Coulomb constant

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The Coulomb constant, the electric force constant, or the electrostatic constant (denoted ke, k or K) is a proportionality constant in electrodynamics equations. In SI units, it is exactly equal to 8987551787.3681764 N·m2·C−2, or approximately 8.99×109 N·m2·C−2. It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law.

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 and


where α is the fine-structure constant, c is the speed of light, ħ is the reduced Planck constant, and e is elementary charge.[1] In SI:


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


Taking this integral for a sphere, radius r, around a point charge, we note that the electric field points radially outwards at all times and is normal to a differential surface element[disambiguation needed] on the sphere, and is constant for all points equidistant from the point charge.


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

In 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/ and in SI ke = 1/ε0, where the vacuum permittivity ε0 = 1/μ0c2 8.85418782×10−12 F⋅m−1, the speed of light in vacuum c is 299792458 m/s, the vacuum permeability μ0 is 4π×107 H⋅m−1,[2] so that[3]


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. ^ 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.
  2. ^ CODATA Value: electric constant. Retrieved on 2010-09-28.
  3. ^ Coulomb's constant, HyperPhysics