We consider an experimentally relevant model of a geometric ratchet in which particles undergo drift and diffusive motion in a two-dimensional periodic array of obstacles, and which is used for the continuous separation of particles subject to different forces. The macroscopic drift velocity and diffusion tensor are calculated by a Monte Carlo simulation and by a master-equation approach, using the corresponding microscopic quantities and the shape of the obstacles as input. We define a measure of separation quality and investigate its dependence on the applied force and the shape of the obstacles.