The so-called "classical" electron radius , also called the Compton radius, is defined in cgs by equating the electrostatic potential energy of a sphere of charge e and radius with the rest energy of the electron,

(1)

where is the charge on the electron, is the electron mass, and c is the speed of light. Solving for gives

(2)

Similarly in MKS,

(3)

(4)

where is the permittivity of free space.

Numerically,

(5)

Electron, Point Charge