Wetting is important in many applications, and the solid surfaces being wet invariably feature some amount of surface roughness. A free energy-based computational simulation is used to study the effect of roughness on wetting and especially contact angle hysteresis. On randomly rough, self-affine surfaces, it is found that hysteresis depends primarily on the value of the Wenzel roughness parameter r, increasing in proportion with r - 1. Micrometer-level roughness causes hysteresis of a few degrees.