The COSMO-SAC model for the calculation of activity coefficients has been improved by incorporating three-dimensional geometric information on molecules. This information is added to the model by means of the effective contact area of the molecules. We define a procedure to compute this contact area by using a probing sphere. The probing sphere rolls around the COSMO surfaces of two contacting atoms to define a spherical cap on each atom. The segments of the COSMO surfaces within the spherical caps are marked, and the summation of their areas defines the contact area for a pair of contacting molecules. The effective contact areas are used to compute the sigma-profiles and the Onsager screening energies in the calculation of the surface activity coefficients, allowing us to remove one parameter from the COSMO-SAC model. The s-profiles and effective areas need to be calculated only once and can be stored in a database. We show that the new model, named COSMO-3D because some three-dimensional information (the position of surface segments and atom centers in 3D-space) is taken from the COSMO-output files, agrees better with experimental data than the COSMO-SAC implementation for nonpolar and polar mixtures, even though it uses one parameter less. We feel that the new concept of system-dependent effective contact area is a suitable starting point for the further improvement of COSMO-SAC.