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Rational Method Peak Runoff

Also known as Q = CiA · rational formula · peak discharge · storm sewer sizing · runoff coefficient

Q=C i AQ = C \, i \, A

Worked example: C 0.5, 50 mm/h on 10 ha → 0.694 m3/s — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

See also
Kirpich Time of Concentration — The intensity must be read off the IDF curve at a duration equal to the time of concentration.SCS Curve Number Runoff Depth — For anything larger than about 80 hectares, use a curve-number volume method instead.
Learning zone

Rational Method Peak Runoff explained

iCAQ

The rational method is the oldest formula in urban drainage and still the one that sizes most storm sewers. Its logic is a single sentence: if rain of intensity ii falls long enough for the whole catchment to be contributing at once, and a fraction CC of it runs off, the peak flow is that fraction of the rainfall arriving on the area. Written with consistent units there is no bridging factor at all. Half of a 50 mm/h storm off ten hectares is 0.5×1.389×10−5 m/s×100 000 m2=0.6940.5 \times 1.389\times10^{-5}\ \mathrm{m/s} \times 100\,000\ \mathrm{m^2} = 0.694 m³/s. The constants in the textbook forms — 3.6×10⁶ for millimetres an hour with square metres, or 0.00278 for the hectare shorthand — are unit conversions wearing the costume of physics. This page does not carry one, because the units engine does that work: enter the intensity in whatever your IDF curve is drawn in and the area in whatever the survey gave you.

The condition hidden in that sentence is the whole method. The storm duration must equal the time of concentration, and no shorter storm is allowed to win, because a shorter storm is more intense but only part of the catchment contributes. That is why you cannot pick an intensity without first computing a time of concentration and reading it off an IDF curve at that duration. It is also why the method is capped: most agencies stop at 80 hectares or so, and Ontario practice is often stricter, because on a large catchment the assumption of uniform rainfall over the whole area for the full travel time stops being remotely true.

The coefficient is where the judgement lives, and the classic mistake is treating it as a property of the surface. It is not. CC rises with return period, because a 100-year storm saturates soil that a 2-year storm never wets, and most manuals publish a frequency adjustment of 1.1 to 1.25 for the rarer events. Use an area-weighted composite for mixed land use, remember that 0.95 pavement is not the ceiling once you add frozen ground, and treat any answer with a coefficient above about 0.9 as a statement that the catchment is effectively a parking lot.

Rational Method Peak Runoff formula

Q=C i AQ = C \, i \, A
Where
  • QQ= Peak runoff rate (m³/s)
  • CC= Runoff coefficient
  • ii= Rainfall intensity (mm/h)
  • AA= Drainage area (m²)

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