Surface Runoff Coefficient Calculator

The runoff coefficient C is the dimensionless fraction of rainfall that leaves a drainage area as surface flow, obtained here by dividing an observed runoff depth by the storm rainfall depth that produced it. Everything not represented in C has gone to infiltration, depression storage, canopy interception, or evaporation. Because the ratio is computed from a measured pair rather than read from a table, it is an event-specific back-calculation, which is both its strength and its constraint: it describes the storm that occurred, not a design condition. Published design values span a wide range, roughly 0.05 to 0.20 for woodland on sandy Group A soils, 0.20 to 0.40 for pasture and cultivated ground, 0.50 to 0.70 for typical suburban development, and 0.85 to 0.95 for asphalt and roofs. The adjustments applied here reflect two well-documented controls. Steeper ground shortens the residence time available for infiltration, so gradients above about 2 percent and again above 5 percent warrant upward corrections of a few hundredths. Soil hydrologic group shifts C in the same direction as it shifts runoff potential, with Group D clays yielding far more surface flow than Group A sands under identical cover. Users should note the important limitations: C is not a constant for a given surface, since it rises with antecedent wetness, with rainfall intensity relative to infiltration capacity, and with storm return period, which is why many drainage manuals apply frequency factors of about 1.1 for 25-year events and 1.25 for 100-year events. Frozen ground can push C toward 1.0 regardless of soil texture.

The coefficient is inseparable from the Rational Method that employs it. The relation between rainfall intensity, catchment area, and peak discharge was set out by the Irish engineer Thomas Mulvaney in an 1851 paper to the Institution of Civil Engineers of Ireland, addressing the drainage of agricultural land. Mulvaney also articulated the idea that the greatest discharge occurs when rain persists long enough for the whole catchment to contribute, which is the concept later formalized as time of concentration. His formulation circulated slowly and was arrived at again in other national contexts. The method entered mainstream engineering practice through Emil Kuichling, city engineer of Rochester, New York, who published an analysis of sewer drainage in the Transactions of the American Society of Civil Engineers in 1889 based on measurements from Rochester districts of differing imperviousness. Kuichling's data gave the coefficient an empirical footing tied to land cover. A parallel line of development in Britain led to the work of D. E. Lloyd-Davies, published in 1906, and in the United Kingdom the approach is still sometimes called the Lloyd-Davies method. Through the twentieth century professional bodies compiled the tabulated C values now embedded in municipal codes, and agencies including the American Society of Civil Engineers issued manuals of practice standardizing their use for urban stormwater design. Regulatory demands under the Clean Water Act municipal stormwater program later made pre- and post-development comparison of weighted C values a routine permitting requirement.