# Template:Physical constants

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This template provides easy inclusion of the latest CODATA recommended values of physical constants in articles. It gives the most recent values published, and will be updated when newer values become available, which is typically every four years.

The values have been updated to the CODATA 2018 values. This includes the 2019 redefinition of SI base units, which made the values of several constants exact (e.g. e), whereas some previously exactly defined constants acquired an uncertainty (e.g. μ0).

### Usage

#### Arguments

`symbol`
If set to `yes`, the value is preceded by the symbol of the constant, followed by or = depending on whether or not `round` is set.
`round`
If omitted, the value is shown along with its standard uncertainty. If set to an integer n, the value is rounded to the first n digits after the decimal point (retaining trailing zeros).
`unit`
If set to `no`, the unit of measurement is not shown.
`ref`
If set to `no`, no reference is given. If set to `only`, only the reference is given.
`after`
Text (e.g. punctuation) to be shown after the constant before the reference.
`runc`
If set to `yes`, this will provide only the relative standard uncertainty of the value and its reference.

#### Available constants

Code Constant Value Relative standard uncertainty
`a0` Bohr radius a0 = 5.29177210903(80)×10−11 m ur(a0) = 1.5×10−10[1]
`alpha` fine-structure constant α = 7.2973525693(11)×10−3 ur(α) = 1.5×10−10[2]
`A90` conventional ampere A90 = 1.00000008887... A ur(A90) = 0[3]
`atm` standard atmosphere atm = 101325 Pa ur(atm) = 0[4]
`bwien` Wien wavelength displacement law constant b = 2.897771955...×10−3 m⋅K ur(b) = 0[5]
`bwien'` Wien frequency displacement law constant b′ = 5.878925757...×1010 Hz⋅K−1 ur(b′) = 0[6]
`c` speed of light c = 299792458 m⋅s−1 ur(c) = 0[7]
`c1` first radiation constant c1 = 3.741771852...×10−16 W⋅m2 ur(c1) = 0[8]
`c1L` first radiation constant for spectral radiance c1L = 1.191042972...×10−16 W⋅m2⋅sr−1 ur(c1L) = 0[9]
`c2` second radiation constant c2 = 1.438776877...×10−2 m⋅K ur(c2) = 0[10]
`C90` conventional coulomb C90 = 1.00000008887... C ur(C90) = 0[11]
`DnuCs` hyperfine structure transition frequency of caesium-133 Δν(133Cs)hfs = 9192631770 Hz urν(133Cs)hfs) = 0[12]
`e` elementary charge e = 1.602176634×10−19 C ur(e) = 0[13]
`Eh` Hartree energy Eh = 4.3597447222071(85)×10−18 J ur(Eh) = 1.9×10−12[14]
`EheV` Hartree energy in eV Eh = 27.211386245988(53) eV ur(Eh) = 1.9×10−12[15]
`eps0` vacuum electric permittivity ε0 = 8.8541878128(13)×10−12 F⋅m−1 ur(ε0) = 1.5×10−10[16]
`eV` electronvolt eV = 1.602176634×10−19 J ur(eV) = 0[17]
`F` Faraday constant F = 96485.33212... C⋅mol−1 ur(F) = 0[18]
`F90` conventional farad F90 = 0.99999998220... F ur(F90) = 0[19]
`G` gravitational constant G = 6.67430(15)×10−11 m3⋅kg−1⋅s−2 ur(G) = 2.2×10−5[20]
`G0` conductance quantum G0 = 7.748091729...×10−5 S ur(G0) = 0[21]
`g0` standard acceleration of gravity g0 = 9.80665 m⋅s−2 ur(g0) = 0[22]
`ge` electron g-factor ge = −2.00231930436256(35) ur(ge) = 1.7×10−13[23]
`GF/hbarc3` Fermi coupling constant GF/(ħc)3 = 1.1663787(6)×10−5 GeV−2 ur(GF/(ħc)3) = 5.1×10−7[24]
`gmu` muon g-factor gμ = −2.0023318418(13) ur(gμ) = 6.3×10−10[25]
`gp` proton g-factor gp = 5.5856946893(16) ur(gp) = 2.9×10−10[26]
`h` Planck constant h = 6.62607015×10−34 J⋅s ur(h) = 0[27]
`H90` conventional henry H90 = 1.00000001779... H ur(H90) = 0[28]
`hbar` reduced Planck constant ħ = 1.054571817...×10−34 J⋅s ur(ħ) = 0[29]
`h/2me` quantum of circulation h/2me = 3.6369475516(11)×10−4 m2⋅s−1 ur(h/2me) = 3.0×10−10[30]
`invalpha` inverse fine-structure constant 1/α = 137.035999084(21) ur(1/α) = 1.5×10−10[31]
`invG0` inverse conductance quantum G0−1 = 12906.40372... Ω ur(G0−1) = 0[32]
`k` Boltzmann constant k = 1.380649×10−23 J⋅K−1 ur(k) = 0[33]
`KJ` Josephson constant KJ = 483597.8484...×109 Hz⋅V−1 ur(KJ) = 0[34]
`KJ90` conventional value of Josephson constant KJ-90 = 483597.9×109 Hz⋅V−1 ur(KJ-90) = 0[35]
`lP` Planck length lP = 1.616255(18)×10−35 m ur(lP) = 1.1×10−5[36]
`MC12` molar mass of carbon-12 M(12C) = 11.9999999958(36)×10−3 kg⋅mol−1 ur(M(12C)) = 3.0×10−10[37]
`me` electron mass me = 9.1093837015(28)×10−31 kg ur(me) = 3.0×10−10[38]
`meDa` electron mass in daltons me = 5.48579909065(16)×10−4 Da ur(me) = 2.9×10−11[39]
`mmu` muon mass mμ = 1.883531627(42)×10−28 kg ur(mμ) = 2.2×10−8[40]
`mn` neutron mass mn = 1.67492749804(95)×10−27 kg ur(mn) = 5.7×10−10[41]
`mnDa` neutron mass in daltons mn = 1.00866491595(49) Da ur(mn) = 4.8×10−10[42]
`mP` Planck mass mP = 2.176434(24)×10−8 kg ur(mP) = 1.1×10−5[43]
`mp` proton mass mp = 1.67262192369(51)×10−27 kg ur(mp) = 3.1×10−10[44]
`mpome` proton-to-electron mass ratio mp/me = 1836.15267343(11) ur(mp/me) = 6.0×10−11[45]
`mtau` tau mass mτ = 3.16754(21)×10−27 kg ur(mτ) = 6.8×10−5[46]
`Mu` molar mass constant Mu = 0.99999999965(30)×10−3 kg⋅mol−1 ur(Mu) = 3.0×10−10[47]
`mu` atomic mass constant mu = 1.66053906660(50)×10−27 kg ur(mu) = 3.0×10−10[48]
`muc2` atomic mass constant energy equivalent muc2 = 1.49241808560(45)×10−10 J ur(muc2) = 3.0×10−10[49]
`mueV` atomic mass constant energy equivalent in MeV muc2 = 931.49410242(28) MeV ur(muc2) = 3.0×10−10[50]
`mu0` vacuum magnetic permeability μ0 = 1.25663706212(19)×10−6 N⋅A−2 ur(μ0) = 1.5×10−10[51]
`muB` Bohr magneton μB = 9.2740100783(28)×10−24 J⋅T−1 ur(μB) = 3.0×10−10[52]
`muN` nuclear magneton μN = 5.0507837461(15)×10−27 J⋅T−1 ur(μN) = 3.1×10−10[53]
`mW/mZ` W-to-Z mass ratio mW/mZ = 0.88153(17) ur(mW/mZ) = 1.9×10−4[54]
`NA` Avogadro constant NA = 6.02214076×1023 mol−1 ur(NA) = 0[55]
`NAh` molar Planck constant NAh = 3.990312712...×10−10 J⋅Hz−1⋅mol−1 ur(NAh) = 0[56]
`ohm90` conventional ohm Ω90 = 1.00000001779... Ω ur(Ω90) = 0[57]
`Phi0` magnetic flux quantum Φ0 = 2.067833848...×10−15 Wb ur(Φ0) = 0[58]
`R` molar gas constant R = 8.314462618... J⋅mol−1⋅K−1 ur(R) = 0[59]
`re` classical electron radius re = 2.8179403262(13)×10−15 m ur(re) = 4.5×10−10[60]
`Rinf` Rydberg constant R = 10973731.568160(21) m−1 ur(R) = 1.9×10−12[61]
`RK` von Klitzing constant RK = 25812.80745... Ω ur(RK) = 0[62]
`RK90` conventional value of von Klitzing constant RK-90 = 25812.807 Ω ur(RK-90) = 0[63]
`sigma` Stefan–Boltzmann constant σ = 5.670374419...×10−8 W⋅m−2⋅K−4 ur(σ) = 0[64]
`sigmae` Thomson cross section σe = 6.6524587321(60)×10−29 m2 ur(σe) = 9.1×10−10[65]
`TP` Planck temperature TP = 1.416784(16)×1032 K ur(TP) = 1.1×10−5[66]
`tP` Planck time tP = 5.391247(60)×10−44 s ur(tP) = 1.1×10−5[67]
`V90` conventional volt V90 = 1.00000010666... V ur(V90) = 0[68]
`VmSi` molar volume of silicon Vm(Si) = 1.205883199(60)×10−5 m3⋅mol−1 ur(Vm(Si)) = 4.9×10−8[69]
`W90` conventional watt W90 = 1.00000019553... W ur(W90) = 0[70]
`Z0` characteristic impedance of vacuum Z0 = 376.730313668(57) Ω ur(Z0) = 1.5×10−10[71]

#### Examples

`{{Physical constants|c|unit=no|after=&nbsp;[[metre per second|metres per second]].}}`

299792458 metres per second.[7]

`{{Physical constants|mu0|symbol=yes}}`

μ0 = 1.25663706212(19)×10−6 N⋅A−2[51]

`{{Physical constants|G|symbol=yes}}`

G = 6.67430(15)×10−11 m3⋅kg−1⋅s−2[20]

`{{Physical constants|hbar|round=2|symbol=yes}}`

ħ ≈ 1.05×10−34 J⋅s[29]

`The relative standard uncertainty of ''m''<sub>u</sub> is {{Physical constants|mu|runc=yes|after=.}}`

The relative standard uncertainty of mu is 3.0×10−10.[48]

`For the electron mass, {{Physical constants|me|runc=yes|symbol=yes|ref=no}}.`

For the electron mass, ur(me) = 3.0×10−10.

`NIST publishes the CODATA value of the [[elementary charge]].{{Physical constants|e|ref=only}}`

NIST publishes the CODATA value of the elementary charge.[13]

• /data, the subtemplate that holds all of the data
• {{CODATA2010}}, the older version of this template used for the 2010 values

### References

1. ^ "2018 CODATA Value: Bohr radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
2. ^ "2018 CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
3. ^ "2018 CODATA Value: conventional value of ampere-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-01.
4. ^ "2018 CODATA Value: standard atmosphere". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
5. ^ "2018 CODATA Value: Wien wavelength displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
6. ^ "2018 CODATA Value: Wien frequency displacement law constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
7. ^ a b "2018 CODATA Value: speed of light in vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
8. ^ "2018 CODATA Value: first radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
9. ^ "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.
10. ^ "2018 CODATA Value: second radiation constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
11. ^ "2018 CODATA Value: conventional value of coulomb-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-01.
12. ^ "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.
13. ^ a b "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
14. ^ "2018 CODATA Value: Hartree energy". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
15. ^ "2018 CODATA Value: Hartree energy in eV". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-09-01.
16. ^ "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
17. ^ "2018 CODATA Value: electron volt". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
18. ^ "2018 CODATA Value: Faraday constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
19. ^ "2018 CODATA Value: conventional value of farad-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-01.
20. ^ a b "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
21. ^ "2018 CODATA Value: conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
22. ^ "2018 CODATA Value: standard acceleration of gravity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
23. ^ "2018 CODATA Value: electron g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-03-13.
24. ^ "2018 CODATA Value: Fermi coupling constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
25. ^ "2018 CODATA Value: muon g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
26. ^ "2018 CODATA Value: proton g factor". The NIST Reference on Constants, Units, and Uncertainty. NIST. June 2015. Retrieved 2019-03-08.
27. ^ "2018 CODATA Value: Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
28. ^ "2018 CODATA Value: conventional value of henry-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-01.
29. ^ a b "2018 CODATA Value: reduced Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-28.
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: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
32. ^ "2018 CODATA Value: inverse of conductance quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
33. ^ "2018 CODATA Value: Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
34. ^ "2018 CODATA Value: Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
35. ^ "2018 CODATA Value: conventional value of Josephson constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
36. ^ "2018 CODATA Value: Planck length". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
37. ^ "2018 CODATA Value: molar mass of carbon-12". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
38. ^ "2018 CODATA Value: electron mass in u". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
39. ^ "2018 CODATA Value: electron mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-06-21.
40. ^ "2018 CODATA Value: muon mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
41. ^ "2018 CODATA Value: neutron mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-23.
42. ^ "2018 CODATA Value: neutron mass in u". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-06-24.
43. ^ "2018 CODATA Value: Planck mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
44. ^ "2018 CODATA Value: proton mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
45. ^ "2018 CODATA Value: proton-electron mass ratio". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
46. ^ "2018 CODATA Value: tau mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
47. ^ "2018 CODATA Value: molar mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
48. ^ a b "2018 CODATA Value: atomic mass constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
49. ^ "2018 CODATA Value: atomic mass constant energy equivalent". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-07-21.
50. ^ "2018 CODATA Value: atomic mass constant energy equivalent in MeV". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-07-21.
51. ^ a b "2018 CODATA Value: vacuum magnetic permeability". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
52. ^ "2018 CODATA Value: Bohr magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
53. ^ "2018 CODATA Value: nuclear magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
54. ^ "2018 CODATA Value: W to Z mass ratio". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-12-21.
55. ^ "2018 CODATA Value: Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
56. ^ "2018 CODATA Value: molar Planck constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
57. ^ "2018 CODATA Value: conventional value of ohm-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-01.
58. ^ "2018 CODATA Value: magnetic flux quantum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
59. ^ "2018 CODATA Value: molar gas constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
60. ^ "2018 CODATA Value: classical electron radius". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
61. ^ "2018 CODATA Value: Rydberg constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
62. ^ "2018 CODATA Value: von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
63. ^ "2018 CODATA Value: conventional value of von Klitzing constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
64. ^ "2018 CODATA Value: Stefan–Boltzmann constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
65. ^ "2018 CODATA Value: Thomson cross section". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
66. ^ "2018 CODATA Value: Planck temperature". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
67. ^ "2018 CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
68. ^ "2018 CODATA Value: conventional value of volt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-01.
69. ^ "2018 CODATA Value: molar volume of silicon". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-23.
70. ^ "2018 CODATA Value: conventional value of watt-90". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-06-01.
71. ^ "2018 CODATA Value: characteristic impedance of vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-10-31.