Rational Method Runoff Calculator (Q = CiA)
Calculate peak stormwater runoff with the Rational Method Q = CiA.
Enter surface type, drainage area, and rainfall intensity in metric or imperial units.
The most-used formula in stormwater design
The Rational Method dates to the 1880s and is still the first tool a civil engineer reaches for when sizing a storm drain, culvert, gutter, or detention pond for a small catchment. Its appeal is its honesty: three inputs, one multiplication, a peak flow rate. No calibration, no iteration, no software license.
The formula
Q = C × i × A
Where:
- Q = peak runoff rate (the maximum flow the catchment produces)
- C = runoff coefficient (the fraction of rainfall that becomes runoff, 0 to 1)
- i = rainfall intensity (depth of rain per hour, for a storm lasting as long as the time of concentration)
- A = drainage area
The imperial-unit magic
In US customary units the Rational Method is almost suspiciously clean:
Q (cubic feet per second) = C × i (inches/hour) × A (acres)
No conversion factor. This is a happy coincidence: one inch per hour falling on one acre happens to equal 1.008 cubic feet per second, close enough to 1.0 that engineers drop it. That is why the method became standard in American practice before calculators existed.
The metric version needs a factor
In SI units you cannot ignore conversions. The common working form is:
Q (m³/s) = C × i (mm/hr) × A (hectares) / 360
The 360 absorbs the unit conversions (mm to m, hectares to m², hours to seconds). This calculator handles both unit systems for you.
The runoff coefficient C
C is where judgment enters. It represents how much of the rain runs off versus soaking in or evaporating. Pavement sheds almost everything; a forest soaks up most of it.
| Surface | C |
|---|---|
| Asphalt / concrete pavement | 0.85-0.95 |
| Rooftops | 0.75-0.95 |
| Gravel roads and drives | 0.35-0.70 |
| Commercial / downtown | 0.70-0.95 |
| Suburban residential | 0.25-0.40 |
| Lawns, sandy soil | 0.10-0.35 |
| Lawns, clay soil | 0.25-0.40 |
| Row-crop farmland | 0.30-0.50 |
| Meadow / pasture | 0.10-0.30 |
| Light forest | 0.10-0.20 |
For a mixed catchment (some roof, some lawn, some pavement), engineers compute an area-weighted average C: sum each sub-area times its own C, then divide by total area.
Rainfall intensity i
This is not the total storm depth. It is the average intensity over a window equal to the time of concentration: the time for water to travel from the most distant corner of the catchment to the outlet. Short, intense bursts drive small urban catchments; long, soaking storms drive large rural ones. Engineers read i off an Intensity-Duration-Frequency (IDF) curve for the design storm (often the 10-year or 25-year return-period storm for residential drainage, 50-year or 100-year for critical infrastructure).
The key assumption and its limits
The Rational Method assumes the peak flow occurs when the entire catchment is contributing at once, which happens when the storm lasts at least as long as the time of concentration. This holds for small, fairly uniform catchments. The standard guidance:
- Reliable up to about 80 hectares (200 acres). Some agencies cap it lower, at 8-20 hectares.
- Assumes a single, uniform C across the catchment (or a weighted average).
- Assumes rainfall is uniform over the whole area at once. Fine for a parking lot, wrong for a watershed spanning several kilometers where a storm cell only covers part of it.
- Gives only the peak flow, not the full hydrograph. For detention pond volume design you need a method that produces the time-varying flow (SCS unit hydrograph, for instance).
For large or complex watersheds, engineers move to the NRCS (SCS) curve-number method or full hydrologic models like HEC-HMS.
Worked example
A 2-acre commercial site, mostly paved (C = 0.90), in a region where the 10-year design storm intensity is 3.5 inches/hour for the relevant duration.
Q = 0.90 × 3.5 × 2 = 6.3 cubic feet per second
That 6.3 cfs is what the site’s storm drain and downstream culvert must carry. Undersize it and the parking lot floods in the design storm; oversize it and you have wasted money on concrete.
Why the coefficient matters more than people think
Development is mostly an exercise in raising C. A meadow at C = 0.2 becomes a shopping center at C = 0.9, so the same storm now produces four-plus times the peak flow. This is the entire reason stormwater detention ponds exist: to hold back the extra runoff that pavement creates and release it slowly, so downstream channels see something closer to the pre-development peak. Every runoff calculation a land developer is required to submit traces back to this one little formula.