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Stormwater Runoff Calculator (Rational Method)

Q: What is the Rational Method?

The Rational Method (Q = CiA/360) estimates peak runoff from a catchment. It is suitable for small catchments (< 80 ha) and stormwater infrastructure design.

Q: What is the runoff coefficient C?

C represents the fraction of rainfall that becomes runoff. Pavement: 0.90, Roof: 0.85, Lawn sandy: 0.15, Lawn heavy: 0.25, Forest: 0.15, Cultivated: 0.30.

Q: What is time of concentration?

Time of concentration (tc) is the time required for runoff to travel from the hydraulically most distant point to the outlet. It is used to determine the critical rainfall duration.

Q: What is the Kirpich formula?

The Kirpich formula estimates tc from flow path length and slope: tc = 0.0195 × L^0.77 × S^(-0.385). It is suitable for natural basins with well-defined channels.

Q: When should the Rational Method not be used?

The Rational Method is not suitable for: large catchments (> 80 ha), flat terrains where storage is significant, or where detailed hydrograph routing is required.

Calculate peak stormwater runoff using the Rational Method (Q = CiA/360). Supports IDF rainfall, Kirpich time of concentration, and weighted land use C coefficients.

Hydraulics & Water Resources Civil engineers, drainage designers, stormwater engineers Commercial Intent: HIGH

Engineering Formulas

Rational Method

Q = C × i × A / 360
Q = peak runoff (m³/s)
C = weighted runoff coefficient
i = rainfall intensity (mm/hr)
A = catchment area (ha)

Q: Peak runoff rate (m³/s)

C: Weighted runoff coefficient

i: Rainfall intensity (mm/hr)

A: Catchment area (ha)

Kirpich Time of Concentration

tc = 0.0195 × L0.77 × S^(-0.385)
tc = time of concentration (min)
L = longest flow path (m)
S = basin slope (m/m)

t_c: Time of concentration (min)

L: Length of flow path (m)

S: Basin slope (m/m)

Weighted Runoff Coefficient

C_weighted = Σ(C_i × A_i) / Σ(A_i)

C_i: Runoff coefficient for sub-area i

A_i: Area of sub-area i (ha)

Worked Example

Rational Method — Mixed Urban Catchment

catchmentArea: 10returnPeriod: 10rainfallIntensity: 50tc: 10useKirpich: 0landUse1: pavementlandUse1Area: 3landUse2: lawn-sandylandUse2Area: 4landUse3: rooflandUse3Area: 3

Weighted C

C = (0.90×3 + 0.15×4 + 0.85×3) / 10 = (2.70 + 0.60 + 2.55) / 10 = 0.585

Peak Runoff

Q = 0.585 × 50 × 10 / 360 = 0.813 m³/s

Runoff Volume

Vol = 0.813 × (10 × 60) = 487.5 m³

Result: Q = 0.81 m³/s for a 10-year storm on a 10 ha mixed urban catchment

Engineering Notes

The Rational Method is best for small urban catchments (< 40 ha) with simple drainage patterns.

For larger catchments, use SCS TR-55 or unit hydrograph methods.

Check local regulations — many jurisdictions prescribe specific IDF curves and return periods.

Climate change is increasing rainfall intensities — consider uplift factors per local guidance.

Assumptions

• Rational Method valid for catchments < 80 ha

• Uniform rainfall intensity over catchment

• Peak runoff occurs when entire catchment contributes

• No storage or attenuation effects

• Steady-state conditions during peak

• Kirpich formula for natural basins only

Common Mistakes

✕ Using the Rational Method for catchments larger than 80 ha

✕ Forgetting to convert units (ha, mm/hr) — coefficient 1/360 handles this

✕ Using unweighted C for mixed land use catchments

✕ Ignoring antecedent moisture conditions

✕ Not checking that land use areas sum to total catchment area

Frequently Asked Questions

What is the Rational Method?

The Rational Method (Q = CiA/360) estimates peak runoff from a catchment. It is suitable for small catchments (< 80 ha) and stormwater infrastructure design.

What is the runoff coefficient C?

C represents the fraction of rainfall that becomes runoff. Pavement: 0.90, Roof: 0.85, Lawn sandy: 0.15, Lawn heavy: 0.25, Forest: 0.15, Cultivated: 0.30.

What is time of concentration?

Time of concentration (tc) is the time required for runoff to travel from the hydraulically most distant point to the outlet. It is used to determine the critical rainfall duration.

What is the Kirpich formula?

The Kirpich formula estimates tc from flow path length and slope: tc = 0.0195 × L^0.77 × S^(-0.385). It is suitable for natural basins with well-defined channels.

When should the Rational Method not be used?

The Rational Method is not suitable for: large catchments (> 80 ha), flat terrains where storage is significant, or where detailed hydrograph routing is required.

What is a typical return period for stormwater design?

Minor drainage (pipes, inlets): 2–10 years. Major system (overland flow): 100 years. Bridge culverts: 25–50 years. Check local regulations.

How is runoff volume calculated?

Runoff volume ≈ Q × t_c × 60. This gives a rough volume estimate. For precise detention sizing, use hydrograph methods (SCS, rational hydrograph).

What is the difference between C and weighted C?

When a catchment has multiple land uses, a weighted C is computed as the area-weighted average of the C values for each land use type.