Most Frequently Used Fundamental Constants
CODATA Recommended Values of Fundamental Constants
Quantity Symbol and relation Numerical value Unit Relative standard
uncertainty
Speed of light in vacuum c 299 792 458 m/s Fixed by definition
Magnetic constant µ
0
= 4π ×10
−7
12.566370614 ...×10
−7
N/A
2
Fixed by definition
Electric constant ε
0
= 1/(µ
0
c
2
) 8.854187817 ...×10
−12
F/m Fixed by definition
Newtonian constant G 6.6742(10) ×10
−11
m
3
/(kg s
2
) 1.5×10
−4
of gravitation
Planck constant h 4.13566743(35) ×10
−15
eV s 8.5×10
−8
Reduced Planck constant = h/2π 6.58211915(56) ×10
−16
eV s 8.5×10
−8
Elementary charge e 1.60217653(14) ×10
−19
C 8.5×10
−8
Fine-structure constant α = (1/4πε
0
)(e
2
/ c) 7.297352568(24)×10
−3
3.3×10
−9
Magnetic flux quantum Φ
0
= h/2e 2.06783372(18) ×10
−15
Wb 8.5×10
−8
Conductance quantum G
0
= 2e
2
/h 7.748091733(26) ×10
−5
S 3.3×10
−9
Rydberg constant R
∞
= α
2
m
e
c/2h 10 973 731.568525(73) 1/m 6.6×10
−12
Electron mass m
e
9.1093826(16) ×10
−31
kg 1.7×10
−7
Proton mass m
p
1.67262171(29) ×10
−27
kg 1.7×10
−7
Proton–electron mass ratio m
p
/m
e
1836.15267261(85) 4.6×10
−10
Avogadro number N
A
, L 6.0221415(10) ×10
23
1.7×10
−7
Faraday constant F = N
A
e 96 485.3383(83) C 8.6×10
−8
Molar gas constant R 8.314472(15) J/K 1.7×10
−6
Boltzmann constant k = R/N
A
1.3806505(24) ×10
−23
J/K 1.8×10
−6
8.617343(15) ×10
−5
eV /K 1.8×10
−6
Josephson constant K
J
= 2e/h 483 597.879(41) ×10
9
Hz/V 8.5×10
−8
von Klitzing constant R
K
= h/e
2
= µ
0
c/2α 25 812.807449(86) Ω 3.3×10
−9
Bohr magneton µ
B
= e /2m
e
927.400949(80) ×10
−26
J/T 8.6×10
−8
5.788381804(39) ×10
−5
eV /T 6.7×10
−9
Atomic mass constant u = (1/12)m(
12
C) 1.66053886(28) ×10
−27
kg 1.7×10
−7
= (1/N
A
) ×10
−3
kg
Bohr radius a
0
= α/4πR
∞
0.5291772108(18) ×10
−10
m 3.3×10
−9
= 4πε
0
2
/m
e
e
2
Quantum of circulation h/2m
e
3.636947550(24) ×10
−4
m
2
/s 6.7×10
−9