SCS-CN Runoff Calculator

Estimate the direct-runoff depth of a storm with the curve number method.

The SCS-CN Method

The NRCS curve number (SCS-CN) method is an event loss method that estimates the direct-runoff depth of a rainfall event. Its output is a runoff depth in millimetres, not a discharge or a peak flow.

S = 25400/CN − 254; Ia = λ·S; R = (P − Ia)² / (P − Ia + S) for P > Ia, otherwise R = 0

  • P: rainfall depth (mm)
  • CN: curve number from cover, land use, soil group and condition
  • S: potential maximum retention (mm)
  • Ia: initial abstraction (mm), with ratio λ conventionally 0.2
  • R: direct-runoff depth (mm)

CN is not the runoff coefficient C of the Rational Method. A runoff depth of 1 mm over 1 km² is a volume of 1000 m³; volume is not discharge.

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Potential Maximum Retention (S)

0.00 mm

Initial Abstraction (Ia)

0.00 mm

Direct-Runoff Depth (R)

0.00 mm

Runoff Ratio (R / P)

0.000

P, S, Ia, R: mm · A: km² · volume: m³ (1 mm × 1 km² = 1000 m³). The coefficients include the SI unit conversion. NRCS — National Engineering Handbook, Chapter 10: Direct Runoff

Worked examples and limits

Example 1: CN = 75, P = 60 mm

For CN = 75, S = 25400/75 − 254 = 84.67 mm, and with λ = 0.2 the initial abstraction is Ia = 16.93 mm. Since P > Ia, R = (60 − 16.93)² / (60 − 16.93 + 84.67) = 14.52 mm, a runoff ratio R/P = 0.242. Over A = 1 km² this is a volume of about 14,520 m³.

Example 2: sensitivity to CN and λ

For the same 60 mm storm with CN = 90, S = 28.22 mm, Ia = 5.64 mm and R = 35.78 mm (R/P = 0.596); raising CN from 75 to 90 multiplies the runoff depth by about 2.5. With CN = 75 and λ = 0.05 instead of 0.2, Ia = 4.23 mm and R = 22.15 mm. The ratio λ must therefore be reported and kept consistent with the assumptions under which CN was derived.

Assumptions and limits

  • The result is a runoff depth and a volume, not a hydrograph or a peak flow. A peak needs the time distribution of the rainfall, a transformation model and, where relevant, routing.
  • CN is chosen from cover, land use, hydrologic soil group and condition; similar-looking areas need not share a value. Tabulated values generally lie between roughly 30 and 98.
  • If P ≤ Ia the runoff is zero. At CN = 100, S = 0 and all rainfall becomes runoff (R = P).
  • The method is an event loss method; it is not a continuous water budget or a groundwater model.

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