Stress changes in the Earth's crust are generally estimated from model calculations that use near-surface deformation as an observational constraint. But the widespread correlation of changes of earthquake activity with stress has led to suggestions that stress changes might be calculated from earthquake occurrence rates obtained from seismicity catalogues. Although this possibility has considerable appeal, because seismicity data are routinely collected and have good spatial and temporal resolution, the method has not yet proven successful, owing to the nonlinearity of earthquake rate changes with respect to both stress and time. Here, however, we present two methods for inverting earthquake rate data to infer stress changes, using a formulation for the stress- and time-dependence of earthquake rates. Application of these methods at Kilauea volcano, in Hawaii, yields good agreement with independent estimates, indicating that earthquake rates can provide a practical remote-sensing stress meter.