FUNDAMENTAL PHYSICAL CONSTANTS 

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Planck constant h 

6.6260755e-34 J s 

h / (2 pi) = 1.05457266e-34 J s 

Boltzmann constant k_B 

1.380658e-23 J/K 

Elementary charge e 

1.60217733e-19 C 

Avogadro number N_A 

6.0221367e23 particles/mol 

Speed of light c 

2.99792458e8 m/s 

Permeability of vacuum mu₀ 

mu₀ = 4 pi e-7 T² m³/J 

12.566370614e-7 T² m³/J 

Permittivity of vacuum epsilon₀ 

epsilon₀ = 1 / (mu₀ c²) 

8.854187817e-12 C²/J m 

Fine structure constant 1 / alpha 

137.0359895 

Electron rest mass m_e 

9.1093897e-31 kg 

Proton rest mass m_p 

1.6726231e-27 kg 

Neutron rest mass m_n 

1.6749286e-27 kg 

Bohr magneton mu_B 

mu_B = e h / (4 pi m_e) 

9.2740154e-24 J/T 

Nuclear magneton mu_N 

mu_N = e h / (4 pi m_p) 

5.0507866e-27 J/T 

Free electron g factor g_e 

2.002319304386 

Free electron gyromagnetic ratio gamma_e 

gamma_e = 2 pi g_e mu_B / h 

1.7608592e11 1/s T 

gamma_e / (2 pi) = 28.024944 GHz/T 

Electron magnetic moment mu_e 

mu_e = -(1/2) g_e mu_B 

-9.2847701e-24 J/T 

Proton gyromagnetic ratio (H₂O) gamma_p 

2.67515255e8 1/s T 

gamma_p / (2 pi) = 42.576375 MHz/T 

Proton magnetic moment mu_p 

1.41060761e-26 J/T 

Proton-electron ratios 

m_p / m_e = 1836.152701 

mu_e / mu_p = 658.2106881 

gamma_e / gamma_p = 658.2275841 (protons in water) 

Charge-to-mass ratio for electron e / m_e 

1.75880e11 C/kg 

Atomic mass unit amu 

1.66057e-27 kg 

Bohr radius a₀ 

5.29177e-11 m 

Electron radius r_e 

2.81792e-15 m 

Gas constant R 

R = N_A k_B 

8.31451 m² kg/s² K mol 

Molar volume V_mol 

22.41383 m³/kmol 

Faraday constant F 

F = N_A e 

9.64846e4 C/mol 

Proton g factor (Lande factor) g_H 

5.585 

Gravitational constant G 

(6.673 +- 0.010)e-11 m³/kg s² (CODATA) 

(6.6873 +- 0.0094)e-11 m³/kg s² (Schwarz et al., Science 282, 2230 (1998)) 

Acceleration due to gravity g 

9.80665 m/s² 

Compton wavelength of the electron lambda_c 

lambda_c = h / (m_e c) 

2.42631e-12 m 

FURTHR USEFUL CONSTANTS 

Atomic energy unit Hartree 

1 Hartree = e² / (4 pi epsilon₀ a₀) 

1 Hartree = 2.625501e+06 J/mol (approx. 627.5 kcal/mol) 

USEFUL CONVERSION FACTORS 

NMR (Nuclear Magnetic Resonance)

Proton Larmor frequency 

nu_p = gamma_p / (2 pi) B 

nu_p = 42.5764 MHz/T (H₂O) 

EPR (Electron Paramagnetic Resonance, ESR)

Electron Larmor frequency 

nu_e = gamma_e / (2 pi) g / g_e B 

nu_e [GHz] = 13.9962 g B [T] 

g = 0.07144775 nu_e [GHz] / B [T] 

g = 3.04199 nu_e [GHz] / nu_p [MHz] 

B [T] = 0.0234872 nu_p [MHz] 

Conversion of Units 

1 G = 0.1 mT 

1 T = 10 kG 

1 mT = 10 G 

A [MHz] = 2.80249 (g / g_e) A [G] 

A [MHz] = 28.0249 (g / g_e) A [mT] 

A [MHz] = 13.9962 g A [mT] 

A [MHz] = 2.99792e4 A [1/cm] 

A [1/cm] = 0.333564e-4 A [MHz] 

A [1/cm] = 4.66863e-4 g A [mT] 

• The NIST Reference on Constants, Units, and Uncertainty 
• CODATA Internationally recommended values of the Fundamental Physical Constants 
• Fundamental constants C Header File, FORTRAN Data File 
• Conversion of units 
• Physical Constants and Astronomical Data (U Wisconsin) 
• Astro-Physical Calculator 
• Table of Fundamental Physical Constants (MIT) 
• Index General chemistry