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) 3× 1010 cm/s 2.998× 1010 2.998× 108 L T−1 Natural Unit

Planck’s Constant (h) 4× 10−15 eV·s 6.626× 10−27 6.626× 10−34 L2 M T−1 Natural Unit, 4.136× 10−15

Planck’s Constant (~) 7× 10−16 eV·s 1.055× 10−27 1.055× 10−34 L2 M T−1 ~ ≡ h/2π, 6.582× 10−15

Boltzmann Constant (kB) 9× 10−5 eV/K 1.381× 10−16 1.381× 10−23 L2 M T−2 K−1 Natural Unit, 8.617× 10−5 eV/K

Stefan-Boltzmann Constant (σB) 6× 10−5 erg cm−2 s−1 K−4 5.670× 10−5 5.670× 10−8 M T−3 K−4 π2k4

60~3c2 ,ac4

Avogadro’s Number (NA) 6× 1023 mol−1 6.022× 1023 - - -

Molar Gas Constant (R) 8× 107 erg K−1 mole−1 8.314× 107 8.314 M L2 T−2 K−1 (mole−1) R = NAkB = 5.189× 1019 eV K−1 mole−1

Fine Structure Constant (α) 1/137 7.297× 10−3 - -(

14πε0

)SI

e2

~c

Thomson Cross-Section (σT) 7× 10−25 cm2 6.652× 10−25 6.652× 10−29 L2 σT ≡ 8π3r2e = 8π

3e2

mec2

Electron Mass (me) 9× 10−28 g 9.109× 10−28 9.109× 10−31 M 511 keV; 1/2000 u

Proton Mass (mp) 2× 10−24 g 1.673× 10−24 1.673× 10−27 M 938 MeV; 1.01 u

Neutron Mass (mn) 2× 10−24 g 1.675× 10−24 1.675× 10−27 M 940 MeV; 1.01 u

Elementary Charge (e) 5× 10−10 statC 4.803× 10−10 1.602× 10−19 Q qcgs = qSI/√

4πε0

Bohr Radius (a0) 5× 10−9 cm 5.2918× 10−9 5.2918× 10−11 L (4πε0)SI~2

mee2

Permittivity of Free Space (ε0) 9× 10−12 F·m 1 8.854× 10−12 M−1 L−4 T2 Q2 ε0 ≡ (µ0c2)−1

Permeability of Free Space (µ0) 4π × 10−7 1 4π × 10−7 M L2 Q−2 Bcgs = BSI

√µ0/4π

Coulomb Constant (ke) 1010 N m2 C−2 1 8.988× 109 M L4 T−2 Q−2 ke ≡ 14πε0

Bohr Magneton (µB) 9× 10−12 F·m 1 8.854× 10−12 M−1 L−4 T2 Q2 ε0 ≡ (µ0c2)−1

Hubble Constant (H0) 70 (km/s) Mpc−1 2× 10−18 - T−1 -

Baryon Density (Ωb) 0.05 0.045 - - Ωb ≡ ρb/ρcDark Matter Density (Ωc) 0.22 0.22 - - Ωb ≡ ρc/ρcDark Energy Density (ΩΛ) 0.73 0.734 - - Ωb ≡ ρΛ/ρc

Critical Density (ρc) 10−29 g cm−3 7× 10−30 7× 10−27 M L−3 1 p/cm3, ρc ≡ 3H2

8πGN

Planck Length (lP ) 10−35 m 1.616× 10−37 1.616× 10−35 L√

~ GNc3

Planck Mass (mP ) 10−8 kg 2.177× 10−5 2.177× 10−8 M√

~ cGN

Planck Time (tP ) 10−45 s 5.391× 10−44 - T√

~ GNc5

Planck Charge (qP ) 10−18 C 5.623× 10−9 1.876× 10−18 Q√

4πε0~c

Planck Temperature (TP ) 1032 K 1.417× 1032 - K√

~c5GNk

2B

Distance (‘L’); Mass (‘M’); Time (‘T’); Temperature (‘K’); Charge (‘Q’)