Searches for rare nuclear processes, such as neutrinoless double beta-decay and the interactions of WIMP dark matter, are motivating experiments with ever-decreasing levels of radioactive backgrounds. These background reductions are achieved using various techniques, but amongst the most important is minimizing radioactive contamination in the materials from which the experiment is constructed. To this end there have been decades of advances in material sourcing, manufacture and certification, during which researchers have accumulated many thousands of measurements of material radiopurity. Some of these assays are described in publications, others are in databases, but many are still communicated informally. Until this work, there has been no standard format for encoding assay results and no effective, central location for storing them. The aim of this work is to address these long-standing problems by creating a concise and flexible material assay data format and powerful software application to manipulate it. A public installation of this software, available at http://www.radiopurity.org, is the largest database of assay results ever compiled and is intended as a long-term repository for the community's data.