Stormwater runoff
Two methods answer two different questions and are routinely quoted as if they were interchangeable. The rational method gives a peak discharge from a runoff coefficient and a design intensity — that sizes a pipe. The NRCS curve number gives a runoff depth from a rainfall depth — that sizes a detention basin. A site needs both, and the numbers do not reconcile because one is a rate and the other is a volume.
| Quantity | Value | Method |
|---|---|---|
| Catchment | 5.00 ac | as entered |
| Runoff coefficient | 0.40 | rational method |
| Design intensity | 3.00 in/hr | from the local IDF curve |
| Peak flow | 6.00 cfs | Q = C i A |
| Peak in gpm | 2,693 gpm | × 448.8 |
| Time of concentration | 4.2 min | Kirpich, 0.0078 L^0.77 S^−0.385 |
| Curve number | 75 | TR-55, HSG B |
| Retention S | 3.33 in | 1000/CN − 10 |
| Initial abstraction | 0.67 in | 0.2 S |
| Runoff depth | 2.45 in | (P − 0.2S)² / (P + 0.8S) |
| Runoff volume | 1.021 ac-ft | depth × area |
The catchment sheds 2.45 in from a 5.00 in storm — an effective coefficient of 0.49, against the 0.40 entered for the peak calculation.
Q = C · i · A · A in acres, i in in/hr, Q in cfs.
Tc = 0.0078 L^0.77 S^−0.385 · Kirpich, minutes.
S = 1000/CN − 10 · Inches.
Q = (P − 0.2S)² / (P + 0.8S) · NRCS, valid above Ia.
A clear path from inputs to results.
Two methods answer two different questions and are routinely quoted as if they were interchangeable. The rational method gives a peak discharge — that sizes a pipe. The NRCS curve number gives a runoff depth — that sizes a detention basin. The numbers do not reconcile because one is a rate and the other is a volume.
How to use
- Enter the catchment area and runoff coefficient.
- Set the design intensity and the 24-hour rainfall depth.
- Choose a curve number and the flow path length and slope.
- Read the peak flow, the runoff depth and the volume.
The formula
Reference: Rational method (ASCE / FHWA HEC-22); NRCS curve number from TR-55; time of concentration from Kirpich.
Worked example
Five acres at C = 0.4 under 3 in/hr
- 5 acres, runoff coefficient 0.40.
- Design intensity 3 in/hr; 5 in of rain in 24 hours.
- Curve number 75, flow path 500 ft at 2% slope.
- 1
The rational peak is 0.40 × 3 × 5 = 6.0 cfs, or about 2,693 gpm.
- 2
Kirpich gives a time of concentration of 4.2 minutes for the 500 ft path at 2%.
- 3
The retention S is 1000/75 − 10 = 3.33 in, so the initial abstraction is 0.67 in.
- 4
Runoff depth is (5 − 0.67)² / (5 + 2.67) = 2.45 in.
- 5
Over 5 acres that is 1.02 acre-feet of runoff.
- 6
The implied coefficient is 2.45/5 = 0.49, against the 0.40 entered for the peak.
6.0 cfs peak · 2.45 in runoff · 1.02 acre-feet.
Interpreting the result
The two coefficients disagree — 0.40 for the peak and 0.49 implied by the volume — and that is not an error. The rational coefficient describes the peak rate at a design intensity; the curve number describes how much of a storm becomes runoff. A designer needs both and should not force them to match.
Assumptions & limitations
- The rational method is valid for catchments up to about 200 acres.
- Kirpich is calibrated for slopes between 1% and 10%.
- Curve numbers are TR-55 Table 2-2 for hydrologic soil group B.
- No routing, no detention storage and no snowmelt.
Frequently asked questions
Which method should I use?
Both. The peak sizes the conveyance — pipes, swales, culverts. The volume sizes the storage — detention basins and infiltration. Using one for the other is the standard mistake.
What is a curve number?
A single number from 30 to 98 that describes the runoff potential of a soil-cover complex. Paved surfaces are 98; good woodland on group B soil is 30.
How do I pick the design storm?
From the local rainfall frequency atlas for the return period the authority requires — commonly the 10-year for conveyance and the 100-year for detention.
Why is the rational method criticised?
Because it assumes a uniform rainfall intensity over the whole catchment and a constant runoff coefficient, which is poor for large or elongated catchments. It survives because it is simple and conservative for small ones.
Why does the curve number give zero runoff for small storms?
Because of the initial abstraction — 0.2S — which represents interception, depression storage and infiltration before runoff begins. Below that depth nothing runs off.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.