Algorithms are presented for characterizing the long-range accessibilities of protein surfaces. First, we describe an analytical method for determining the maximum contact radius for each atom in a structure. The problem is simplified greatly by geometric inversion in a sphere, a type of conformal mapping. Second, we introduce the concept of diffusion accessibility of a protein surface, which we evaluate either by random-walk simulations or by numerical solution of the equations of diffusion with the protein acting as an adsorber. These two measures of exposure are compared to each other as well as to the more common notion of solvent accessibility. These new procedures provide longer-range descriptions of surface geometry which may be useful in docking studies and other areas where surface comparison is required.