# List of physical constants

## Table of physical constants

Symbol Quantity Value[1] Relative
standard
uncertainty
Group
${\displaystyle c}$  speed of light in vacuum 299792458 m⋅s−1[2] 0 ud
${\displaystyle h}$  Planck constant 6.62607015×10−34 J⋅s[3] 0 ud   f
${\displaystyle \hbar =h/2\pi }$  reduced Planck constant 1.054571817...×10−34 J⋅s[4] 0 ud   f
${\displaystyle G}$  Newtonian constant of gravitation 6.67430(15)×10−11 m3⋅kg−1⋅s−2[5] 2.2×10−5 u    f
${\displaystyle \varepsilon _{0}=1/\mu _{0}c^{2}}$  vacuum electric permittivity 8.8541878128(13)×10−12 F⋅m−1[6] 1.5×10−10 u    f
${\displaystyle \mu _{0}}$  vacuum magnetic permeability 1.25663706212(19)×10−6 N⋅A−2[7] 1.5×10−10 u    f
${\displaystyle Z_{0}=\mu _{0}c}$  characteristic impedance of vacuum 376.730313668(57) Ω[8] 1.5×10−10 u
${\displaystyle e,q_{\text{e}}}$  elementary charge 1.602176634×10−19 C[9] 0  de  f
${\displaystyle \Delta \nu _{\text{Cs}}}$  hyperfine transition frequency of 133Cs 9192631770 Hz[10] 0  d
${\displaystyle N_{\text{A}},L}$  Avogadro constant 6.02214076×1023 mol−1[11] 0  d  pf
${\displaystyle k,k_{\text{B}}}$  Boltzmann constant 1.380649×10−23 J⋅K−1[12] 0  d  pf
${\displaystyle G_{0}=2e^{2}/h}$  conductance quantum 7.748091729...×10−5 S[13] 0   e  f
${\displaystyle K_{\mathrm {J} }=2e/h}$  Josephson constant 483597.8484...×109 Hz⋅V−1[14] 0   e  f
${\displaystyle R_{\mathrm {K} }=h/e^{2}}$  von Klitzing constant 25812.80745... Ω[15] 0   e  f
${\displaystyle \Phi _{0}=h/2e}$  magnetic flux quantum 2.067833848...×10−15 Wb[16] 0   e  f
${\displaystyle G_{0}^{-1}=h/2e^{2}}$  inverse conductance quantum 12906.40372... Ω[17] 0   e
${\displaystyle \mu _{\mathrm {B} }=e\hbar /2m_{\mathrm {e} }}$  Bohr magneton 9.2740100783(28)×10−24 J⋅T−1[18] 3.0×10−10   e
${\displaystyle \mu _{\mathrm {N} }=e\hbar /2m_{\mathrm {p} }}$  nuclear magneton 5.0507837461(15)×10−27 J⋅T−1[19] 3.1×10−10   e
${\displaystyle \alpha =e^{2}/4\pi \varepsilon _{0}\hbar c}$  fine-structure constant 7.2973525693(11)×10−3[20] 1.5×10−10    a f
${\displaystyle \alpha ^{-1}}$  inverse fine-structure constant 137.035999084(21)[21] 1.5×10−10    a f
${\displaystyle m_{\mathrm {e} }}$  electron mass 9.1093837015(28)×10−31 kg[22] 3.0×10−10    a f
${\displaystyle m_{\mathrm {p} }}$  proton mass 1.67262192369(51)×10−27 kg[23] 3.1×10−10    a f
${\displaystyle m_{\mathrm {n} }}$  neutron mass 1.67492749804(95)×10−27 kg[24] 5.7×10−10    a
${\displaystyle a_{0}=\hbar /\alpha m_{\text{e}}c}$  Bohr radius 5.29177210903(80)×10−11 m[25] 1.5×10−10    a
${\displaystyle r_{\mathrm {e} }=e^{2}/4\pi \varepsilon _{0}m_{\mathrm {e} }c^{2}}$  classical electron radius 2.8179403262(13)×10−15 m[26] 4.5×10−10    a
${\displaystyle g_{\mathrm {e} }}$  electron g-factor −2.00231930436256(35)[27] 1.7×10−13    a
${\displaystyle G_{\mathrm {F} }/(\hbar c)^{3}}$  Fermi coupling constant 1.1663787(6)×10−5 GeV−2[28] 5.1×10−7    a
${\displaystyle E_{\mathrm {h} }=2R_{\infty }hc}$  Hartree energy 4.3597447222071(85)×10−18 J[29] 1.9×10−12    a
${\displaystyle h/2m_{\mathrm {e} }}$  quantum of circulation 3.6369475516(11)×10−4 m2⋅s−1[30] 3.0×10−10    a
${\displaystyle R_{\infty }=\alpha ^{2}m_{\mathrm {e} }c/2h}$  Rydberg constant 10973731.568160(21) m−1[31] 1.9×10−12    a
${\displaystyle \sigma _{\text{e}}=(8\pi /3)r_{\mathrm {e} }^{2}}$  Thomson cross section 6.6524587321(60)×10−29 m2[32] 9.1×10−10    a
${\displaystyle m_{\mathrm {W} }/m_{\mathrm {Z} }}$  W-to-Z mass ratio 0.88153(17)[33] 1.9×10−4
${\displaystyle \sin ^{2}\theta _{\mathrm {W} }=1-(m_{\mathrm {W} }/m_{\mathrm {Z} })^{2}}$  weak mixing angle 0.22290(30)[34] 1.3×10−3    a
${\displaystyle m_{\text{u}}=1\,{\text{Da}}}$  atomic mass constant 1.66053906660(50)×10−27 kg[35] 3.0×10−10     pf
${\displaystyle F=N_{\text{A}}e}$  Faraday constant 96485.33212... C⋅mol−1[36] 0     pf
${\displaystyle R=N_{\text{A}}k_{\text{B}}}$  molar gas constant 8.314462618... J⋅mol−1⋅K−1[37] 0     pf
${\displaystyle M_{\text{u}}=M({}^{12}{\text{C}})/12}$  molar mass constant 0.99999999965(30)×10−3 kg⋅mol−1[38] 3.0×10−10     pf
${\displaystyle \sigma =\pi ^{2}k^{4}/60\hbar ^{3}c^{2}}$  Stefan–Boltzmann constant 5.670374419...×10−8 W⋅m−2⋅K−4[39] 0     pf
${\displaystyle c_{1}=2\pi hc^{2}}$  first radiation constant 3.741771852...×10−16 W⋅m2[40] 0     p
${\displaystyle c_{\text{1L}}=c_{1}/\pi }$  first radiation constant for spectral radiance 1.191042972...×10−16 W⋅m2⋅sr−1[41] 0     p
${\displaystyle M({}^{12}{\text{C}})=N_{\text{A}}m({}^{12}{\text{C}})}$  molar mass of carbon-12 11.9999999958(36)×10−3 kg⋅mol−1[42] 3.0×10−10     p
${\displaystyle N_{\text{A}}h}$  molar Planck constant 3.990312712...×10−10 J⋅Hz−1⋅mol−1[43] 0     p
${\displaystyle c_{2}=hc/k}$  second radiation constant 1.438776877...×10−2 m⋅K[44] 0     p
${\displaystyle b}$  Wien wavelength displacement law constant 2.897771955...×10−3 m⋅K[45] 0     p
${\displaystyle b'}$  Wien frequency displacement law constant 5.878925757...×1010 Hz⋅K−1[46] 0     p
${\displaystyle b_{\text{entropy}}}$  Wien entropy displacement law constant 3.002916077...×10−3 m⋅K[47] 0     p

'Group' reflects categorization on the NIST website:[48]

u: universal
d: defined
e: electromagnetic
a: atomic and nuclear
p: physico-chemical
f: frequently used
n: non-SI units

There are some notable omissions in the site's classification: the speed of light (f), vacuum electric permittivity (e), vacuum magnetic permeability (e), hyperfine transition frequency of 133Cs (p).

## References

1. ^ The values are given in the so-called concise form; the number in parentheses is the standard uncertainty and indicates the amount by which the least significant digits of the value are uncertain.
2. ^ "2018 CODATA Value: speed of light in vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
3. ^ "2018 CODATA Value: Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
4. ^ "2018 CODATA Value: reduced Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-28.
5. ^ "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
6. ^ "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
7. ^ "2018 CODATA Value: vacuum magnetic permeability". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
8. ^ "2018 CODATA Value: characteristic impedance of vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-10-31.
9. ^ "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
10. ^ "2018 CODATA Value: hyperfine transition frequency of Cs-133". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-18.
11. ^ "2018 CODATA Value: Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
12. ^ "2018 CODATA Value: Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
13. ^ "2018 CODATA Value: conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
14. ^ "2018 CODATA Value: Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
15. ^ "2018 CODATA Value: von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
16. ^ "2018 CODATA Value: magnetic flux quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
17. ^ "2018 CODATA Value: inverse of conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
18. ^ "2018 CODATA Value: Bohr magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
19. ^ "2018 CODATA Value: nuclear magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
20. ^ "2018 CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
21. ^ "2018 CODATA Value: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
22. ^ "2018 CODATA Value: electron mass in u". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
23. ^ "2018 CODATA Value: proton mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
24. ^ "2018 CODATA Value: neutron mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-23.
25. ^ "2018 CODATA Value: Bohr radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
26. ^ "2018 CODATA Value: classical electron radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
27. ^ "2018 CODATA Value: electron g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-03-13.
28. ^ "2018 CODATA Value: Fermi coupling constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
29. ^ "2018 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
30. ^ "2018 CODATA Value: quantum of circulation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
31. ^ "2018 CODATA Value: Rydberg constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
32. ^ "2018 CODATA Value: Thomson cross section". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
33. ^ "2018 CODATA Value: W to Z mass ratio". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-12-21.
34. ^ "2018 CODATA Value: weak mixing angle". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
35. ^ "2018 CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
36. ^ "2018 CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
37. ^ "2018 CODATA Value: molar gas constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
38. ^ "2018 CODATA Value: molar mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
39. ^ "2018 CODATA Value: Stefan–Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
40. ^ "2018 CODATA Value: first radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
41. ^ "2018 CODATA Value: first radiation constant for spectral radiance". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
42. ^ "2018 CODATA Value: molar mass of carbon-12". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
43. ^ "2018 CODATA Value: molar Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
44. ^ "2018 CODATA Value: second radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
45. ^ "2018 CODATA Value: Wien wavelength displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
46. ^ "2018 CODATA Value: Wien frequency displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
47. ^ Delgado-Bonal A (May 2017). "Entropy of radiation: the unseen side of light". Scientific Reports. 7 (1): 1642. Bibcode:2017NatSR...7.1642D. doi:10.1038/s41598-017-01622-6. PMC 5432030. PMID 28490790.
48. ^