Despite contemporary relevance in understanding how cities historically overcame demographic, social and economic constraints imposed by the lack of clean, fresh water, the value of estimating aqueduct delivery rates and their potential relationship with population size in the Roman Empire remains uncertain. Here, the authors use settlement scaling theory to examine recent statistics for city size and aqueduct capacity, revealing a systematic but sublinear relationship between these variables, whereby water supply increased at a slower rate than population size. Far from merely ostentatious displays of power, aqueducts were carefully planned to ensure an adequate supply of clean and fresh water.