  A fluid in equilibrium in a finite volume $V$ with particle number $N$ at a
density $\rho = N/V$ exceeding the onset density $\rho_f $ of freezing may
exhibit phase coexistence between a crystalline nucleus and surrounding fluid.
Using a method suitable for the estimation of the chemical potential of dense
fluids we obtain the excess free energy due to the surface of the crystalline
nucleus. There is neither a need to precisely locate the interface nor to
compute the (anisotropic) interfacial tension. As a test case, a soft version
of the Asakura-Oosawa model for colloid polymer-mixtures is treated. While our
analysis is appropriate for crystal nuclei of arbitrary shape, we find the
nucleation barrier to be compatible with a spherical shape, and consistent with
classical nucleation theory.
