CV-02Civil & Construction

Rational Method Calculator

What to calculate next

Tools commonly used alongside this calculation

Explanation

The Rational Method is the standard way to estimate the peak rate of stormwater runoff from a small drainage area. It ties three things together — how much of the rain runs off rather than soaks in, how hard it is raining, and how big the area is — into one equation, Q = C · i · A. This calculator builds a weighted runoff coefficient from the surfaces in your catchment and returns the peak flow in cubic feet per second.

How the Rational Method works

Peak runoff is the runoff coefficient times the rainfall intensity times the area. When a catchment has more than one cover type, each area is given its own coefficient and the results are combined into an area-weighted composite C, so paved and grassed portions are counted correctly.

Q = C × i × A  |  C(weighted) = Σ(Cᵢ × Aᵢ) ⁄ ΣAᵢ
SymbolMeaning
QPeak runoff rate (cubic feet per second, cfs)
CRunoff coefficient (0–1) — the fraction that runs off
iRainfall intensity (inches per hour)
ADrainage area (acres)

In US customary units the conversion factor between in/hr × acres and cfs is almost exactly one, so it is dropped. Once you have the peak flow, size the pipe that carries it with the culvert size calculator.

Runoff coefficients and rainfall intensity

The runoff coefficient depends on the surface, the soil, and the slope. Hard surfaces shed almost all of the rain, while flat lawns on sandy soil absorb most of it. The typical values below are a starting point — local manuals may specify others.

SurfaceTypical C
Asphalt / concrete pavement0.90
Roofs0.90
Gravel / macadam0.45
Downtown / business0.85
Industrial0.70
Residential, multi-unit0.60
Residential, single-family0.40
Cultivated / agricultural0.35
Lawn, heavy soil, steep0.35
Park / cemetery / open space0.20
Forest / woodland0.15
Lawn, sandy soil, flat0.10

Rainfall intensity i comes from the local intensity-duration-frequency (IDF) curve — in the United States from NOAA Atlas 14 — read at the design return period and a duration equal to the time of concentration of the catchment.

These coefficients are calibrated for storms of about a 10-year return period or less. For a 25-, 50-, or 100-year design storm, standard practice multiplies C by a frequency factor Cf (about 1.10, 1.20, and 1.25 respectively), with the product C × Cf capped at 1.0.

Notes and limitations

The Rational Method assumes a steady, uniform rainfall and a single peak, so it is intended for small catchments — generally under about 100 acres — without ponds, swamps, or other significant storage. Larger or more complex watersheds need a hydrograph method such as NRCS (SCS) unit hydrographs. The result is only as good as the coefficient and the rainfall intensity you enter; confirm both, and the method itself, against the authority having jurisdiction.

Frequently asked questions