Rational Method (Q = CIA)

Runoff coefficient C

C is the most uncertain parameter. Standard values from ASCE Manual 77:

• Asphalt and concrete: 0.70 to 0.95
• Roof: 0.75 to 0.95
• Gravel: 0.30 to 0.70
• Lawn, sandy soil, flat: 0.05 to 0.10
• Lawn, sandy soil, steep: 0.15 to 0.20
• Lawn, heavy soil, flat: 0.13 to 0.17
• Lawn, heavy soil, steep: 0.25 to 0.35
• Park, cemetery: 0.10 to 0.25
• Pasture: 0.05 to 0.30
• Forest: 0.05 to 0.25
• Commercial — downtown: 0.70 to 0.95
• Commercial — neighborhood: 0.50 to 0.70
• Residential — single-family: 0.30 to 0.50
• Residential — multi-family attached: 0.60 to 0.75
• Industrial — light: 0.50 to 0.80
• Industrial — heavy: 0.60 to 0.90

For mixed-cover watersheds, compute an area-weighted composite C: C_w = Σ(C_i × A_i) / Σ(A_i).

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 ≥ t_c. Use the time of concentration calculator to estimate t_c, 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).