Using the combination of the histogram reweighting and expanded ensemble simulation methods a new generic algorithm for predicting liquid-solid equilibria is proposed. This method avoids the fitting procedures and numerical integration previously required to obtain the equation of state and free energy. Using the expanded ensemble simulation we calculate the free energy difference between hard-sphere crystal and the corresponding Einstein crystal without the need to constrain the center of mass of the system. The liquid-solid equilibria for hard-sphere systems of varying size up to 1372 particles are studied with NpT Monte Carlo simulation and histogram reweighting. We find only a slight size dependence of coexistence properties with this method, and the limit for the infinitely large system is easily and accurately determined. (C) 2003 American Institute of Physics.