  Starting from the T-Q equation of an open integrable spin-1/2 XXZ quantum
spin chain with nondiagonal boundary terms, we derive a nonlinear integral
equation (NLIE) of the sine-Gordon model on a finite interval. We compute the
boundary energy and the Casimir energy for the sine-Gordon model with both left
and right boundaries. A relation between the boundary parameters of the
continuum model and the lattice model is given. We also present numerical
results for the effective central charge of an open spin-1/2 XXZ quantum spin
chain which find agreement with our analytical result for the central charge of
the sine-Gordon model in the ultraviolet (UV) limit.
