New computer programs, SurfRace and FastSurf, perform fast calculations of the solvent accessible and molecular (solvent excluded) surface areas of macromolecules. Program SurfRace also calculates the areas of cavities inaccessible from the outside. We introduce the definition of average curvature of molecular surface and calculate average molecular surface curvatures for each atom in a structure. All surface area and curvature calculations are analytic and therefore yield exact values of these quantities. High calculation speed of this software is achieved primarily by avoiding computationally expensive mathematical procedures wherever possible and by efficient handling of surface data structures. The programs are written initially in the language C for PCs running Windows 2000/98/NT, but their code is portable to other platforms with only minor changes in input‐output procedures. The algorithm is robust and does not ignore either multiplicity or degeneracy of atomic overlaps. Fast, memory‐efficient and robust execution make this software attractive for applications both in computationally expensive energy minimization algorithms, such as docking or molecular dynamics simulations, and in stand‐alone surface area and curvature calculations. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 600–609, 2002