Identification of regions in space that a robotic manipulator can reach in a given amount of time is important for many applications, such as safety monitoring of industrial manipulators and trajectory and task planning. However, due to the high-dimensional configuration space of many robots, reasoning about possible physical motion is often intractable. In this paper, we propose a novel method for creating a <i>reachability grid</i>, a voxel-based representation that estimates the minimum time needed for a manipulator to reach any physical location within its workspace. We use up to second-degree constraints on joint motion to model motion limits for each joint independently, followed by successive voxel approximations to map these limits on to the robot’s physical workspace. Results using a simulated manipulator indicate that our method can produce accurate reachability grids in real-time, even for robots with many degrees of freedom. Furthermore, errors are almost exclusively biased towards producing more optimistic reachability estimates, which is a desirable characteristic for many applications.