g at shpere at 293.15 [K])
\(\frac{\mu_e}{\mu_\alpha}\)
\(864.058255\)
proton rest mass
\(m_p\)
\(1.67262158 \times 10^{-27} [\mathrm{kg}]\)
\(1.00727646688 [\mathrm{u}]\)
\(938.271998 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]\)
proton molar mass
\(M_p\)
\(1.007272646688 \times 10^{-3} \left[\frac{\mathrm{kg}}{\mathrm{mol}}\right]\)
specific charge of proton
\(\frac{e}{m_p}\)
\(9.57883408 \times 10^{7}\left[\frac{\mathrm{C}}{\mathrm{kg}}\right]\)
proton-electron rest mass ratio
\(\frac{m_p}{m_e}\)
\(1836.1526675\)
proton-muon rest mass ratio
\(\frac{m_p}{m_\mu}\)
\(8.88024408\)
proton-tau rest mass ratio
\(\frac{m_p}{m_r}\)
\(0.527994\)
proton-neutron rest mass ratio
\(\frac{m_p}{m_n}\)
\(0.99862347855\)
proton magnetic moment
\(\mu_p\)
\(1.410606633 \times 10^{-26} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(1.521032203 \times 10^{-3} \mu_B\)
proton Compton wavelength
\(\Lambda_{C,p} = \frac{h}{m_pc}\)
\(1.321409847 \times 10^{-15} [\mathrm{m}]\)
proton Compton rationalized wavelength
\(\frac{\hbar}{m_p c}\)
\(2.103089089 \times 10^{-16} [\mathrm{m}]\)
proton gyromagnetic ratio
\(\gamma_p\)
\(2.675221212 \times 10^8 \left[\frac{1}{\mathrm{s}\mathrm{T}}\right]\)
proton Lande factor
\(g_p\)
\(5.585694675\)
proton-shielded magnetic moment (H\(_2\)O sphere at 298.15 [K])
\(\mu_p^{'}\)
\(1.410570399 \times 10^{-26} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(1.520993132 \times 10^{-3} \mu_B\)
proton shielding corretion
\(\sigma_p^{'}\)
\(25.687 \times 10^{-6}\)
proton shielded gyromagnetic ratio
\(\gamma_p^{'}\)
\(2.67515341 \times 10^8 \left[\frac{1}{\mathrm{s}\mathrm{T}}\right]\)
neutron rest mass
\(m_n\)
\(1.67492716 \times 10^{-27} [\mathrm{kg}]\)
\(1.00866491578 [\mathrm{u}]\)
\(939.565330 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]\)
neutron molar mass
\(M_n\)
\(1.00866491578 \times 10^{-3} \left[\frac{\mathrm{kg}}{\mathrm{mol}}\right]\)
neutron-proton rest mass ratio
\(\frac{m_n}{m_p}\)
\(1.00137841887\)
neutron-electron rest mass ratio
\(\frac{m_n}{m_e}\)
\(1838.6836550\)
neutron mean life time
\(\tau\)
\(889.1 [\mathrm{s}]\)
neutron Compton wavelength
\(\Lambda_{C,n} = \frac{h}{m_n c}\)
\(1.319590898 \times 10^{-15} [\mathrm{m}]\)
neutron Compton rationalized wavelength
\(\frac{\hbar}{m_n c}\)
\(2.100194142 \times 10^{-16} [\mathrm{m}]\)
neutron magnetic moment
\(\mu_n\)
\(0.96623640 \times 10^{-26} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(1.04187563 \times 10^{-3}\mu_B\)
\(1.91304275 \mu_N\)
neutron-electron magnetic moment ratio
\(\frac{\mu_n}{\mu_e}\)
\(1.04066882 \times 10^{-3}\)
neutron-proton magnetic moment ratio
\(\frac{\mu_n}{\mu_p}\)
\(-0.68497934\)
neutron-muon rest mass ratio
\(\frac{m_n}{m_\mu}\)
\(8.89248478\)
neutron-tau rest mass ratio
\(\frac{m_n}{m_r}\)
\(0.528722\)
neutron-shielded proton magnetic moment ratio (H\(2\)O sphere 298.15 [K]
\(\frac{\mu_n}{\mu_p^{'}}\)
\(0.68499694\)
neutron gyromagnetic ratio
\(\gamma\)
\(1.83247188 \times 10^{-8} \left[\frac{1}{\mathrm{s}\mathrm{T}}\right]\)
neutron Lande factor (g-factor)
\(g_n\)
\(-3.82608545\)
muon rest mass
\(m_\mu\)
\(1.88353109 \times 10^{-28} [\mathrm{kg}]\)
\(0.1134289168 [\mathrm{u}]\)
\(105.658389 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]\)
muon molar mass
\(M_\mu\)
\(0.1134289168 \times 10^{-3} \left[\frac{\mathrm{kg}}{\mathrm{mol}}\right]\)
muon mean life time
\(\tau\)
\(2.19703 \times 10^{-6} [\mathrm{s}]\)
muon-electron rest mass ratio
\(\frac{m_\mu}{m_e}\)
\(206.7682657\)
muon-tau rest mass ratio
\(\frac{m_\mu}{m_\tau}\)
\(5.94572 \times 10^{-2}\)
muon-proton rest mass ratio
\(\frac{m_\mu}{m_p}\)
\(0.1126095173\)
muon-neutron rest mass ratio
\(\frac{m_\mu}{m_n}\)
\(0.1124545079\)
muon magnetic moment
\(\mu_\mu\)
\(4.49044813 \times 10^{-26} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(4.84197085 \times 10^{-3} \mu_B\)
\(8.89059770 \mu_N\)
muon magnetic moment anomaly
\(a_\mu = \left[\frac{\mu_\mu}{\frac{\hbar e}{2 m_\mu}}\right] -1\)
\(1.16591602 \times 10^{-3}\)
muon Lande factor (g-factor)
\(g_\mu = 2(1+a_\mu)\)
\(2.0023318320\)
muon-proton magnetic moment ratio
\(\frac{\mu_\mu}{\mu_p}\)
\(-3.18334539\)
deuteron rest mass
\(m_d\)
\(3.34358309 \times 10^{-27} [\mathrm{kg}]\)
\(2.013553212171 [\mathrm{u}]\)
\(1875.612762 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]\)
deuteron molar mass
\(M_d\)
\(2.013553212171 [\mathrm{u}]\)
deuteron-electron rest mass ratio
\(\frac{m_d}{m_e}\)
\(3670.4829550\)
deuteron-proton rest mass ratio
\(\frac{m_d}{m_p}\)
\(1.99900750083\)
deuteron magnetic moment
\(\mu_d\)
\(0.433073457 \times 10^{-26} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(0.4669754556 \times 10^{-3} \mu_B\)
\(0.8574382284 \mu_N\)
detueron-electron magnetic moment ratio
\(\frac{\mu_d}{\mu_e}\)
\(0.4664345537 \times 10^{-3}\)
deuteron-proton magnetic moment ratio
\(\frac{\mu_d}{\mu_p}\)
\(0.3070122083\)
deuteron-neutron magnetic moment ratio
\(\frac{\mu_d}{\mu_n}\)
\(-0.44820652\)
Helion rest mass
\(m_h\)
\(5.00641174 \times 10^{-27} [\mathrm{kg}]\)
\(3.01493223469 [\mathrm{u}]\)
\(2808.39132 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]\)
Helion molar mass
\(M_h = N_Am_h\)
\(3.01493223469 \times 10^{-3} \left[\frac{\mathrm{kg}}{\mathrm{mol}}\right]\)
Helion-electron rest mass ratio
\(\frac{m_h}{m_e}\)
\(5495.885238\)
Helion-proton rest mass ratio
\(\frac{m_h}{m_p}\)
\(2.99315265850\)
Helion shielded magnetic moment (gas sphere 298.15 [K])
\(\mu_h^{'}\)
\(-1.074552967 \times 10^{-26} \left[\frac{\mathrm{J}}{\mathrm{T}}\right]\)
\(-1.158671474 \times 10^{-3} \mu_B\)
\(-2.127497718 \mu_N\)
Shielded helion-proton magnetic moment ratio (gas sphere 298.15 [K])
\(\frac{\mu_h^{'}}{\mu_p}\)
\(-0.761766563\)
Shielded helion-shielded proton magnetic moment ratio (gas sphere 298.15 [K])
\(\frac{\mu_h^{'}}{\mu_p^{'}}\)
\(-0.7617861313\)
Shielded helion gyromagnetic ratio
\(\gamma_h = \frac{4\pi\mu_h}{h}\)
\(2.037894764 \times 10^8 \left[\frac{1}{\mathrm{s}\mathrm{T}}\right]\)
alpha particle rest mass
\(m_\alpha\)
\(6.64465598 \times 10^{-27} [\mathrm{kg}]\)
\(4.0015061747 [\mathrm{u}]\)
\(3727.37904 \left[\frac{\mathrm{MeV}}{\mathrm{c}^2}\right]\)
alpha particle molar mass
\(M_\alpha = N_A m_\alpha\)
\(4.0015061747 \times 10^{-3} \left[\frac{\mathrm{kg}}{\mathrm{mol}}\right]\)
Alpha particle-electron rest mass ratio
\(\frac{m_\alpha}{m_e}\)
\(7294.299508\)
alpha particle-proton rest mass ratio
\(\frac{m_\alpha}{m_p}\)
\(3.9725996846\)

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