What it does
When rain falls on a catchment, some soaks in and some runs off to the nearest ditch, drain or stream. This tool gives two everyday estimates of how much runs off:
- The rational method, Q = C × i × A, gives the peak flow from a small catchment, used to size gutters, pipes, culverts and ditches.
- The SCS curve number method (now the NRCS method) gives the depth and volume of runoff from a whole storm, used to size ponds and to compare land uses, and a simple triangular hydrograph shows when the flow peaks.
Both start from the same catchment: split it into parts by land use, give each an area, a runoff coefficient C and a curve number CN, and the tool works out the area-weighted values.
How to use it
- Choose SI (hectares, millimetres, metres) or US (acres, inches, feet).
- Fill in up to four parts of the catchment. The Typical list fills C and CN with rounded starting values for a medium soil; change them for your soil and local guidance. Empty rows are skipped.
- Give the longest flow path and its average slope to get the time of concentration by the Kirpich formula, the time water takes to travel from the far edge to the outlet. If you know it from elsewhere, type it instead.
- For the rational method, give a rainfall intensity, or the three constants of your local intensity-duration-frequency curve, i = a / (t + b)^c, so the tool reads the intensity at the time of concentration. Pick a return period adjustment for rare storms.
- For the curve number method, give the storm rainfall and duration, the state of the ground before the storm, and the initial abstraction ratio.
What the results mean
- C is the share of the rain falling at the peak that leaves as flow: about 0.9 for roofs and paving, under 0.3 for grass and woods.
- CN runs from about 30 (deep sand under forest, almost nothing runs off) to 98 (paving). The potential retention S is the most the ground could hold, and the initial abstraction Ia is the rain held on leaves, in hollows and in the soil before any runs off.
- Dry and wet ground (conditions I and III) change CN a lot: a field after a week of rain behaves very differently from the same field in a drought.
- The triangular hydrograph spreads the runoff over time: it rises to its peak at Tp = D/2 + 0.6 tc and ends at 2.67 Tp.
Worked example
A made-up 20 ha catchment: 12 ha of houses with gardens (C 0.45, CN 75) and 8 ha of pasture (C 0.25, CN 61). The area-weighted C is 0.37 and CN 69.4. The longest flow path is 600 m at a slope of 0.02, so Kirpich gives a time of concentration of 12.1 minutes. With a made-up rainfall curve a = 1500, b = 12, c = 0.8, the intensity at 12.1 minutes is 118 mm/h and the peak flow is 2.42 m³/s.
For an 80 mm storm lasting an hour on average ground, S = 112 mm and Ia = 22.4 mm, so 19.6 mm runs off (24.5 %), a volume of 3,913 m³. The triangular hydrograph peaks at 1.31 m³/s, 0.62 hours after the rain starts.
FAQ
Why do the two methods give different peaks? They answer different questions. The rational method assumes the most intense burst of rain lasting exactly the time of concentration; the curve number hydrograph spreads a whole storm’s runoff over time. Design manuals say which one to use for which job.
How big a catchment can I use? The rational method is meant for small areas, under about 80 ha (200 acres). The curve number method works for larger catchments, but the single triangle is crude for long storms or long, thin catchments; a full unit hydrograph model does better.
Is this good enough for a design? It is a first estimate and a sense check. Real drainage design follows local rules, local rainfall data and a qualified engineer’s judgement.
Where the numbers come from
- Rational method (Q = CiA), Kirpich (1940) time of concentration and intensity-duration curves of the form i = a/(t + b)^c: standard hydrology, for example Chow, V. T., Maidment, D. R. and Mays, L. W. (1988), Applied Hydrology (equations only).
- SCS curve number method, the dry and wet condition conversions and the triangular unit hydrograph: USDA Natural Resources Conservation Service, National Engineering Handbook Part 630 Hydrology and Technical Release 55 (public domain), and Chow, Maidment and Mays (1988). The 0.05 initial abstraction option uses the S conversion factor 1.42 from Hawkins and others (2002).
- Typical C and CN values for each land use are rounded, general figures chosen by fibub for a first estimate, not copied from any table. The return period factors are the commonly quoted round numbers.
- Checked against an independent Python calculation written for the tests. The example catchment and its rainfall curve are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.