Scs Curve Number Calculator

The Curve Number method converts a storm rainfall depth P into a direct runoff depth Q using a single land-surface index. Its core assumption is that once runoff begins, the ratio of actual retention to maximum potential retention S equals the ratio of actual runoff to available rainfall. Solving that proportionality gives Q = (P - Ia)^2 / (P - Ia + S), an equation that is asymptotic to the 1:1 line for very large storms and returns zero runoff whenever P does not exceed the initial abstraction Ia. The Curve Number is a re-scaling of S through S = 25400/CN - 254 mm, chosen so practitioners work with a bounded 0 to 100 index instead of a retention depth. CN 30 to 55 characterizes woodland and pasture on deep sands, CN 70 to 80 covers row crops and residential lots on loams, and CN 98 is assigned to pavement and roofs. The main caveats are structural rather than computational. The equation contains no rainfall intensity term, so a 100 mm cloudburst and a 100 mm drizzle return identical runoff. Reported CN values are keyed to average antecedent wetness (AMC-II), and shifting to dry or saturated soil can move effective CN by 15 to 20 points. The standard Ia = 0.2S assumption has been challenged repeatedly; analyses of gauged plot data suggest 0.05S fits observed rainfall-runoff pairs better, which is why the abstraction ratio is exposed as an input here. Estimates are least reliable for small storms and for basins outside the original agricultural calibration set.

The method grew out of the runoff plot and small-watershed monitoring programs the US Soil Conservation Service ran across agricultural experiment stations from the 1930s onward, assembled in response to Dust Bowl era erosion. Victor Mockus, a hydraulic engineer with the agency, is generally credited with synthesizing those records into the rainfall-runoff relation that became the Curve Number procedure, first published in Section 4 (Hydrology) of the SCS National Engineering Handbook in 1954. The design goal was explicitly practical: field conservationists needed a way to size farm ponds, terraces, and grassed waterways using only a soil survey and a land use map, without streamflow gauges or calibration. Subsequent revisions of NEH-4 refined the CN tables, added the four Hydrologic Soil Groups, and extended coverage to urban land uses. Technical Release 55, Urban Hydrology for Small Watersheds, appeared in 1975 and was substantially revised in 1986, carrying the method into municipal drainage practice and stormwater ordinances. The agency was renamed the Natural Resources Conservation Service in 1994, so the same procedure is cited as both SCS and NRCS Curve Number depending on the vintage of the reference. From the 1990s onward researchers including Richard Hawkins re-examined the method against measured data, documenting the initial abstraction problem and the way fitted CN values drift with storm size, work later collected in the ASCE task committee volume Curve Number Hydrology.