Rational Method — Q = CiA Reference
The oldest and still the most-used peak-flow method in drainage design. It returns a single number — the peak discharge — and nothing else: no hydrograph, no volume, no routing. Knowing precisely what it does and does not give you is most of using it correctly.
The Equation
| Units | Equation | Q | i | A |
|---|---|---|---|---|
| US customary | Q = C · i · A | cfs | in/hr | acres |
| SI | Q = C · i · A / 360 | m³/s | mm/hr | hectares |
| SI (alternate) | Q = 0.00278 · C · i · A | m³/s | mm/hr | hectares |
The Three Inputs
| Term | What it is | Where it comes from |
|---|---|---|
| C | Runoff coefficient, 0 to 1 — the fraction of rainfall that becomes direct runoff | Land-cover table; see the runoff coefficient reference |
| i | Average rainfall intensity over a duration equal to Tc, at the design return period | NOAA Atlas 14 IDF curves for the site |
| A | Contributing drainage area | Delineated to the design point |
Composite C for Mixed Land Cover
Area-weight the individual coefficients. Do not average them unweighted, and do not apply a single "residential" C to a site that is 40 percent pavement — the weighted value is usually meaningfully higher than the eyeball estimate.
Frequency Adjustment Factor Cf
Published C values are calibrated for storms up to roughly the 10-year event. For rarer events the soil saturates and a larger fraction of rainfall runs off, so C is adjusted upward:
| Return period | Cf | Applied as |
|---|---|---|
| 2 to 10 year | 1.0 | Cadjusted = C · Cf |
| 25 year | 1.1 | |
| 50 year | 1.2 | |
| 100 year | 1.25 |
Assumptions You Are Accepting
| Assumption | Consequence when it fails |
|---|---|
| Rainfall is uniform over the whole area | Breaks down on large watersheds where a storm cell covers only part of the area |
| Rainfall duration equals or exceeds Tc | The peak is not reached; the method over-predicts |
| Peak flow occurs when the whole area contributes | Not true where a small, highly impervious sub-area peaks earlier — check partial-area conditions |
| C is constant through the storm | Ignores the saturation trend that Cf partially patches |
| Return period of Q equals that of i | An approximation, not a derivation |
| No storage anywhere in the system | Ponds, swales and pipe storage all attenuate the peak; the method cannot see them |
When You May Use It
| Limit | Typical threshold | Note |
|---|---|---|
| Drainage area | ≤ 200 acres | Many agencies cap far lower — 20 to 50 acres is common; check the local manual, which governs |
| Output needed | peak flow only | If you need a volume or a hydrograph, use TR-55 / TR-20 / HEC-HMS instead |
| Storage present | none | Any detention or routing puts you outside the method |
| Tc | ≥ 5 min | Most agencies enforce a 5 or 10 minute floor on the IDF read |
Sources: Kuichling, E. (1889), the original statement of the method. FHWA HEC-22, Urban Drainage Design Manual, 3rd ed. ASCE/WEF MOP 77, Design and Construction of Urban Stormwater Management Systems. Intensity from NOAA Atlas 14. Cf values as tabulated in HEC-22 and most state DOT drainage manuals — confirm against the manual with jurisdiction over your project, which governs over any general reference including this one.
Related cheat sheets and tools
The Rational Method is one of three inputs working together: time of concentration sets the duration, runoff coefficient C sets the fraction, and the IDF curve supplies i — see design rainfall from Atlas 14. Past 200 acres, or where you need volume rather than a peak, switch to NRCS curve numbers and SCS storm distributions. Once you have Q, size the conveyance with Manning's n. For the full watershed-to-outfall workflow with routing, see HydroComplete, the SaaS sister product to PE-Calc.