Contents

List of physical constants

Table of physical constants[edit]

Symbol	Quantity	Value[a][b]	Relative standard uncertainty	Ref[1]
${\displaystyle c}$	speed of light in vacuum	299792458 m⋅s−1	0	‍[2]
${\displaystyle h}$	Planck constant	6.62607015×10−34 J⋅Hz−1	0	‍[3]
${\displaystyle \hbar =h/2\pi }$	reduced Planck constant	1.054571817...×10−34 J⋅s	0	‍[4]
${\displaystyle \mu _{0}=4\pi \alpha \hbar /e^{2}c}$	vacuum magnetic permeability	1.25663706127(20)×10−6 N⋅A−2	1.6×10−10	‍[5]
${\displaystyle Z_{0}=4\pi \alpha \hbar /e^{2}}$	characteristic impedance of vacuum	376.730313412(59) Ω	1.6×10−10	‍[6]
${\displaystyle \varepsilon _{0}=e^{2}/4\pi \alpha \hbar c}$	vacuum electric permittivity	8.8541878188(14)×10−12 F⋅m−1	1.6×10−10	‍[7]
${\displaystyle k,k_{\text{B}}}$	Boltzmann constant	1.380649×10−23 J⋅K−1	0	‍[8]
${\displaystyle G}$	Newtonian constant of gravitation	6.67430(15)×10−11 m3⋅kg−1⋅s−2	2.2×10−5	‍[9]
${\displaystyle \Lambda }$	cosmological constant	1.089(29)×10−52 m−2 [c] 1.088(30)×10−52 m−2 [d]	0.027 0.028	[10] [11]
${\displaystyle \sigma =\pi ^{2}k_{\text{B}}^{4}/60\hbar ^{3}c^{2}}$	Stefan–Boltzmann constant	5.670374419...×10−8 W⋅m−2⋅K−4	0	‍[12]
${\displaystyle c_{1}=2\pi hc^{2}}$	first radiation constant	3.741771852...×10−16 W⋅m2	0	‍[13]
${\displaystyle c_{\text{1L}}=2hc^{2}/\mathrm {sr} }$	first radiation constant for spectral radiance	1.191042972...×10−16 W⋅m2⋅sr−1	0	‍[14]
${\displaystyle c_{2}=hc/k_{\text{B}}}$	second radiation constant	1.438776877...×10−2 m⋅K	0	‍[15]
${\displaystyle b}$ [e]	Wien wavelength displacement law constant	2.897771955...×10−3 m⋅K	0	‍[16]
${\displaystyle b'}$ [f]	Wien frequency displacement law constant	5.878925757...×1010 Hz⋅K−1	0	‍[17]
${\displaystyle b_{\text{entropy}}}$	Wien entropy displacement law constant	3.002916077...×10−3 m⋅K	0	[18]
${\displaystyle e}$	elementary charge	1.602176634×10−19 C	0	‍[19]
${\displaystyle G_{0}=2e^{2}/h}$	conductance quantum	7.748091729...×10−5 S	0	‍[20]
${\displaystyle G_{0}^{-1}=h/2e^{2}}$	inverse conductance quantum	12906.40372... Ω	0	‍[21]
${\displaystyle R_{\text{K}}=h/e^{2}}$	von Klitzing constant	25812.80745... Ω	0	‍[22]
${\displaystyle K_{\text{J}}=2e/h}$	Josephson constant	483597.8484...×109 Hz⋅V−1	0	‍[23]
${\displaystyle \Phi _{0}=h/2e}$	magnetic flux quantum	2.067833848...×10−15 Wb	0	‍[24]
${\displaystyle \alpha =e^{2}/4\pi \varepsilon _{0}\hbar c}$	fine-structure constant	0.0072973525643(11)	1.6×10−10	‍[25]
${\displaystyle \alpha ^{-1}}$	inverse fine-structure constant	137.035999177(21)	1.6×10−10	‍[26]
${\displaystyle m_{\text{e}}}$	electron mass	9.1093837139(28)×10−31 kg	3.1×10−10	‍[27]
${\displaystyle m_{\mu }}$	muon mass	1.883531627(42)×10−28 kg	2.2×10−8	‍[28]
${\displaystyle m_{\tau }}$	tau mass	3.16754(21)×10−27 kg	6.8×10−5	‍[29]
${\displaystyle m_{\text{p}}}$	proton mass	1.67262192595(52)×10−27 kg	3.1×10−10	‍[30]
${\displaystyle m_{\text{n}}}$	neutron mass	1.67492750056(85)×10−27 kg	5.1×10−10	‍[31]
${\displaystyle m_{\text{t}}}$	top quark mass	3.0784(53)×10−25 kg	1.7×10−3	[32]
${\displaystyle m_{\text{p}}/m_{\text{e}}}$	proton-to-electron mass ratio	1836.152673426(32)	1.7×10−11	‍[33]
${\displaystyle m_{\text{W}}/m_{\text{Z}}}$	W-to-Z mass ratio	0.88145(13)	1.5×10−4	‍[34]
${\displaystyle \sin ^{2}\theta _{\text{W}}}$ ${\displaystyle =1-(m_{\text{W}}/m_{\text{Z}})^{2}}$	sine-square weak mixing angle	0.22305(23) [g] 0.23121(4) [h] 0.23153(4) [i]	1.0×10−3 1.7×10−4 1.7×10−4	‍[35] [36] [36]
${\displaystyle g_{\text{e}}}$	electron g-factor	−2.00231930436092(36)	1.8×10−13	‍[37]
${\displaystyle g_{\mu }}$	muon g-factor	−2.00233184123(82)	4.1×10−10	‍[38]
${\displaystyle g_{\text{p}}}$	proton g-factor	5.5856946893(16)	2.9×10−10	‍[39]
${\displaystyle h/2m_{\text{e}}}$	quantum of circulation	3.6369475467(11)×10−4 m2⋅s−1	3.1×10−10	‍[40]
${\displaystyle \mu _{\text{B}}=e\hbar /2m_{\text{e}}}$	Bohr magneton	9.2740100657(29)×10−24 J⋅T−1	3.1×10−10	‍[41]
${\displaystyle \mu _{\text{N}}=e\hbar /2m_{\text{p}}}$	nuclear magneton	5.0507837393(16)×10−27 J⋅T−1	3.1×10−10	‍[42]
${\displaystyle r_{\text{e}}=\alpha \hbar /m_{\text{e}}c}$	classical electron radius	2.8179403205(13)×10−15 m	4.7×10−10	‍[43]
${\displaystyle \sigma _{\text{e}}=(8\pi /3)r_{\text{e}}^{2}}$	Thomson cross section	6.6524587051(62)×10−29 m2	9.3×10−10	‍[44]
${\displaystyle a_{0}=\hbar /\alpha m_{\text{e}}c}$	Bohr radius	5.29177210544(82)×10−11 m	1.6×10−10	‍[45]
${\displaystyle R_{\infty }=\alpha ^{2}m_{\text{e}}c/2h}$	Rydberg constant	10973731.568157(12) m−1	1.1×10−12	‍[46]
${\displaystyle \mathrm {Ry} =R_{\infty }hc=E_{\text{h}}/2}$	Rydberg unit of energy	2.1798723611030(24)×10−18 J	1.1×10−12	‍[47]
${\displaystyle E_{\text{h}}=\alpha ^{2}m_{\text{e}}c^{2}}$	Hartree energy	4.3597447222060(48)×10−18 J	1.1×10−12	‍[48]
${\displaystyle G_{\text{F}}/(\hbar c)^{3}}$	Fermi coupling constant	1.1663787(6)×10−5 GeV−2	5.1×10−7	‍[49]
${\displaystyle N_{\text{A}}}$	Avogadro constant	6.02214076×1023 mol−1	0	‍[50]
${\displaystyle R=N_{\text{A}}k_{\text{B}}}$	molar gas constant	8.31446261815324 J⋅mol−1⋅K−1	0	‍[51]
${\displaystyle F=N_{\text{A}}e}$	Faraday constant	96485.3321233100184 C⋅mol−1	0	‍[52]
${\displaystyle N_{\text{A}}h}$	molar Planck constant	3.9903127128934314×10−10 J⋅s⋅mol−1	0	‍[53]
${\displaystyle M({}^{12}{\text{C}})=N_{\text{A}}m({}^{12}{\text{C}})}$	molar massofcarbon-12	12.0000000126(37)×10−3 kg⋅mol−1	3.1×10−10	‍[54]
${\displaystyle m_{\text{u}}=m({}^{12}{\text{C}})/12}$	atomic mass constant	1.66053906892(52)×10−27 kg	3.1×10−10	‍[55]
${\displaystyle M_{\text{u}}=M({}^{12}{\text{C}})/12}$	molar mass constant	1.00000000105(31)×10−3 kg⋅mol−1	3.1×10−10	‍[56]
${\displaystyle V_{\text{m}}({\text{Si}})}$	molar volume of silicon	1.205883199(60)×10−5 m3⋅mol−1	4.9×10−8	‍[57]
${\displaystyle \Delta \nu _{\text{Cs}}}$	hyperfine transition frequency of 133Cs	9192631770 Hz	0	‍[58]

Uncertainties[edit]

While the values of the physical constants are independent of the system of units in use, each uncertainty as stated reflects our lack of knowledge of the corresponding value as expressed in SI units, and is strongly dependent on how those units are defined. For example, the atomic mass constant ${\displaystyle m_{\text{u}}}$ is exactly known when expressed using the dalton (its value is exactly 1 Da), but the kilogram is not exactly known when using these units, the opposite of when expressing the same quantities using the kilogram.

Technical constants[edit]

Some of these constants are of a technical nature and do not give any true physical property, but they are included for convenience. Such a constant gives the correspondence ratio of a technical dimension with its corresponding underlying physical dimension. These include the Boltzmann constant ${\displaystyle k_{\text{B}}}$, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant ${\displaystyle N_{\text{A}}}$, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless). By implication, any product of powers of such constants is also such a constant, such as the molar gas constant ${\displaystyle R}$.

See also[edit]

• List of mathematical constants
• Physical constant
• List of particles

Notes[edit]

^ ${\displaystyle b={\frac {hc}{k\left(5+W_{0}\left(-5e^{-5}\right)\right)}}}$, where ${\displaystyle W_{0}}$ is the principal branch of the Lambert W function.

^ ${\displaystyle b'=\left(3+W_{0}\left(-3e^{-3}\right)\right){\frac {k}{h}}}$, where ${\displaystyle W_{0}}$ is the principal branch of the Lambert W function.

References[edit]