Piezoelectric materials are used in numerous applications requiring a coupling between electrical fields and mechanical strain. Despite the technological importance of this class of materials, for only a small fraction of all inorganic compounds which display compatible crystallographic symmetry, has piezoelectricity been characterized experimentally or computationally. In this work we employ first-principles calculations based on density functional perturbation theory to compute the piezoelectric tensors for nearly a thousand compounds, thereby increasing the available data for this property by more than an order of magnitude. The results are compared to select experimental data to establish the accuracy of the calculated properties. The details of the calculations are also presented, along with a description of the format of the database developed to make these computational results publicly available. In addition, the ways in which the database can be accessed and applied in materials development efforts are described.