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Inland flood risk in the United States is most often conveyed through maps of 1% annual exceedance probability (AEP) or "100-year" floodplains. However, monetary damages from flooding arise from a full distribution of events, including floods both larger and smaller than the 1% AEP event. Furthermore, floodplains are not static, since both the frequency and magnitude of flooding are likely to change in a warming climate. We explored the implications of a changing frequency and magnitude of flooding across a wide spectrum of flood events, using a sample of 376 watersheds in the United States where floodplains from multiple recurrence intervals have been mapped. Using an inventory of assets within these mapped floodplains, we first calculated expected annual damages (EADs) from flooding in each watershed under baseline climate conditions. We find that the EAD is typically a factor of 5-7 higher than the expected damages from 100-year events alone and that much of these damages are attributable to floods smaller than the 1% AEP event. The EAD from flooding typically increases by 25-50% under a 1 degrees C warming scenario and in most regions more than double under a 3 degrees C warming scenario. Further increases in EAD are not as pronounced beyond 3 degrees C warming, suggesting that most of the projected increases in flood damages will have already occurred, for most regions of the country, by that time. Adaptations that protect against today's 100-year flood will have increasing benefits in a warmer climate by also protecting against more frequent, smaller events.