Physical Constants
Name
Common
c.g.s.
m.k.s.
units
other
Newton’s Constant (GN )
6.67 × 10−8 cm3 g−1 s−2
6.674 × 10−8
6.674 × 10−11
L3 M−1 T−2
Natural Unit
Speed of Light (c)
10
3 × 10
Planck’s Constant (h)
4 × 10
Planck’s Constant (~)
7 × 10−16 eV·s
Avogadro’s Number (NA )
Molar Gas Constant (R)
Fine Structure Constant (α)
6.626 × 10
eV·s
9 × 10−5 eV/K
Boltzmann Constant (kB )
Stefan-Boltzmann Constant (σB )
2.998 × 10
cm/s
−15
−5
−2
6 × 10
erg cm
s
−1
K
−4
6 × 1023 mol−1
−1
7
8 × 10 erg K
10
−27
mole
1/137
2.998 × 10
−34
−1
LT
Natural Unit
−1
2
Natural Unit, 4.136 × 10−15
6.626 × 10
L MT
1.055 × 10−27
1.055 × 10−34
L2 M T−1
~ ≡ h/2π, 6.582 × 10−15
1.381 × 10−16
1.381 × 10−23
L2 M T−2 K−1
Natural Unit, 8.617 × 10−5 eV/K
−5
5.670 × 10
6.022 × 1023
−1
8
7
5.670 × 10
−8
−3
MT
-
8.314 × 10
8.314
7.297 × 10−3
-
K
π 2 k4
60~3 c2
−4
2
ML T
−2
,
ac
4
K
−1
-
R = NA kB = 5.189 × 1019 eV K−1 mole−1
2
1
4π0
e
~c
SI
8π e2
3 me c 2
Thomson Cross-Section (σT )
7 × 10−25 cm2
6.652 × 10−25
6.652 × 10−29
L2
Electron Mass (me )
9 × 10−28 g
9.109 × 10−28
9.109 × 10−31
M
511 keV; 1/2000 u
1.673 × 10
−24
−27
M
938 MeV; 1.01 u
1.675 × 10
−24
−27
M
4.803 × 10
−10
−19
Q
940 MeV; 1.01 u
√
qcgs = qSI / 4πε0
Proton Mass (mp )
Neutron Mass (mn )
Elementary Charge (e)
Bohr Radius (a0 )
−24
2 × 10
−24
2 × 10
−10
5 × 10
g
g
statC
−9
5 × 10
cm
−9
5.2918 × 10
1.673 × 10
1.675 × 10
1.602 × 10
−11
5.2918 × 10
L
σT ≡
8π 2
r
3 e
=
(4π0 )SI
~2
m e e2
Permittivity of Free Space (ε0 )
9 × 10−12 F·m
1
8.854 × 10−12
M−1 L−4 T2 Q2
Permeability of Free Space (µ0 )
4π × 10−7
1
4π × 10−7
M L2 Q−2
Coulomb Constant (ke )
1010 N m2 C−2
1
8.988 × 109
M L3 T−2 Q−2
Bohr Magneton (µB )
9 × 10−12 F·m
1
8.854 × 10−12
M−1 L−4 T2 Q2
Hubble Constant (H0 )
70 (km/s) Mpc−1
2 × 10−18
-
T−1
-
Baryon Density (Ωb )
0.05
0.045
-
-
Ωb ≡ ρb /ρc
Dark Matter Density (Ωc )
0.22
0.22
-
-
Ωb ≡ ρc /ρc
Dark Energy Density (ΩΛ )
0.73
0.734
-
-
Critical Density (ρc )
10−29 g cm−3
7 × 10−30
7 × 10−27
M L−3
Planck Length (lP )
10−35 m
1.616 × 10−37
1.616 × 10−35
L
Planck Mass (mP )
Planck Time (tP )
10−8 kg
10−45 s
Planck Charge (qP )
10−18 C
Planck Temperature (TP )
32
10
K
Distance (‘L’); Mass (‘M’); Time (‘T’); Temperature (‘K’); Charge (‘Q’)
2.177 × 10−5
5.391 × 10−44
5.623 × 10−9
1.417 × 10
32
2.177 × 10−8
-
M
T
1.876 × 10−18
Q
-
K
ε0 ≡ (µ0 c2 )−1
p
Bcgs = BSI µ0 /4π
1
4πε0
(µ0 c2 )−1
ke ≡
ε0 ≡
Ωb ≡ ρΛ /ρc
1 p/cm3 , ρc ≡
q
~ GN
c3
q
q
~c
GN
~ GN
c5
√
4πε0 ~c
q
5
~c
2
GN kB
3H2
8πGN