CODATA RECOMMENDED VALUES OF THE FUNDAMENTAL PHYSICAL CONST

NIST SP 961 (Sept/2015) Values from: P. J. Mohr, D. B. Newell, and B. N. Taylor, arXiv:1507.07956

A more extensive listing of constants is available in the above reference and on the NIST Physics Laboratory Web site physics.nist

The number in parentheses is the one-standard-deviation uncertainty in the last two digits of the given value.

Quantity Symbol Numerical value Unit Quantity Symbol 

speed of light in vacuum c, c0 299 792 458 (exact) m s

−1 muon g-factor

−2(1 + aμ) gμ 

magnetic constant μ0 4π × 10

−7 (exact) N A

−2 muon-proton magnetic moment ratio μμ/μp 

= 12.566 370 614... × 10

−7 N A

−2 proton mass

mp 

electric constant 1/μ0c

2

ǫ0 8.854 187 817... × 10

−12 F m−1 in u 

Newtonian constant of gravitation

G 6.674 08(31) × 10

−11

m3 kg

−1

s

−2 energy equivalent in MeV

mpc

2 

Planck constant h 6.626 070 040(81) × 10

−34 J s proton-electron mass ratio

mp/me 

in eV s 4.135 667 662(25) × 10

−15 eV s proton magnetic moment μp 

h/2π h ̄ 1.054 571 800(13) × 10

−34 J s to nuclear magneton ratio μp/μN 

in eV s 6.582 119 514(40) × 10

−16 eV s proton magnetic shielding correction 1

− μ

′p/μp σ

′

p 

elementary charge e 1.602 176 6208(98) × 10

−19

C (H2O, sphere, 25

◦C)

magnetic flux quantum h/2e Φ0 2.067 833 831(13) × 10

−15 Wb proton gyromagnetic ratio 2μp/h γ  ̄ p 

Josephson constant 2e/h KJ 483 597.8525(30) × 10

9 Hz V

−1 γp/2π 

von Klitzing constant h/e

2 = μ0c/2α RK 25 812.807 4555(59) Ω shielded proton gyromagnetic ratio 2μ

′p

/h γ  ̄

′

p

Bohr magneton eh/ ̄ 2me μB 927.400 9994(57) × 10

−26 J T

−1 (H2O, sphere, 25

◦C)

in eV T

−1

5.788 381 8012(26) × 10

−5 eV T

−1 γ

′

p

/2π 

nuclear magneton eh/ ̄ 2mp μN 5.050 783 699(31) × 10

−27 J T

−1 neutron mass in u

mn 

in eV T

−1

3.152 451 2550(15) × 10

−8 eV T

−1 energy equivalent in MeV

mnc

2 

fine-structure constant e

2/4πǫ0hc α  ̄ 7.297 352 5664(17) × 10

−3 neutron-proton mass ratio

mn/mp 

inverse fine-structure constant α

−1 137.035 999 139(31) neutron magnetic moment μn 

Rydberg constant α

2mec/2h R

∞ 10 973 731.568 508(65) m−1 to nuclear magneton ratio μn/μN 

R

∞c 3.289 841 960 355(19) × 1015 Hz deuteron mass in u

md 

energy equivalent in eV

R

∞hc 13.605 693 009(84) eV energy equivalent in MeV

mdc

2 

Bohr radius α/4πR

∞ = 4πǫ0h ̄

2/mee

2 a0 0.529 177 210 67(12) × 10

−10

m deuteron-proton mass ratio

md/mp 

Hartree energy e

2/4πǫ0a0 = 2

R

∞hc

= α

2mec

2 Eh 4.359 744 650(54) × 10

−18 J deuteron magnetic moment μd 

in eV 27.211 386 02(17) eV to nuclear magneton ratio μd/μN 

electron mass

me 9.109 383 56(11) × 10

−31 kg helion (

3He nucleus) mass in u

mh 

in u 5.485 799 090 70(16) × 10

−4 u energy equivalent in MeV

mhc

2 

energy equivalent in MeV

mec

2

0.510 998 9461(31) MeV shielded helion magnetic moment μ

′h 

electron-muon mass ratio

me/mμ 4.836 331 70(11) × 10

−3 (gas, sphere, 25

◦C)

electron-proton mass ratio

me/mp 5.446 170 213 52(52) × 10

−4 to Bohr magneton ratio μ

′h/μB 

electron charge to mass quotient

−e/me −1.758 820 024(11) × 1011 C kg

−1 to nuclear magneton ratio μ

′h/μN 

Compton wavelength h/mec λC 2.426 310 2367(11) × 10

−12

m alpha particle mass in u

mα 

λC/2π = αa0 = α

2/4πR

∞ λC 386.159 267 64(18) × 10

−15

m energy equivalent in MeV

mαc

2 

classical electron radius α

2a0 re 2.817 940 3227(19) × 10

−15

m Avogadro constant

NA, L 

Thomson cross section (8π/3)r

2

e σe 0.665 245 871 58(91) × 10

−28

m2 atomic mass constant

1

12

m(12C) = 1 u

mu 

electron magnetic moment μe −928.476 4620(57) × 10

−26 J T

−1 energy equivalent in MeV

muc

2 

to Bohr magneton ratio μe/μB −1.001 159 652 180 91(26) Faraday constant

NAe F 

to nuclear magneton ratio μe/μN −1838.281 972 34(17) molar gas constant

R 

electron magnetic moment anomaly |μe|/μB − 1 ae 1.159 652 180 91(26) × 10

−3 Boltzmann constant R/NA k 

electron g-factor

−2(1 + ae) ge −2.002 319 304 361 82(52) in eV K−1

electron-proton magnetic moment ratio μe/μp −658.210 6866(20) molar volume of ideal gas RT /p Vm muon mass in u

mμ 0.113 428 9257(25) u (T = 273.15 K, p = 101.325 kPa)

energy equivalent in MeV

mμc

2 105.658 3745(24) MeV Stefan-Boltzmann constant π

2k

4/60 ̄h

3

c

2 σ 

muon-electron mass ratio

mμ/me 206.768 2826(46) first radiation constant 2πhc

2

c1 

muon magnetic moment μμ −4.490 448 26(10) × 10

−26 J T

−1 second radiation constant hc/k c2 

to Bohr magneton ratio μμ/μB −4.841 970 48(11) × 10

−3 Wien displacement law constant

to nuclear magneton ratio μμ/μN −8.890 597 05(20) b = λmax

T

= c2/4.965 114 231... b 

muon magnetic moment anomaly Cu x unit: λ(Cu Kα1)/1 537.400 xu(Cu Kα1

|μμ|/(eh/ ̄ 2mμ) − 1 aμ 1.165 920 89(63) × 10

−3 Mo x unit: λ(Mo Kα1)/707.831 xu(Mo Kα1

Energy equivalents

(1 m−1

)c = 299 792 458 Hz (1 Hz)h/k = 4.799 2447(28) × 10

−11 K (1 J) = 6.241 509 126(38) × 1018 eV (1 eV)/

(1 m−1

)hc/k = 1.438 777 36(83) × 10

−2 K (1 Hz)h = 4.135 667 662(25) × 10

−15 eV (1 eV) = 1.602 176 6208(98) × 10

−19 J (1 kg) 

(1 m−1

)hc = 1.239 841 9739(76) × 10

−6 eV (1 K)k/hc = 69.503 457(40) m−1 (1 eV)/hc = 8.065 544 005(50) × 10

5 m−1 (1 u) 

(1 m−1

)h/c = 1.331 025 049 00(61) × 10

−15 u (1 K)k/h = 2.083 6612(12) × 1010 Hz (1 eV)/h = 2.417 989 262(15) × 1014 Hz (1 u)c/

(1 Hz)/c = 3.335 640 951 . . . × 10

−9 m−1 (1 K)k = 8.617 3303(50) × 10

−5 eV (1 eV)/k = 1.160 452 21(67) × 10

4 K (1 u)c

2