1.5 Fundamental physical constants
The following values were recommended by the CODATA Task Group on Fundamental
Constants in 1986. For each constant the standard deviation uncertainty in the least significant
digits is given in parentheses.
Quantity
Symbol
Value
permeability of vacuum
speed of light in vacuum
1
permittivity of vacuum
Planck constant
µ0
c0
2
ε0 = 1/µ0c0
h
h = h / 2π
elementary charge
electron rest mass
proton rest mass
neutron rest mass
atomic mass constant,
(unified atomic mass unit)
Avogadro constant
Boltzmann constant
Faraday constant
gas constant
zero of the Celsius scale
molar volume, ideal gas,
p = 1 bar, θ = 0 °C
standard atmosphere
Bohr radius
Rydberg constant
Bohr magneton
electron magnetic moment
e
me
mp
mn
mu = 1 u
4π×10 H m (defined)
-1
299 792 458 m s (defined)
-12
-1
8.854 187 816 ...×10 F m
-34
6.626 075 5(40) ×10 J s
-34
1.054 572 66(63)×10 J s
-19
1.602 177 33(49)×10 C
-31
9.109 389 7(54)×10 kg
-27
1.672 623 1(10)×10 kg
-27
1.674 928 6(10)×10 kg
-27
1.660 540 2(10)×10 kg
1
(1)
-1
-2
2
-2
-7
-1
23
-1
L, NA
k
F
R
6.022 136 7(36)×10 mol
-23
-1
1.380 658 (12)×10 J K
4
-1
9.648 530 9(29)×10 C mol
-1
-1
8.314 510 (70) J K mol
273.15 K (defined)
-1
22.711 08(19) L mol
atm
2
2
a0 = 4πε0h /mee
R∞ = Eh/2hc0
µB = eh/2me
µe
101 325 Pa (defined)
-11
5.291 772 49(24)×10 m
7
-1
1.097 373 153 4(13)×10 m
-24
-1
9.274 015 4(31)×10 J T
-24
-1
9.284 770 1(31)×10 J T
-1
2
-1
-1
H m = N A = N s C ; F m = C J m ; ε0 may be calculated exactly from the
defined values of µ0 and c0.
Chapter 1 - 1
Quantity
Symbol
Value
Landé g-factor for free electron
nuclear magneton
proton magnetic moment
proton magnetogyric ratio
magnetic moment of
ge = 2µe/µB
µN = (me/mp)µB
µp
γp
µ p′ /µB
2.002 319 304 386 (20)
-27
-1
5.050 786 6(17)×10 J T
-26
-1
1.410 607 61(47)×10 J T
8 -1 -1
2.675 221 28(81)×10 s T
-3
1.520 993 129(17)×10
proton resonance
γ p′
42.576 375(13) MHz T
frequency per field in H2O
Stefan-Boltzmann constant
first radiation constant
second radiation constant
gravitational constant
standard acceleration of free fall
σ / 2π k /15h c0
2
c1 = 2πhc0
c2 = hc0/k
G
gn
protons in H2O, µ p′
-1
5 4
3
2
-8
-2
-4
5.670 51(19)×10 W m K
-16
2
3.741 774 9(22)×10 W m
-2
1.438 769(12)×10 m K
-11
3
-1 -2
6.672 59(85)×10 m kg s
-2
9.806 65 m s (defined)
Values of common mathematical constants
Mathematical constant
Symbol
Value
ratio of circumference to diameter of a circle
base of natural logarithms
natural logarithm of 10
π
e
ln 10
3.141 592 653 59
2.718 281 828 46
2.302 585 092 99
Reference: Cohen, E.R. and Taylor, B.N., The 1986 Adjustment of the Fundamental Physical
Constants, CODATA Bull. 63 (1986) 1-49.
Chapter 1 - 2