Coulomb constant

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Value of k Units
8.9875517923(14)×109 N·m2/C2
14.3996 eV·Å·e−2
10−7 (N·s2/C2)c2

The Coulomb constant, the electric force constant, or the electrostatic constant (denoted ke, k or K) is a proportionality constant in electrostatics equations. In SI base units it is equal to 8.9875517923(14)×109 kg⋅m3⋅s−4⋅A−2.[1] It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law.[2][3]

Value of the constant[edit]

The Coulomb constant is the constant of proportionality in Coulomb's law,

where êr is a unit vector in the r-direction.[4] In SI:

where is the vacuum permittivity. This formula can be derived from Gauss' law,


Taking this integral for a sphere, radius r, centered on a point charge, the electric field points radially outwards and is normal to a differential surface element on the sphere with constant magnitude for all points on the sphere.


Noting that E = F/q for some test charge q,

Coulomb's law is an inverse-square law, and thereby similar to many other scientific laws ranging from gravitational pull to light attenuation. This law states that a specified physical quantity is inversely proportional to the square of the distance.

In some modern systems of units, the Coulomb constant ke has an exact numeric value; in Gaussian units ke = 1, in Lorentz–Heaviside units (also called rationalized) ke = 1/. This was previously true in SI when the vacuum permeability was defined as μ0 = 4π×10−7 H⋅m−1. Together with the speed of light in vacuum c, defined as 299792458 m/s, the vacuum permittivity ε0 can be written as 1/μ0c2, which gave an exact value of[5]

Since the redefinition of SI base units,[6][7] the Coulomb constant is no longer exactly defined and is subject to the measurement error in the fine structure constant, as calculated from CODATA 2018 recommended values being[1]


The Coulomb constant is used in many electric equations, although it is sometimes expressed as the following product of the vacuum permittivity constant:

The Coulomb constant appears in many expressions including the following:

Coulomb's law
Electric potential energy
Electric field

See also[edit]


  1. ^ a b Derived from ke = 1/(4πε0) – "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
  2. ^ Britannica, The Editors of Encyclopaedia. "Coulomb". Encyclopedia Britannica. Retrieved 3 March 2021. {{cite web}}: |last1= has generic name (help)
  3. ^ Britannica, The Editors of Encyclopaedia. "Charles-Augustin de Coulomb". Encyclopedia Britannica. Retrieved 3 March 2021. {{cite web}}: |last1= has generic name (help)
  4. ^ Tomilin, K. (1999). "Fine-structure constant and dimension analysis". European Journal of Physics. 20 (5): L39–L40. Bibcode:1999EJPh...20L..39T. doi:10.1088/0143-0807/20/5/404. S2CID 250841835.
  5. ^ Coulomb's constant, HyperPhysics
  6. ^ BIPM statement: Information for users about the proposed revision of the SI (PDF)
  7. ^ "Decision CIPM/105-13 (October 2016)". The day is the 144th anniversary of the Metre Convention.