Goal-directed reaching movements are guided by visual feedback from both target and hand. The classical view is that the brain extracts information about target and hand positions from a visual scene, calculates a difference vector between them, and uses this estimate to control the movement. Here we show that during fast feedback control, this computation is not immediate, but evolves dynamically over time. Immediately after a change in the visual scene, the motor system generates independent responses to the errors in hand and target location. Only about 200 ms later, the changes in target and hand positions are combined appropriately in the response, slowly converging to the true difference vector. Therefore, our results provide evidence for the temporal evolution of spatial computations in the human visuomotor system, in which the accurate difference vector computation is first estimated by a fast approximation.