Rational Method (Q = CIA)
The simplest peak-runoff equation. Best for drainage areas under 200 acres — pipe sizing, ditch design, parking-lot drainage. Not appropriate for runoff hydrograph generation or large watersheds.
In US customary units, the equation is Q = CIA exactly because 1 acre·in/hr = 1.008 cfs ≈ 1 cfs (Mulvany's coincidence).
Runoff coefficient C — full reference table
C is the most uncertain parameter. Use range midpoints for typical conditions; bias toward higher end for steep slopes, less-pervious soils, or older/aged surfaces. For mixed-cover watersheds, area-weight: Cw = Σ(Ci × Ai) / Σ(Ai).
| Surface / land use | C (range) | C (typical) |
|---|---|---|
| Asphalt / concrete pavement | 0.70–0.95 | 0.85 |
| Roof (composition shingle, metal) | 0.75–0.95 | 0.90 |
| Brick paver | 0.70–0.85 | 0.78 |
| Gravel surface | 0.30–0.70 | 0.50 |
| Pervious concrete / asphalt | 0.10–0.40 | 0.25 |
| Lawn, sandy soil, flat (< 2%) | 0.05–0.10 | 0.08 |
| Lawn, sandy soil, average (2–7%) | 0.10–0.15 | 0.13 |
| Lawn, sandy soil, steep (> 7%) | 0.15–0.20 | 0.18 |
| Lawn, heavy soil, flat | 0.13–0.17 | 0.15 |
| Lawn, heavy soil, average | 0.18–0.22 | 0.20 |
| Lawn, heavy soil, steep | 0.25–0.35 | 0.30 |
| Park, cemetery, golf course | 0.10–0.25 | 0.18 |
| Pasture, grassland | 0.05–0.30 | 0.20 |
| Forest, fair cover | 0.05–0.25 | 0.15 |
| Cultivated row crops | 0.20–0.40 | 0.30 |
| Land-use category | C (range) | C (typical) |
|---|---|---|
| Commercial — downtown CBD | 0.70–0.95 | 0.85 |
| Commercial — neighborhood | 0.50–0.70 | 0.60 |
| Residential — single-family detached | 0.30–0.50 | 0.40 |
| Residential — multi-family detached | 0.40–0.60 | 0.50 |
| Residential — multi-family attached | 0.60–0.75 | 0.68 |
| Apartments / dense urban | 0.50–0.70 | 0.60 |
| Industrial — light | 0.50–0.80 | 0.65 |
| Industrial — heavy | 0.60–0.90 | 0.75 |
| Schools, institutional | 0.50–0.70 | 0.60 |
| Railroad yards | 0.20–0.40 | 0.30 |
Source: ASCE Manual 77 — Design and Construction of Urban Stormwater Management Systems (1992). Cross-checked against FHWA HEC-22 (3rd ed., 2009) and TxDOT Hydraulic Design Manual.
Frequency adjustment factor Cf
For higher return periods, agencies often require a frequency multiplier on C, since larger storms saturate more of the watershed:
| Return period | Cf |
|---|---|
| 2-, 5-, 10-, 25-yr | 1.00 |
| 50-yr | 1.10 |
| 100-yr | 1.20 |
Worked examples
Example 1 — 5-acre commercial parking lot, 25-yr storm
Example 2 — Mixed residential subdivision, composite C, 100-yr
Rainfall intensity I
I is the average rainfall intensity for a storm duration equal to the watershed's time of concentration. Look up I from local IDF (intensity-duration-frequency) curves — NOAA Atlas 14 in the US is the common source. The design recurrence interval is selected by code: 10-year for residential streets, 25- to 50-year for arterials, 100-year for floodplain crossings.
Use the right time of concentration
The Rational Method assumes the entire watershed contributes to peak flow simultaneously, which only happens for storm durations ≥ tc. Use the time of concentration calculator to estimate tc, then read I off the IDF curve at that duration.
Limitations
- Drainage area should be under 200 acres (some agencies cap at 100 or 50).
- Assumes uniform rainfall over the basin and a single design storm.
- No detention or storage routing — Q is the instantaneous peak.
- Not valid for snowmelt or mixed events.
- For larger watersheds or where you need a hydrograph, use NRCS TR-20/TR-55, HEC-HMS, or SWMM.
Reference: ASCE Manual 77 — Design and Construction of Urban Stormwater Management Systems. Original: Mulvany, T.J. (1851), Kuichling, E. (1889).