Geomorphologists often use drainage area as a convenient proxy for river discharge to model sediment transport and bedrock erosion. But how does discharge actually scale with drainage area? Prior work has suggested that this relationship has a power-law form, Q = kAc, where Q is river discharge, A is drainage area, k is a coefficient, and c is a power-law exponent. Using this as a starting point, I analyze the relationship between discharge and drainage-basin area systematically across the network of U.S. Geological Survey reference gauges with at least 20 years of record, whose mean recorded discharges span over three orders of magnitude. The power-law scaling exponent to convert drainage area into discharge decreases as flood recurrence interval increases, and is approximately 0.77 for a 1-2-year flood. This weakening dependence on drainage area as flood magnitude increases may result, at least in part, from the decreasing probability of simultaneous rain events across a whole drainage basin as basin area increases. Furthermore, the scaling exponent systematically increases as catchment mean rainfall rate (derived from PRISM) increases.