CODATA RECOMMENDED VALUES OF THE FUNDAMENTAL PHYSICAL CONSTANTS: 2014
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.gov/constants.
The number in parentheses is the one-standard-deviation uncertainty in the last two digits of the given value.
Quantity
Symbol
speed of light in vacuum
magnetic constant
c, c0
µ0
electric constant 1/µ0 c2
Newtonian constant of gravitation
Planck constant
in eV s
h/2π
in eV s
elementary charge
magnetic flux quantum h/2e
Josephson constant 2e/h
von Klitzing constant h/e2 = µ0 c/2α
Bohr magneton eh̄/2me
in eV T−1
nuclear magneton eh̄/2mp
in eV T−1
fine-structure constant e2/4πǫ0 h̄c
inverse fine-structure constant
Rydberg constant α2 me c/2h
ǫ0
G
h
energy equivalent in eV
Bohr radius α/4πR∞ = 4πǫ0 h̄2/me e2
Hartree energy e2/4πǫ0 a0 = 2R∞ hc = α2 me c2
in eV
electron mass
in u
energy equivalent in MeV
electron-muon mass ratio
electron-proton mass ratio
electron charge to mass quotient
Compton wavelength h/me c
λC /2π = αa0 = α2/4πR∞
classical electron radius α2 a0
Thomson cross section (8π/3)re2
electron magnetic moment
to Bohr magneton ratio
to nuclear magneton ratio
electron magnetic moment anomaly |µe |/µB − 1
electron g-factor −2(1 + ae )
electron-proton magnetic moment ratio
muon mass in u
energy equivalent in MeV
muon-electron mass ratio
muon magnetic moment
to Bohr magneton ratio
to nuclear magneton ratio
muon magnetic moment anomaly
|µµ |/(eh̄/2mµ ) − 1
Numerical value
me c
me /mµ
me /mp
−e/me
λC
λC
re
σe
µe
µe /µB
µe /µN
ae
ge
µe /µp
mµ
mµ c 2
mµ /me
µµ
µµ /µB
µµ /µN
299 792 458 (exact)
4π × 10−7 (exact)
= 12.566 370 614... × 10−7
8.854 187 817... × 10−12
6.674 08(31) × 10−11
6.626 070 040(81) × 10−34
4.135 667 662(25) × 10−15
1.054 571 800(13) × 10−34
6.582 119 514(40) × 10−16
1.602 176 6208(98) × 10−19
2.067 833 831(13) × 10−15
483 597.8525(30) × 109
25 812.807 4555(59)
927.400 9994(57) × 10−26
5.788 381 8012(26) × 10−5
5.050 783 699(31) × 10−27
3.152 451 2550(15) × 10−8
7.297 352 5664(17) × 10−3
137.035 999 139(31)
10 973 731.568 508(65)
3.289 841 960 355(19) × 1015
13.605 693 009(84)
0.529 177 210 67(12) × 10−10
4.359 744 650(54) × 10−18
27.211 386 02(17)
9.109 383 56(11) × 10−31
5.485 799 090 70(16) × 10−4
0.510 998 9461(31)
4.836 331 70(11) × 10−3
5.446 170 213 52(52) × 10−4
−1.758 820 024(11) × 1011
2.426 310 2367(11) × 10−12
386.159 267 64(18) × 10−15
2.817 940 3227(19) × 10−15
0.665 245 871 58(91) × 10−28
−928.476 4620(57) × 10−26
−1.001 159 652 180 91(26)
−1838.281 972 34(17)
1.159 652 180 91(26) × 10−3
−2.002 319 304 361 82(52)
−658.210 6866(20)
0.113 428 9257(25)
105.658 3745(24)
206.768 2826(46)
−4.490 448 26(10) × 10−26
−4.841 970 48(11) × 10−3
−8.890 597 05(20)
aµ
1.165 920 89(63) × 10−3
h̄
e
Φ0
KJ
RK
µB
µN
α
α−1
R∞
R∞ c
R∞ hc
a0
Eh
me
2
Unit
m s−1
N A−2
N A−2
F m−1
m3 kg−1 s−2
Js
eV s
Js
eV s
C
Wb
Hz V−1
Ω
J T−1
eV T−1
J T−1
eV T−1
m−1
Hz
eV
m
J
eV
kg
u
MeV
C kg−1
m
m
m
m2
J T−1
u
MeV
J T−1
Quantity
muon g-factor −2(1 + aµ )
muon-proton magnetic moment ratio
proton mass
in u
energy equivalent in MeV
proton-electron mass ratio
proton magnetic moment
to nuclear magneton ratio
proton magnetic shielding correction 1 − µ′p /µp
(H2 O, sphere, 25 ◦ C)
proton gyromagnetic ratio 2µp /h̄
shielded proton gyromagnetic ratio 2µ′p /h̄
(H2 O, sphere, 25 ◦ C)
neutron mass in u
energy equivalent in MeV
neutron-proton mass ratio
neutron magnetic moment
to nuclear magneton ratio
deuteron mass in u
energy equivalent in MeV
deuteron-proton mass ratio
deuteron magnetic moment
to nuclear magneton ratio
helion (3 He nucleus) mass in u
energy equivalent in MeV
shielded helion magnetic moment
(gas, sphere, 25 ◦ C)
to Bohr magneton ratio
to nuclear magneton ratio
alpha particle mass in u
energy equivalent in MeV
Avogadro constant
1
atomic mass constant 12
m(12 C) = 1 u
energy equivalent in MeV
Faraday constant NA e
molar gas constant
Boltzmann constant R/NA
in eV K−1
molar volume of ideal gas RT /p
(T = 273.15 K, p = 101.325 kPa)
Stefan-Boltzmann constant π2 k4/60h̄3 c2
first radiation constant 2πhc2
second radiation constant hc/k
Wien displacement law constant
b = λmax T = c2 /4.965 114 231...
Cu x unit: λ(Cu Kα1 )/1 537.400
Mo x unit: λ(Mo Kα1 )/707.831
Symbol
gµ
µµ /µp
mp
Numerical value
Unit
mp c 2
mp /me
µp
µp /µN
′
σp
−2.002 331 8418(13)
−3.183 345 142(71)
1.672 621 898(21) × 10−27
1.007 276 466 879(91)
938.272 0813(58)
1836.152 673 89(17)
1.410 606 7873(97) × 10−26
2.792 847 3508(85)
25.691(11) × 10−6
γp
γp /2π
γp′
2.675 221 900(18) × 108
42.577 478 92(29)
2.675 153 171(33) × 108
s−1 T−1
MHz T−1
s−1 T−1
γp′ /2π
mn
mn c 2
mn /mp
µn
µn /µN
md
md c 2
md /mp
µd
µd /µN
mh
mh c 2
µ′h
42.576 385 07(53)
1.008 664 915 88(49)
939.565 4133(58)
1.001 378 418 98(51)
−0.966 236 50(23) × 10−26
−1.913 042 73(45)
2.013 553 212 745(40)
1875.612 928(12)
1.999 007 500 87(19)
0.433 073 5040(36) × 10−26
0.857 438 2311(48)
3.014 932 246 73(12)
2808.391 586(17)
−1.074 553 080(14) × 10−26
MHz T−1
u
MeV
u
MeV
J T−1
µ′h /µB
µ′h /µN
mα
mα c 2
NA , L
mu
mu c 2
F
R
k
Vm
−1.158 671 471(14) × 10−3
−2.127 497 720(25)
4.001 506 179 127(63)
3727.379 378(23)
6.022 140 857(74) × 1023
1.660 539 040(20) × 10−27
931.494 0954(57)
96 485.332 89(59)
8.314 4598(48)
1.380 648 52(79) × 10−23
8.617 3303(50) × 10−5
22.413 962(13) × 10−3
u
MeV
mol−1
kg
MeV
C mol−1
J mol−1 K−1
J K−1
eV K−1
m3 mol−1
σ
c1
c2
5.670 367(13) × 10−8
3.741 771 790(46) × 10−16
1.438 777 36(83) × 10−2
W m−2 K−4
W m2
mK
b
2.897 7729(17) × 10−3
xu(Cu Kα1 ) 1.002 076 97(28) × 10−13
xu(Mo Kα1 ) 1.002 099 52(53) × 10−13
kg
u
MeV
J T−1
J T−1
u
MeV
J T−1
mK
m
m
Energy equivalents
(1
(1
(1
(1
(1
m−1 )c
= 299 792 458 Hz
m−1 )hc/k = 1.438 777 36(83) × 10−2 K
m−1 )hc = 1.239 841 9739(76) × 10−6 eV
m−1 )h/c = 1.331 025 049 00(61) × 10−15 u
Hz)/c
= 3.335 640 951 . . . × 10−9 m−1
(1
(1
(1
(1
(1
Hz)h/k = 4.799 2447(28) × 10−11 K
Hz)h = 4.135 667 662(25) × 10−15 eV
K)k/hc = 69.503 457(40) m−1
K)k/h = 2.083 6612(12) × 1010 Hz
K)k
= 8.617 3303(50) × 10−5 eV
(1
(1
(1
(1
(1
J)
= 6.241 509 126(38) × 1018 eV
eV)
= 1.602 176 6208(98) × 10−19 J
eV)/hc = 8.065 544 005(50) × 105 m−1
eV)/h = 2.417 989 262(15) × 1014 Hz
eV)/k = 1.160 452 21(67) × 104 K
(1
(1
(1
(1
(1
eV)/c2 = 1.073 544 1105(66) × 10−9 u
kg)
= 6.022 140 857(74) × 1026 u
u)
= 1.660 539 040(20) × 10−27 kg
u)c/h = 7.513 006 6166(34) × 1014 m−1
u)c2
= 931.494 0954(57) × 106 eV