  Understanding the finite-size corrections to the fundamental excitations of a
theory is the first step towards completely solving for the spectrum in finite
volume. We compute the leading exponential correction to the quantum energy of
the fundamental excitation of the light-cone gauged string in AdS(5) x S(5),
which is the giant magnon solution. We present two independent ways to obtain
this correction: the first approach makes use of the algebraic curve
description of the giant magnon. The second relies on the purely
field-theoretical Luscher formulas, which depend on the world-sheet S-matrix.
We demonstrate the agreement to all orders in g/Delta of these approaches,
which in particular presents a further test of the S-matrix. We comment on
generalizations of this method of computation to other string configurations.
