Governing Formula
The Rational Method is the classic peak-flow estimator for small urban and rural catchments used in storm sewer and culvert sizing. It relates the peak runoff rate to the catchment area, a runoff coefficient, and the rainfall intensity.
Q = 2.78 × C × i × A Where:
-
Q= Peak runoff rate at the design point [L/s] -
C= Runoff coefficient: fraction of rainfall that runs off the catchment [—] -
i= Average rainfall intensity over the time of concentration [mm/h] -
A= Drainage catchment (contributing) area [ha] -
t_c= Time of concentration: time for runoff to reach the design point [min]
Derived Equations:
Q = 2.78 × C × i × A Q = 10 × C × i × A V = Q × t_c How the Calculation Works
Each input is multiplied together with the 2.78 factor, which is the standard SI aggregation of units: 1 ha = 10,000 m², and an intensity in mm/h is converted to a flow in L/s:
Q (L/s) = (i × 10⁻³ m/h) × (A × 10⁴ m²) × 10³ / 3600 = 2.777… × i × A
The runoff coefficient C is the fraction of rainfall that becomes runoff; grass and open soil absorb more (lower C), while paved and roofed surfaces shed nearly all rainfall (higher C). The intensity i is the average rainfall rate over the time of concentration — the time for the most remote drop of the catchment to reach the design point — so it depends on the local IDF (intensity–duration–frequency) curve for the chosen design storm. The runoff volume over the storm is the peak rate times the storm duration (taken as the time of concentration here).
Worked Engineering Example
Design Scenario: 1.0 ha Paved Service Yard, C = 0.90, Design Intensity 60 mm/h
- Peak runoff rate (L/s):
Q = 2.78 × 0.90 × 60 × 1.0 = 150.1 L/s - Peak runoff rate (m³/h):
Q = 10 × 0.90 × 60 × 1.0 = 540 m³/h - Runoff volume over a 60-minute storm:
V = 540 × (60/60) = 540 m³ - Drainage connection:
150 L/s peak flow must pass through the collected and conveyance system without surcharge
Engineering Notes & Design Benchmarks
| Surface Type | Typical Runoff Coefficient C |
|---|---|
| Roofs, asphalt, concrete paving | 0.70 – 0.95 |
| Gravel / macadam surfaces | 0.40 – 0.60 |
| Lawn, grass on light soil | 0.10 – 0.25 |
| Forest / natural open ground | 0.05 – 0.20 |
The Rational Method is well suited to small catchments (typically less than ~80 ha, and below that in many codes). For larger or complex catchments with routing or storage effects, unit hydrograph or continuous simulation methods should be used. The chosen C value should reflect the weighted average of the catchment land cover at the design storm frequency.
Assumptions & Limitations
- Uniform rainfall intensity across the whole catchment for the duration of the storm.
- Peak runoff occurs when the total catchment contributes, i.e. storm duration equals the time of concentration.
- No routing, storage, or detention is modelled — the calc estimates instantaneous peak, not hydrograph shape.
- The runoff coefficient lumps all losses (infiltration, interception, depression storage) into one factor; it varies with storm frequency and antecedent conditions.
- Intensity must come from the local IDF curve; design frequency (e.g. 5- or 10-year storm) is applied at the intensity.
- Volumes are estimates for design sizing; flood routing and local ordinance requirements must be verified by a drainage engineer.
Frequently Asked Questions
Why use 2.78 as the constant?
It is the unit-aggregation factor for the SI combination: area in hectares (×10⁴ m²), intensity in mm/h (×10⁻³ m/h), and the requested result in L/s. The same formula with 10 gives m³/h directly. It is not a calibration factor — the method is a simple lumped product, not a hydrodynamic model.
Where do I get the rainfall intensity?
From the local IDF (intensity–duration–frequency) curve or rainfall atlas for the design return period. For a 60-minute storm the intensity is the rate that is exceeded on average once in the chosen return period for that duration; use the duration equal to the time of concentration.
When should I not use the Rational Method?
For large catchments (roughly above 80 ha, or less per local code), catchments with significant storage, or where you need a flow hydrograph rather than a peak. Turbulent routing, pond attenuation, or regulated discharge need continuous simulation or unit-hydrograph methods and professional design.
Engineering Disclaimer
Engineering Note: This calculator estimates peak stormwater runoff for preliminary drainage design and education. Site drainage, pipe sizing, detention requirements, and runoff coefficients must be verified with local rainfall data, codes, and a licensed drainage engineer before construction.
Technical References
- Chow, V. T., Maidment, D. R., & Mays, L. W., Applied Hydrology, McGraw-Hill, 1988.
- Pilgrim, D. H., & Cordery, I., Flood Runoff, in Handbook of Hydrology, McGraw-Hill, 1993.
- Urban Drainage Design Manual (HEC-22), FHWA, (Rational Method for drainage design of small catchments).