A new expression to compute the cavitation free energy has been derived by integrating a new model to fit its derivative with respect to the cavity radius. The derivatives were obtained from Monte Carlo simulations data of the contact values of distribution functions for hard-sphere solutes in TIP4P water at 298 K and I atm. The new expression, formulated in the framework of the thermodynamics of surfaces and unlike the classical simple models, gives good results also for very small cavities with a radius of similar to 1 angstrom. The contribution to the free energy of a term, which depends on the excess number of molecules at the dividing surface, has been taken into account and discussed for the assumed dependence on r of the surface tension. The asymptotic behavior of the derivative has thus been considered, and a function t(r), which is 0 at r = 0 and I at infinity, has been introduced to describe the transition from small to large length regimes. The value of the surface tension obtained by fitting is in very good agreement with that obtained from a simulation of the liquid/vapor interface by using the TIP4P model.