How to use the Rational Method Peak Runoff Calculator
- 1. Enter the areasOne line per surface: area and its runoff coefficient C, in ha, km², m² or acres.
- 2. Enter intensityRainfall intensity in mm/h for a storm lasting the time of concentration.
- 3. Get peak runoffPeak discharge, weighted C and the working. Add flow length and fall for tc.
The rational formula
Q = C·i·A / 360 with Q in m³/s, i in mm/h and A in hectares. With A in km² the same formula is Q = 0.278 C·i·A.
When the catchment has different surfaces, use the weighted coefficient C = Σ(Cᵢ·Aᵢ)/ΣAᵢ. The intensity must be for a storm whose duration equals the time of concentration tc, the time water takes to flow from the farthest point to the outlet. Kirpich's formula gives tc (min) = 0.01947 L^0.77 S^−0.385, with L in m and S in m/m.
Worked example and exam tips
A 50 ha catchment with C = 0.6 and i = 60 mm/h: Q = 0.6 × 60 × 50/360 = 5.0 m³/s. For a flow path of 1500 m with a fall of 15 m, Kirpich gives tc ≈ 32 min, so read the intensity for a 32-minute storm from the IDF curve.
- The rational method suits small catchments. Large basins need unit hydrograph methods.
- Typical textbook C values: roofs and paved areas 0.7–0.95, lawns 0.05–0.35. Use the values given in your question.
- Check your units. Mixing ha and km² is the most common mistake.
Frequently asked questions
What is the runoff coefficient C?
It is the fraction of rainfall that becomes direct runoff. Paved surfaces have high C (0.7–0.95) and grassy areas low C.
Why must the storm duration equal tc?
Peak runoff from the whole catchment happens only when the rain lasts long enough for water from the farthest point to reach the outlet. Shorter storms do not drain the full area; longer ones have lower intensity.
What is 360 in the formula?
It is a unit conversion: with i in mm/h and A in hectares, dividing by 360 gives Q in m³/s.
Is this calculator free?
Yes. You fill a short form once to see your result, and other Uncodemy tools then open without the form. Everything is calculated in your browser and nothing you type is uploaded.