Future rainfall extremes are projected to increase with global warming according to theory and climate models, but common (annual) and rare (decennial or centennial) extremes could be affected differently. Here, using 25 models from the Coupled Model Intercomparison Project Phase 6 driven by a range of plausible scenarios of future greenhouse gas emissions, we show that the rarer the event, the more likely it is to increase in a future climate. By the end of this century, daily land rainfall extremes could increase in magnitude between 10.5% and 28.2% for annual events, and between 13.5% and 38.3% for centennial events, for low and high emission scenarios respectively. The results are consistent across models though with regional variation, but the underlying mechanisms remain to be determined.@en