Using a procedure to minimize the total Helmholtz free energy of a system composed of an idealized substrate, a collection of surface clusters, and a vapor in contact with the surface, an expression is derived for the concentration of clusters of a given size on the substrate. The result is based on several assumptions about the system, the most important being that the surface clusters do not interact and that the substrate remains intact. The expression for the concentration of surface clusters together with the conventional form for the growth rate of clusters on a surface can be used to calculate surface nucleation rates.