About Rational Method Peak Runoff Calculator
The rational runoff calculator estimates the peak stormwater flow from a small catchment with the rational method, Q = C·i·A. In SI units Q (m³/s) = 0.278·C·i·A with intensity i in mm/hr and area A in km²; in US customary units Q (cfs) = C·i·A with i in in/hr and A in acres, the classic “1 acre at 1 in/hr gives about 1 cfs” identity. Mixed land covers are handled with an area-weighted composite runoff coefficient built from up to five sub-areas.
Two companion modes complete a preliminary drainage design. The time-of-concentration mode evaluates both the Kirpich (1940) formula tc = 0.0078·L^0.77·S^−0.385 and the FAA (1970) formula tc = 1.8·(1.1 − C)·L^0.5 / S%^(1/3), the travel time that fixes the design storm intensity. The SCS Curve Number mode computes the direct runoff depth Q = (P − 0.2S)² / (P + 0.8S) per NRCS TR-55, plus the runoff volume when a catchment area is supplied.
How It Works
- Pick the unit system (SI or US customary) and the calculation mode: rational peak flow, time of concentration, or SCS Curve Number runoff.
- Rational mode: enter up to five sub-areas with their runoff coefficients C (0–1) and the design rainfall intensity; the tool computes the area-weighted composite C and the peak flow in m³/s, cfs, and L/s.
- Time-of-concentration mode: enter the hydraulic flow-path length, the average slope (m/m or ft/ft), and a surface runoff coefficient; the tool reports tc by both the Kirpich and FAA formulas in minutes.
- SCS mode: enter the curve number (30–100) and the storm precipitation depth; the tool computes S, the initial abstraction Ia = 0.2S, the runoff depth Q, the runoff ratio, and — with an optional catchment area — the runoff volume in m³ and acre-ft.
Worked Example
A 1 ha (0.01 km²) commercial site is mostly paved, with a composite runoff coefficient C = 0.9. The design storm from the local IDF curve at the site’s time of concentration has an intensity of 100 mm/hr. The rational method gives Q = 0.278 × 0.9 × 100 × 0.01 = 0.2502 m³/s ≈ 250 L/s (8.8 cfs), the peak flow the site storm drain must carry. For a check on the storm duration, a 1000 ft flow path at 1% slope gives a Kirpich time of concentration of tc = 0.0078 × 1000^0.77 × 0.01^−0.385 ≈ 9.4 minutes, so a 10-minute storm intensity is appropriate.
Formulas
- Rational method (SI)
Q = 0.278 · C · i · A- Rational method (US customary)
Q = C · i · A- Composite runoff coefficient
C_w = Σ(C_j · A_j) / Σ(A_j)- Kirpich time of concentration
tc = 0.0078 · L^0.77 · S^−0.385- FAA time of concentration
tc = 1.8 · (1.1 − C) · L^0.5 / S%^(1/3)- SCS Curve Number runoff
S = 1000/CN − 10; Q = (P − 0.2S)² / (P + 0.8S) for P > 0.2S
Standards & References
- ASCE / WEF urban stormwater drainage design practice (rational method)
- Kirpich, Z. P. (1940) time of concentration of small agricultural watersheds
- FAA AC 150/5320-5 airport drainage (FAA tc formula)
- USDA NRCS TR-55 Urban Hydrology for Small Watersheds (Curve Number method)
Frequently Asked Questions
What is the rational method and when is it valid?
The rational method Q = CiA estimates the peak runoff from a catchment assuming rainfall of uniform intensity falls long enough for the whole area to contribute — that is, the storm duration equals the time of concentration. It is standard practice for small urban catchments, typically below about 80 ha (200 acres); larger or more complex watersheds should use hydrograph methods such as the SCS unit hydrograph.
What runoff coefficient C should I use?
C represents the fraction of rainfall that becomes direct runoff. Typical values: asphalt and concrete pavement 0.85–0.95, roofs 0.75–0.95, gravel 0.35–0.70, lawns on flat sandy soil 0.05–0.10, lawns on steep heavy soil 0.25–0.35, and dense residential areas 0.50–0.70. For mixed sites, compute the area-weighted composite C — this calculator does that from up to five sub-areas.
Why is the SI rational formula Q = 0.278 CiA?
The 0.278 factor (1/3.6) simply converts units. Multiplying intensity in mm/hr by area in km² gives a volume rate in mm·km²/hr; converting millimetres to metres, square kilometres to square metres, and hours to seconds yields 10⁻³ × 10⁶ / 3600 = 0.2778 m³/s. In US units the conversion factor from in/hr times acres to cfs is 1.008, close enough to 1 that it is conventionally dropped.
What is the time of concentration and why does it matter?
The time of concentration tc is how long runoff takes to travel from the hydraulically most remote point of the catchment to the outlet. The rational method uses a design storm whose duration equals tc, because that produces the highest intensity for which the whole catchment contributes simultaneously — the critical peak. Kirpich suits channelized rural flow paths, while the FAA formula was developed for overland flow on paved areas such as airports; comparing both brackets the estimate.
How does the SCS Curve Number method differ from the rational method?
The rational method predicts a peak flow rate from a rainfall intensity, while the Curve Number method predicts a runoff depth (and hence volume) from a storm rainfall depth. CN encodes soil group, land cover, and antecedent moisture: 30 is very pervious, 98 is pavement. The method subtracts an initial abstraction Ia = 0.2S and routes the rest through Q = (P − 0.2S)²/(P + 0.8S). Use it to size detention storage, where volume governs, and the rational method to size conveyance, where peak flow governs.
What rainfall intensity should I enter?
Use the local intensity-duration-frequency (IDF) curve for your design return period — commonly 2 to 10 years for minor drainage and 25 to 100 years for major systems — read at a duration equal to the time of concentration. Compute tc first in the time-of-concentration mode (with a 5–10 minute practical minimum), then look up the corresponding intensity and enter it in the rational mode.