Rational Method Runoff Calculator (Q = C·i·A)

Rational Method basics

The Rational Method is a simple hydrologic technique used to estimate the peak runoff discharge from small drainage areas such as parking lots, streets, and small urban catchments.

Unit-specific forms

In many US references, the Rational Method is written explicitly with unit conversion factors:

• US customary: Q (cfs) = 0.278 · C · i (mm/hr) · A (ha) — or equivalently Q (cfs) = C · i (in/hr) · A (acres)
• SI: Q (m³/s) = 0.278 · C · i (mm/hr) · A (ha)

This calculator handles the appropriate factor automatically based on your unit selection.

Choosing the runoff coefficient C

The runoff coefficient represents the fraction of rainfall that becomes direct runoff. It depends on land use, soil type, slope, and antecedent moisture.

• Impervious surfaces (roofs, asphalt, concrete): C ≈ 0.8–0.95
• Residential areas (¼–½ acre lots): C ≈ 0.4–0.7
• Lawns / parks (good condition): C ≈ 0.2–0.4
• Wooded areas: C ≈ 0.1–0.3

For mixed land use, compute a weighted C using the helper table above and then apply it in the main calculator.

Time of concentration and rainfall intensity

The rainfall intensity i must correspond to a storm duration equal to the time of concentration t_c and the selected return period (e.g., 10-year, 25-year).

1. Estimate t_c using an appropriate method (e.g., Kirpich, NRCS, local standard).
2. Use local IDF curves (Intensity–Duration–Frequency) to find i for duration = t_c and the desired return period.
3. Enter that intensity into the calculator.

Limitations of the Rational Method

• Best suited for small watersheds (often < 200 acres or < 0.8 km², depending on local guidance).
• Assumes uniform rainfall intensity over the area and duration.
• Does not account for storage, routing, or complex hydrograph shapes.
• Primarily used for peak flow design, not full hydrographs.

For larger or more complex catchments, methods such as unit hydrograph, NRCS (SCS) methods, or hydrologic modeling software are usually recommended.

Worked example

Suppose you have a 10-acre commercial site with the following characteristics:

• 40% impervious (C = 0.9)
• 60% lawn (C = 0.3)
• Time of concentration t_c = 15 minutes
• From IDF curves, 10-year, 15-minute intensity i = 3.0 in/hr

Weighted C:

Peak discharge (US units):

If you apply a safety factor of 1.2, design Q = 16.2 × 1.2 ≈ 19.4 cfs.

Frequently asked questions

Can I use the Rational Method for detention pond design?

The Rational Method is often used to estimate inflow peak to a detention facility, but storage routing and outflow design usually require additional methods or software. Always follow your local design manual.

What if my area is partly outside the recommended size?

Many agencies allow limited use of the Rational Method beyond strict area limits if justified, but you should check your local standards. For larger basins, more advanced hydrologic methods are preferred.