SCS Curve Number Runoff Calculator

Understanding the SCS curve number runoff calculator — concept and principle

The SCS (now NRCS) curve number method estimates how many millimetres of a storm's rainfall become direct runoff. It is widely used for flood studies, culvert and pond design and land-use impact checks because a single number, CN, captures soil type, land cover and wetness. Enter the storm rainfall depth and the curve number to get the runoff depth, the potential retention and the initial abstraction.

Only about a third of the 80 mm becomes runoff on CN-75 ground.

How it is calculated

Potential maximum retention: S = 25400/CN − 254 (mm).
Initial abstraction: Ia = 0.2·S, the rain lost before runoff begins (interception, depression storage, early infiltration).
Runoff depth: Q = (P − Ia)²/(P − Ia + S) when P > Ia; otherwise Q = 0.

P is the storm rainfall depth (mm) and CN a value from 0 to 100, found in tables by hydrologic soil group (A to D) and land cover.

The principle

The method assumes the ratio of water actually retained to the maximum possible retention equals the ratio of actual runoff to potential runoff: F/S = Q/(P − Ia). Combining this with the water balance P = Ia + F + Q gives the runoff formula. As rain continues, the soil fills up, so runoff starts slowly and later approaches the rainfall rate. CN is just a convenient transform of S: CN = 100 means S = 0 (all rain runs off), and lower CN means more storage. Sandy soils under forest may have CN in the 30s, while paved surfaces are about 98.

Worked example

Inputs: P = 80 mm, CN = 75.
S = 25400/75 − 254 = 84.67 mm.
Ia = 0.2 × 84.67 = 16.93 mm.
P − Ia = 63.07 mm; squared = 3977.4.
Q = 3977.4/(63.07 + 84.67) = 3977.4/147.73 = 26.92 mm.

Each point is the calculator re-run with only “Curve number” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Curve number	Runoff depth (mm)
18.8	0
37.5	0
56.2	6.88673969
75	26.92286402
93.8	62.74518434
112	127.7374957
150	765.984058

How to read the result

About 34% of the 80 mm storm becomes runoff in the example. Multiply Q by catchment area to get runoff volume: 26.92 mm over 1 ha is 269 m³. Small changes in CN have a large effect for moderate storms, so the choice of soil group and land cover deserves the most care. The method gives a depth, not a peak rate; for a hydrograph, combine it with a unit hydrograph and time of concentration.

Common mistakes

Using the inch form (S = 1000/CN − 10) with millimetre rainfall.
Applying daily rainfall totals from several separate storms as one event.
Ignoring antecedent wetness; tabulated CNs represent average conditions.
Using it for very small storms, where Ia dominates and errors are large.

Keep in mind: The curve number method is empirical and calibrated mainly on small US agricultural watersheds. Ia = 0.2S is a convention, and some studies suggest a smaller ratio. Use local guidance and calibrated data for design, and have results reviewed by a qualified engineer.

Frequently asked questions

Where do I find CN values?

In NRCS TR-55 and the National Engineering Handbook, Part 630, tables by land use and hydrologic soil group.

How do I combine several land uses?

Area-weight the CN values, or compute runoff for each area and add the volumes, which is more accurate.

Why is runoff zero for small rain?

Until rainfall exceeds Ia, all of it is held back by interception, depressions and infiltration.

Sources: USDA NRCS, National Engineering Handbook, Part 630 Hydrology, Chapter 10 · USDA SCS, Urban Hydrology for Small Watersheds, Technical Release 55, 1986

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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