The GRACE satellite mission is mapping the Earth's gravity field at monthly intervals. The solutions can be used to determine monthly changes in the distribution of water on land and in the ocean. Most GRACE studies to-date have focussed on producing maps of mass variability, with little discussion of the errors in those maps. Error estimates, though, are necessary if GRACE is to be used as a diagnostic tool for assessing and improving hydrology and ocean models. Furthermore, only with error estimates can it be decided whether some feature of the data is real, and how accurately that feature is determined by GRACE. Here, we describe a method of constructing error estimates for GRACE mass values. The errors depend on latitude and smoothing radius. Once the errors are adjusted for these factors, we find they are normally-distributed. This allows us to assign confidence levels to GRACE mass estimates.