The classical electron radius is based on a classical (i.e., non-quantum) relativistic model of the electron. Its value is calculated as

where e and m are the electric charge and the mass of the electron, c is the speed of light, and ε₀ is the permittivity of free space. Using classical electrostatics, the amount of energy required to assemble a sphere of constant charge density , of radius r_e and charge e is just

.

If this is equated to the relativistic energy of the electron (E = mc²) and solved for r_e, the above result is obtained. As a physical concept, the classical electron radius has been outdated by the advent of the quantum mechanical description of the electron. However, the above expression appears even in the quantum description, but without the classical interpretation.

References

• CODATA value for the classical electron radius at NIST.
• Arthur N. Cox, Ed. "Allen's Astrophysical Quantities", 4th Ed, Springer, 1999.