Tropical cyclone rainfall rates have been projected to increase in a warmer climate. The area coverage of tropical cyclones influences their impact on human lives, yet little is known about how tropical cyclone rainfall area will change in the future. Here, using satellite data and global atmospheric model simulations, we show that tropical cyclone rainfall area is controlled primarily by its environmental sea surface temperature (SST) relative to the tropical mean SST (that is, the relative SST), while rainfall rate increases with increasing absolute SST. Our result is consistent with previous numerical simulations that indicated tight relationships between tropical cyclone size and mid-tropospheric relative humidity. Global statistics of tropical cyclone rainfall area are not expected to change markedly under a warmer climate provided that SST change is relatively uniform, implying that increases in total rainfall will be confined to similar size domains with higher rainfall rates.