Here we highlight the fact that total changes in extreme precipitation are a result of combined changes in both intensity and frequency. A main result from this study is that there is a strong monotonic strengthening of frequency increase and thereby relative increase in total extreme precipitation with rareness of the precipitation events. We argue that the impact of extreme precipitation on society results from both the number of events above the present tolerance and the severity of these events, and hence indices used to indicate impacts of climate change should encompass both. These increases are much higher than found in studies of precipitation intensity alone1,43, including the IPCC 5th Assessment Report. Such large increases are not taken into account by adaptation management, and our findings imply that society may not be adequately prepared for the coming changes in extreme rainfall.