Rational Method Runoff Calculator

The rational method estimates a peak rate of runoff, not a volume and not a hydrograph. Its form Q equals C times i times A is dimensionally a rainfall volume rate multiplied by a loss fraction: in customary units one inch per hour falling on one acre yields 1.008 cubic feet per second, so the unit conversion is treated as unity and the answer emerges directly in cfs. The runoff coefficient C bundles infiltration, depression storage, interception, and antecedent wetness into a single number. It ranges from about 0.10 for flat wooded ground on sandy soil to 0.95 for asphalt and roofs, with suburban residential areas typically between 0.35 and 0.50 and dense commercial districts between 0.70 and 0.90. The central assumption is that rainfall of uniform intensity, lasting at least as long as the time of concentration, produces the peak, because at that instant the entire catchment contributes flow simultaneously. Intensity must therefore be read from an intensity-duration-frequency curve at a duration equal to the time of concentration and at the chosen return period, commonly 10 years for storm sewers and 25 or 50 years for culverts and major conveyance. The method carries no storage routing, so it cannot size a detention basin directly, and most agencies cap its application at 200 acres. Mixed land cover requires an area-weighted C value, and many drainage manuals apply a frequency adjustment factor that raises C for events rarer than the 10-year storm.

The idea that peak discharge scales with catchment area, rainfall intensity, and an imperviousness fraction was set out by Thomas James Mulvaney, an Irish engineer, in a paper read to the Institution of Civil Engineers of Ireland in 1851. Mulvaney was concerned with arterial land drainage, and he was the first to state clearly that the critical storm duration is the time required for water to travel from the most remote point of a catchment to its outlet, the concept later named the time of concentration. The formula entered American engineering practice through Emil Kuichling, city engineer of Rochester, New York, who published rainfall and runoff measurements from that city in the Transactions of the American Society of Civil Engineers in 1889 and used them to size sewers. In Britain the same relationship was popularized by E. Lloyd-Davies in 1906, and British practice long referred to it as the Lloyd-Davies method. Twentieth-century refinement came mostly through better rainfall statistics rather than any change to the equation: the U.S. Weather Bureau published Technical Paper 40 in 1961, and NOAA Atlas 14 has since replaced it region by region with updated partial-duration frequency estimates. The Soil Conservation Service curve number procedure, developed in the 1950s and packaged as TR-55 in 1975, now handles the larger and more complex watersheds the rational method was never intended to cover.