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Under climate change, increases in precipitation extremes are expected due to higher atmospheric moisture. However, the total precipitation in an event also depends on the condensation rate, precipitation efficiency, and duration. Here, a new approach following an ‘ingredients-based methodology’ from severe weather forecasting identifies important aspects of the heavy precipitation response to climate change, relevant from an impacts perspective and hitherto largely neglected. Using 2.2km climate simulations, we show that a future increase in precipitation extremes across Europe occurs, not only because of higher moisture and updraft velocities, but also due to slower storm movement, increasing local duration. Environments with extreme precipitation potential are 7x more frequent than today by 2100, whilst the figure for quasi-stationary ones is 11x (14x for land). We find that a future reduction in storm speeds, possibly through Arctic Amplification, could enhance event accumulations and flood risk beyond expectations from studies focusing on precipitation rates.