Stormwater
Rational Method Runoff Calculator (Q = CiA)
The rational method is the standard way to estimate peak runoff from small drainage areas for sizing inlets, swales and storm pipes. Rainfall intensity must be taken for a duration equal to the time of concentration.
Formula
Q = Cf × C × i × A, where Q is in cubic feet per second, i in inches per hour and A in acres. The units work because 1 acre-inch per hour = 1.008 cfs, which is taken as 1.0. The product Cf × C is capped at 1.0. 1 cfs = 448.83 gpm.
Worked example
A 10 acre mixed residential area with C = 0.5 and a 10-year intensity of 4.0 in/hr: Q = 0.5 × 4.0 × 10 = 20 cfs (about 8,977 gpm).
Assumptions and limits
- Intended for small watersheds, commonly under about 200 acres (many agencies set lower limits).
- Rainfall intensity is uniform over the area for a duration equal to the time of concentration.
- Gives a peak flow only, not a runoff volume or hydrograph.
- Frequency factors per FHWA HEC-22: 1.1 for 25-year, 1.2 for 50-year, 1.25 for 100-year.
Frequently asked questions
What runoff coefficient should I use?
Typical ranges from FHWA HEC-22: about 0.70 to 0.95 for pavement and roofs, 0.30 to 0.50 for single-family residential and 0.05 to 0.35 for lawns depending on soil and slope. Your local drainage manual may prescribe values.
Where do I get rainfall intensity?
From the NOAA Atlas 14 Precipitation Frequency Data Server (PFDS) or your local IDF curves, using a duration equal to the time of concentration and the design return period.
When should I not use the rational method?
For large or complex watersheds, or when you need runoff volume for detention design, use NRCS TR-55 or a hydrograph method instead.