The electronic and magnetic structure of bulk NiO and the NiO(100) surface is calculated using density-functional theory (DFT) in the local-spin-density (LSD) approximation including self-interaction corrections. We calculate the exchange coupling constants in bulk NiO and at the NiO(100) surface and show that in the case of bulk they agree better with experiment than the standard DFT calculations in the LSD approximation. We develop a model for the exchange interactions at the NiO(100) surface and discuss how they change from the surface to the bulk.