# Fundamental Constants

Fundamental ConstantsNote: These constants are the values recommended in 2006 by CODATA, based on a least-squares adjustment of data from different measurements. The numbers in parentheses for the values represent the uncertainties of the last two digits.
Quantity Symbol Value
Atomic mass unit u $\begin{array}{c}1.660 538 782\,(83)\times {10}^{-27}\,\text{kg}\hfill \\ 931.494 028\,(23)\,\text{MeV/}{c}^{2}\hfill \end{array}$
Avogadro’s number ${N}_{\text{A}}$ $6.022 141 79\,(30)\times {10}^{23}\,\text{particles/mol}$
Bohr magneton ${\mu }_{\text{B}}=\frac{e\hslash }{2{m}_{e}}$ $9.274 009 15\,(23)\times {10}^{-24}\,\text{J/T}$
Bohr radius ${a}_{0}=\frac{{\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}}$ $5.291 772 085 9\,(36)\times {10}^{-11}\,\text{m}$
Boltzmann’s constant ${k}_{\text{B}}=\frac{R}{{N}_{\text{A}}}$ $1.380 650 4\,(24)\times {10}^{-23}\,\text{J/K}$
Compton wavelength ${\lambda }_{\text{C}}=\frac{h}{{m}_{e}c}$ $2.426 310 217 5\,(33)\times {10}^{-12}\,\text{m}$
Coulomb constant ${k}_{e}=\frac{1}{4\pi {\text{ε}}_{0}}$ $8.987 551 788...\times {10}^{9}\,\text{N}\cdot {\text{m}}^{2}{\text{/C}}^{2}(\text{exact})$
Deuteron mass ${m}_{d}$ $\begin{array}{c}3.343 583 20\,(17)\times {10}^{-27}\,\text{kg}\hfill \\ 2.013 553 212 724(78)\,\text{u}\hfill \\ 1875.612 859\,\text{MeV/}{c}^{2}\hfill \end{array}$
Electron mass ${m}_{e}$ $\begin{array}{c}9.109 382 15\,(45)\times {10}^{-31}\,\text{kg}\hfill \\ 5.485 799 094 3(23)\times {10}^{-4}\,\text{u}\hfill \\ 0.510 998 910\,(13)\,\text{MeV/}{c}^{2}\hfill \end{array}$
Electron volt eV $1.602 176 487\,(40)\times {10}^{-19}\,\text{J}$
Elementary charge e $1.602 176 487\,(40)\times {10}^{-19}\,\text{C}$
Gas constant R $8.314 472\,(15)\,\text{J/mol}\cdot \text{K}$
Gravitational constant G $6.674 28\,(67)\times {10}^{-11}\,\text{N}\cdot {\text{m}}^{2}{\text{/kg}}^{2}$
Neutron mass ${m}_{n}$ $\begin{array}{c}1.674 927 211\,(84)\times {10}^{-27}\,\text{kg}\hfill \\ 1.008 664 915 97\,(43)\,\text{u}\hfill \\ 939.565 346\,(23)\,\text{MeV/}{c}^{2}\hfill \end{array}$
Nuclear magneton ${\mu }_{n}=\frac{e\hslash }{2{m}_{p}}$ $5.050 783 24\,(13)\times {10}^{-27}\,\text{J/T}$
Permeability of free space ${\mu }_{0}$ $4\pi \times {10}^{-7}\,\text{T}\cdot \text{m/A}(\text{exact})$
Permittivity of free space ${\text{ε}}_{0}=\frac{1}{{\mu }_{0}{c}^{2}}$ $8.854 187 817...\times {10}^{-12}\,{\text{C}}^{2}\text{/}\text{N}\cdot {\text{m}}^{2}(\text{exact})$
Planck’s constant h

$\hslash =\frac{h}{2\pi }$

$\begin{array}{c}6.626 068 96\,(33)\times {10}^{-34}\,\text{J}\cdot \text{s}\hfill \\ 1.054 571 628\,(53)\times {10}^{-34}\,\text{J}\cdot \text{s}\hfill \end{array}$
Proton mass ${m}_{p}$ $\begin{array}{c}1.672 621 637\,(83)\times {10}^{-27}\,\text{kg}\hfill \\ 1.007 276 466 77\,(10)\,\text{u}\hfill \\ 938.272 013\,(23)\,\text{MeV/}{c}^{2}\hfill \end{array}$
Rydberg constant ${R}_{\text{H}}$ $1.097 373 156 852 7\,(73)\times {10}^{7}\,{\text{m}}^{-1}$
Speed of light in vacuum c $2.997 924 58\times {10}^{8}\,\text{m/s}\,(\text{exact})$

Useful combinations of constants for calculations:

$hc=12,400\,\text{eV}\cdot Å=1240\,\text{eV}\cdot \text{nm}=1240\,\text{MeV}\cdot \text{fm}$

$\hslash c=1973\,\text{eV}\cdot Å=197.3\,\text{eV}\cdot \text{nm}=197.3\,\text{MeV}\cdot \text{fm}$

${k}_{e}{e}^{2}=14.40\,\text{eV}\cdot Å=1.440\,\text{eV}\cdot \text{nm}=1.440\,\text{MeV}\cdot \text{fm}$

${k}_{\text{B}}T=0.02585\,\text{eV at}\,T=300\,\text{K}$