1. Physical Constants

11. Physical Constants
Table 1.1: Revised 2024 by D. Robinson (LBNL) and P.A. Zyla (LBNL). Mainly from “CODATA Recommended Values of theFundamental Physical Constants: 2018,” E. Tiesinga, D.B. Newell, P.J. Mohr, and B.N. Taylor, NIST SP961 (May 2019) [1].a The
electron charge magnitude e, and the Planck, Boltzmann, and Avogadro constants h, k, and NA , now join c as having defined values; thefree-space permittivity and permeability constants 0 and µ0 are no longer exact. These changes affect practically everything else in theTable. Figures in parentheses after the values are the 1-standard-deviation uncertainties in the last digits; the fractional uncertainties inparts per 109 (ppb) are in the last column. The full 2018 CODATA Committee on Data for Science and Technology set of constants arefound at https://physics.nist.gov/cuu/Constants/archive2018.html. The last set of constants (beginning with the Fermi coupling
constant) comes from the Particle Data Group. See also “The International System of Units (SI),” 9th ed. (2019) of the International
Bureau of Weights and Measures (BIPM), https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf.
Quantity
speed of light in vacuum
Planck constantPlanck constant, reduced

Symbol, equationch~ ≡ h/2π

electron charge magnitude
conversion constantconversion constantelectron mass
proton masse~c(~c)2me
mp

neutron massdeuteron mass
unified atomic mass unit∗∗
permittivity of free spacepermeability of free spacefine-structure constantclassical electron radiusmnmd
u = (mass 12 C atom)/12
0 = 1/µ0 c2µ0 /(4π × 10−7 )α = e2 /4π0 ~c
re = e2 /4π0 me c2−λe = ~/me c = re α−1a∞ = 4π0 ~2 /me e2 = re α−2hc/(1 eV)
hcR∞ = me e4 /2(4π0 )2 ~2 = me c2 α2 /2σT = 8πre2 /3µB = e~/2meµN = e~/2mpeωcycl/B = e/mep
ωcycl/B = e/mpGN(e− Compton wavelength)/2π
Bohr radius (mnucleus = ∞)wavelength of 1 eV/c particle
Rydberg energyThomson cross section
Bohr magneton
nuclear magneton
electron cyclotron freq./field
proton cyclotron freq./field
gravitational constant‡ValueUncertainty (ppb)299 792 458 m s−1
exact
6.626 070 15×10−34 J s (or J/Hz) §exact
1.054 571 817. . . × 10−34 J sexact∗= 6.582 119 569. . . × 10−22 MeV sexact∗
1.602 176 634×10−19 Cexact
197.326 980 4. . . MeV fm
exact∗
20.389 379 372 1. . . GeV mbarn
exact∗
0.510 998 950 00(15) MeV/c2 = 9.109 383 7015(28)×10−31 kg
0.30
938.272 088 16(29) MeV/c2 = 1.672 621 923 69(51)×10−27 kg
0.31= 1.007 276 466 621(53) u = 1836.152 673 43(11) me0.053, 0.060
2939.565 420 52(54) MeV/c = 1.008 664 915 95(49) u0.57, 0.48
1875.612 942 57(57) MeV/c2
0.30
2−27931.494 102 42(28) MeV/c = 1.660 539 066 60(50)×10kg
0.30
8.854 187 8128(13) ×10−12 F m−10.15
1.000 000 000 55(15) N A−20.15
7.297 352 5693(11)×10−3 = 1/137.035 999 084(21) †0.15
2.817 940 3262(13)×10−15 m
0.45

3.861 592 6796(12)×10−13 m
0.30
0.529 177 210 903(80)×10−10 m
0.15
1.239 841 984. . . × 10−6 mexact∗
13.605 693 122 994(26) eV
1.9×10−30.665 245 873 21(60) barn
0.91
5.788 381 8060(17)×10−11 MeV T−1
0.30
−14−1
3.152 451 258 44(96)×10MeV T
0.31
11−1−11.758 820 010 76(53)×10 rad sT
0.30
9.578 833 1560(29)×107 rad s−1 T−1
0.31
6.674 30(15)×10−11 m3 kg−1 s−2
2.2 × 104
= 6.708 83(15)×10−39 ~c (GeV/c2 )−2
2.2 × 104
standard gravitational accel.
gN
9.806 65 m s−2exact
Avogadro constantNA6.022 140 76×1023 mol−1
exact
Boltzmann constant
k1.380 649×10−23 J K−1exact= 8.617 333 262. . . × 10−5 eV K−1exact∗
molar volume, ideal gas at STP NA k (273.15 K)/(101 325 Pa)
22.413 969 54. . . × 10−3 m3 mol−1
exact∗
Wien displacement law constant b = λmax T
2.897 771 955. . . × 10−3 m Kexact∗
Stefan-Boltzmann constantσ = π 2 k4 /60~3 c2
5.670 374 419. . . × 10−8 W m−2 K−4exact∗
Fermi coupling constant‡‡
GF /(~c)3
1.166 378 8(6)×10−5 GeV−2510
weak-mixing angle‡‡
sin2 θb(MZ ) (MS)0.231 29(4)††
1.7 × 105
W ± boson mass
mW80.3692(133) GeV/c2¶
1.7 × 105
Z 0 boson massmZ
91.1880(20) GeV/c2k
2.2 × 104
strong coupling constantαs (mZ )0.1180(9)7.6 × 106
π = 3.141 592 653 589 793 238 . . .
e = 2.718 281 828 459 045 235. . .
γ = 0.577 215 664 901 532 860. . .
1 in ≡ 0.0254 m
1 G ≡ 10−4 T
1 eV = 1.602 176 634 × 10−19 J (exact)
kT at 300 K = [38.681 727 0718 . . .]−1 eV (exact∗ )1 Å ≡ 0.1 nm
1 dyne ≡ 10−5 N(1 kg)c2 = 5.609 588 603 . . . × 1035 eV(exact∗ )0 ◦ C ≡ 273.15K
1 barn ≡ 10−28 m2
1 erg ≡ 10−7 J
1 C = 2.997 924 58 × 109 esu
1 atmosphere ≡ 760 Torr ≡ 101 325Pa
aUpdated values reflecting the “2022 CODATA recommended values”, released online in May 2024, will be incorporated in future editions of the Review.
CODATA recommends that the unit be J/Hz to stress that in h = E/ν the frequency ν is in cycles/sec (Hz), not radians/sec.
These are calculated from exact values and are exact to the number of places given (i.e. no rounding).
∗∗The molar mass of 12 C is 11.999 999 9958(36) g.
†−1
CODATA recommended value at Q2 = 0. At Q2 ≈ m2
= 137.035999178(8). ‡‡W the value is ∼ 1/128. A world average of the latest data yields α‡Absolute laboratory measurements of GN have been made only on scales of about 1 cm to 1 m.
‡‡See the discussion in “Electroweak model and constraints on new physics” review.
††The corresponding sin2 θ for the effective angle is s̄2= 0.23161(4). The value for the collider average is s̄2= 0.23149(13).
``¶
See the “Mass and width of the W boson” and “Electroweak model and constraints on new physics” reviews.
kSee the “Z boson” and “Electroweak model and constraints on new physics” reviews.
§∗

References[1] E. Tiesinga et al., Rev. Mod. Phys. 93, 025010 (2021).