physref

Frequently used fundamental constants

    Numbers in parentheses indicate the one-standard-deviation uncertainty in the last two digits of the value. Values without parentheses or a trailing ellipsis (...) are exact.

    speed of light in vacuum
    c=299 792 458  m s−1c = \text{299 792 458} ~ ~\text{m}~\text{s}^{-1}
    Newtonian constant of gravitation
    G=6.674 30(15)×10−11  m3 kg−1 s−2G = \text{6.674 30(15)} \times 10^{-11} ~ ~\text{m}^{3}~\text{kg}^{-1}~\text{s}^{-2}
    Planck constant
    h=6.626 070 15×10−34  J Hz−1h = \text{6.626 070 15} \times 10^{-34} ~ ~\text{J}~\text{Hz}^{-1}
    h=4.135 667 696...×10−15  eV Hz−1h = \text{4.135 667 696...} \times 10^{-15} ~ ~\text{eV}~\text{Hz}^{-1}
    ℏ=h2π=1.054 571 817...×10−34  J s\hbar = \frac{h}{2 \pi} = \text{1.054 571 817...} \times 10^{-34} ~ ~\text{J}~\text{s}
    ℏ=6.582 119 569...×10−16  eV s\hbar = \text{6.582 119 569...} \times 10^{-16} ~ ~\text{eV}~\text{s}
    elementary charge
    e=1.602 176 634×10−19  Ce = \text{1.602 176 634} \times 10^{-19} ~ ~\text{C}
    vacuum electric permittivity
    ϵ0=1μ0c2=8.854 187 812 8(13)×10−12  F m−1\epsilon_0 = \frac{1}{\mu_0 c^2} = \text{8.854 187 812 8(13)} \times 10^{-12} ~ ~\text{F}~\text{m}^{-1}
    vacuum magnetic permeability
    μ0=4παℏe2c=1.256 637 062 12(19)×10−6  N A−2\mu_0 = \frac{4 \pi \alpha \hbar}{e^2 c} = \text{1.256 637 062 12(19)} \times 10^{-6} ~ ~\text{N}~\text{A}^{-2}
    Josephson constant
    KJ=2eh=483 597.848 4...×109  Hz V−1K_{\text{J}} = \frac{2 e}{h} = \text{483 597.848 4...} \times 10^{9} ~ ~\text{Hz}~\text{V}^{-1}
    von Klitzing constant
    RK=μ0c2α=2πℏe2=25 812.807 45...  ΩR_{\text{K}} = \frac{\mu_0 c}{2 \alpha} = \frac{2 \pi \hbar}{e^2} = \text{25 812.807 45...} ~ ~\text{Ω}
    magnetic flux quantum
    Φ0=2πℏ(2e)=2.067 833 848...×10−15  Wb\varPhi_0 = \frac{2 \pi \hbar}{(2 e)} = \text{2.067 833 848...} \times 10^{-15} ~ ~\text{Wb}
    conductance quantum
    G0=2e22πℏ=7.748 091 729...×10−5  SG_0 = \frac{2 e^2}{2 \pi \hbar} = \text{7.748 091 729...} \times 10^{-5} ~ ~\text{S}
    electron mass
    me=9.109 383 7015(28)×10−31  kgm_e = \text{9.109 383 7015(28)} \times 10^{-31} ~ ~\text{kg}
    proton mass
    mp=1.672 621 923 69(51)×10−27  kgm_p = \text{1.672 621 923 69(51)} \times 10^{-27} ~ ~\text{kg}
    proton-electron mass ratio
    mp/me=1836.152 673 43(11) m_p/m_e = \text{1836.152 673 43(11)} ~
    fine-structure constant
    α=e24πϵ0ℏc=7.297 352 5693(11)×10−3 \alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c} = \text{7.297 352 5693(11)} \times 10^{-3} ~
    inverse fine-structure constant
    α−1=137.035 999 084(21) \alpha^{-1} = \text{137.035 999 084(21)} ~
    Rydberg frequency
    cR∞=α2mec22h=3.289 841 960 2508(64)×1015  HzcR_{\infty} = \frac{\alpha^2 m_e c^2}{2 h} = \text{3.289 841 960 2508(64)} \times 10^{15} ~ ~\text{Hz}
    Boltzmann constant
    k=RNA=1.380 649×10−23  J K−1k = \frac{R}{N_{\text{A}}} = \text{1.380 649} \times 10^{-23} ~ ~\text{J}~\text{K}^{-1}
    Avogadro constant
    NA=6.022 140 76×1023  mol−1N_{\text{A}} = \text{6.022 140 76} \times 10^{23} ~ ~\text{mol}^{-1}
    molar gas constant
    R=NAk=8.314 462 618...  J mol−1 K−1R = N_{\text{A}} k = \text{8.314 462 618...} ~ ~\text{J}~\text{mol}^{-1}~\text{K}^{-1}
    Faraday constant
    F=NAe=96 485.332 12...  C mol−1F = N_{\text{A}} e = \text{96 485.332 12...} ~ ~\text{C}~\text{mol}^{-1}
    Stefan-Boltzmann constant
    σ=π2k460ℏ3c2=5.670 374 419×10−8  W m−2 K−4\sigma = \frac{\pi^2 k^4}{60 \hbar^3 c^2} = \text{5.670 374 419} \times 10^{-8} ~ ~\text{W}~\text{m}^{-2}~\text{K}^{-4}
    Bohr magneton
    μB=eℏ2me=9.274 010 0783(28)×10−24  J T−1\mu_{\text{B}} = \frac{e \hbar}{2 m_e} = \text{9.274 010 0783(28)} \times 10^{-24} ~ ~\text{J}~\text{T}^{-1}
    μB=5.788 381 8060(17)×10−5  eV T−1\mu_{\text{B}} = \text{5.788 381 8060(17)} \times 10^{-5} ~ ~\text{eV}~\text{T}^{-1}
    nuclear magneton
    μN=eℏ2mp=5.050 783 7461(15)×10−27  J T−1\mu_{\text{N}} = \frac{e \hbar}{2 m_p} = \text{5.050 783 7461(15)} \times 10^{-27} ~ ~\text{J}~\text{T}^{-1}
    μN=3.152 451 258 44(96)×10−8  eV T−1\mu_{\text{N}} = \text{3.152 451 258 44(96)} \times 10^{-8} ~ ~\text{eV}~\text{T}^{-1}
    electron volt
    eV=eCJ=1.602 176 634×10−19  J\text{eV} = \frac{e}{\text{C}} \text{J} = \text{1.602 176 634} \times 10^{-19} ~ ~\text{J}
    (unifited) atomic mass unit
    u=m12(12C)=1.660 539 066 60(50)×10−27  kg\text{u} = \frac{m}{12}(^{12}\text{C}) = \text{1.660 539 066 60(50)} \times 10^{-27} ~ ~\text{kg}

    References