A numerical scheme has been developed to calculate the electrical double-layer force between two spherical colloidal particles based on the nonlinear Poisson-Boltzmann theory. Results for identical spheres interacting under constant surface potential, constant surface charge, or equilibrium dissociation of ionizable surface groups are given. The method can be readily applied to the case of nonidentical spheres. These results serve as benchmarks for delineating the accuracy of approximate methods for the calculation of the interaction between particles based on the Deryaguin approximation, the superposition approximation, and the Hogg-Healy-Fuerstenau approximation, as well as numerical solutions of the problem based on the linearized Poisson-Boltzmann (Debye-Huckel) theory.