SCS Curve Number Runoff Calculator (NRCS TR-55 Runoff Depth & Volume)
Calculate storm runoff depth and volume with the SCS / NRCS curve number method — potential retention S, initial abstraction Ia, antecedent moisture adjustment and the updated 0.05 Ia ratio, in mm or inches.
How it works
S = 1000/CN − 10 (inches) = 25,400/CN − 254 (mm) · Ia = 0.2·S · Q = (P − Ia)² / (P − Ia + S) for P > Ia, otherwise 0 · updated ratio: S₀.₀₅ = 1.33·S^1.15 (inches), Ia = 0.05·S₀.₀₅ · AMC I: CN = 4.2·CN/(10 − 0.058·CN); AMC III: CN = 23·CN/(10 + 0.13·CN) · volume = Q × area.
The curve number method of the USDA Natural Resources Conservation Service (formerly the Soil Conservation Service, SCS) estimates how much of a storm runs off rather than soaking in. The curve number, from 30 to 100, combines the hydrologic soil group (A to D) and the land cover; S is the most the ground could still absorb, and the initial abstraction Ia (interception, depression storage and early infiltration) must be filled before any runoff starts. It is documented in the National Engineering Handbook Part 630 and TR-55, and is the standard method for small-watershed runoff in many countries. Hawkins and others showed that Ia = 0.05S fits measured data better; it needs the adjusted S shown.
Worked example
A 75 mm storm falls on a catchment with CN = 80. S = 25,400/80 − 254 = 63.5 mm and Ia = 0.2 × 63.5 = 12.7 mm, so Q = (75 − 12.7)² / (75 − 12.7 + 63.5) = 62.3²/125.8 = 30.9 mm of runoff — a runoff coefficient of 41.1%. Over 10 ha that is 30.85 mm × 10 ha × 10 = 3,085 m³ of water.
Sources: USDA NRCS — Urban Hydrology for Small Watersheds (TR-55) · USDA NRCS — National Engineering Handbook Part 630, Chapter 10: Estimation of Direct Runoff
Frequently asked questions
How do I choose a curve number?
Find the hydrologic soil group (A sandy, high infiltration to D clayey, low infiltration) from a soil survey, then look up the land cover in TR-55 Table 2-2. For mixed catchments use an area-weighted CN, or better, compute runoff for each part separately and add the volumes.
What is the initial abstraction?
The rainfall absorbed before runoff begins — caught by plants, stored in surface hollows and infiltrated early in the storm. TR-55 sets Ia = 0.2S, so with CN 80 the first 12.7 mm (0.5 in) of rain produces no runoff at all.
What does the antecedent moisture condition change?
Table curve numbers are for average conditions (AMC II). After a dry spell (AMC I) the soil absorbs more and the CN drops; after heavy rain in the previous five days (AMC III) the soil is wet and the CN rises — CN 80 becomes about 63 and 90 respectively.
Should I use Ia = 0.2S or 0.05S?
0.2S is still the official TR-55 method and what most regulations require. Research by Hawkins and a 2019 NRCS review support 0.05S with an adjusted S, which gives more runoff from small storms and low curve numbers. Check what your local agency accepts.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.