  The Brown-York quasi-local energy of a charged rotating black hole described
by the Kerr-Newman metric and enclosed by a fixed-radius surface is computed.
No further assumptions on the angular momentum or the radial coordinate in
Boyer-Lindquist coordinates were made. The result can be expressed in terms of
incomplete elliptic integrals and is used to analyze the self-energy of an
electron which is assumed to be described by the Kerr-Newman metric. For this
purpose the small sphere limit is investigated thoroughly comparing the
analysis with known results. Evaluating the energy using the mass, angular
momentum and charge of an electron a value in the order of the Planck energy is
obtained in the small sphere limit as long as the Kerr-Newman metric acting as
exterior solution can be used as a description of spacetime.
