Worked problem

Stormwater Runoff Using the Rational Method

Estimate peak runoff for a 3.5 acre catchment with Q = CiA, show the unit conversion to cfs, and explain why duration equals time of concentration.

Civil & Structural · Last reviewed October 17, 2026

Given

A small catchment of A = 3.5 acres with a composite runoff coefficient C = 0.70. The time of concentration is 15 minutes, and the design rainfall intensity for a 15-minute duration is i = 4.2 in/hr (supplied from a local intensity-duration table).

Find

The peak runoff rate in cubic feet per second, with the unit conversion shown, and the effect of a longer duration.

Solution

Q = C × i × A

Q = 0.70 × 4.2 × 3.5 = 10.29 (in the mixed units of acre·in/hr).
Unit conversion: 1 acre·in/hr = 43,560 ft² × (1 ÷ 12 ft) ÷ 3,600 s = 1.0083 ft³/s. The factor is so close to 1 that the formula is written as Q (cfs) = C i A.
Exact value: 10.29 × 1.0083 = 10.38 cfs.

Answer

Q(peak) ≈ 10.4 cfs

The same result in metric units

In SI the formula is Q (m³/s) = C × i (mm/hr) × A (ha) ÷ 360. With A = 1.416 ha and i = 106.7 mm/hr: Q = 0.70 × 106.7 × 1.416 ÷ 360 = 0.294 m³/s, which is 10.4 cfs.

Why the duration is the time of concentration

The peak flow occurs when the whole catchment contributes at once, which takes one time of concentration (the travel time from the most remote point to the outlet). A shorter storm does not reach the whole area. A longer storm has a lower average intensity. So the design intensity is read for a storm whose duration equals the time of concentration.

Duration used	Intensity	Peak flow
15 min (correct)	4.2 in/hr	10.4 cfs
30 min (too long)	3.1 in/hr	7.7 cfs

Common mistakes

Using one rainfall intensity for every catchment, regardless of its time of concentration.
Applying the rational method to a large catchment. It is normally limited to small areas, with limits set by the local authority.
Using area in square feet or intensity in inches per minute without converting.
Using a runoff coefficient for the wrong surface, or an area-weighted C that left out a paved portion.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

Questions

Where does the intensity come from?

From the local intensity-duration-frequency data for the chosen return period, such as 10 years. The value here is supplied for the exercise.

What does C represent?

The fraction of rainfall that becomes runoff at the peak. It is higher for pavement and roofs and lower for lawns and woods, and it rises for large storms.

Does this give the volume of runoff?

No. It gives the peak rate only. A hydrograph method is needed for volume and routing through a pond.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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