  The Brown-York quasi-local energy of a rotating black hole described by the
Kerr metric and enclosed by a fixed-radius surface is calculated by direct
computation. No special assumptions on the angular momentum or the radial
coordinate in Boyer-Lindquist coordinates were placed. The arbitrary reference
term has been set to zero. The result may be relevant for applications in
astrophysics, for modeling elementary particles or for extensions of the
framework of quasi-local quantities. An analytic expression in terms of
incomplete elliptic integrals is given.
