All augmented reality (AR) systems must deal with registration errors. While most AR systems attempt to minimize registration errors through careful calibration, registration errors can never be completely eliminated in any realistic system. In this paper, we describe a robust and efficient statistical method for estimating registration errors. Our method generates probabilistic error estimates for points in the world, in either 3D world coordinates or 2D screen coordinates. We present a number of examples illustrating how registration error estimates can be used in AR interfaces, and describe a method for estimating registration errors of objects based on the expansion and contraction of their 2D convex hulls.