Cryovolcanism, defined here as the extrusion of icy material from depth, may be an important planetary phenomenon in shaping the surfaces of many worlds in the outer Solar System and revealing their thermal histories1-3. However, the physics, chemistry and ubiquity of this geologic process remain poorly understood, especially in comparison to the better-studied silicate volcanism on the terrestrial planets. Ceres is the only plausibly cryovolcanic world to be orbited by a spacecraft up to now, making it the best opportunity to test the importance of cryovolcanism on bodies in the outer Solar System and compare its effects to silicate volcanism on terrestrial planets. Here, we analyse images from NASA's Dawn mission4 and use the finite element method to show that Ceres has experienced cryovolcanism throughout its geologic history, with an average cryomagma extrusion rate of 104 m3 yr-1. This result shows that volcanic phenomena are important on Ceres, but orders of magnitude less so than on the terrestrial planets.