Runoff Curve Number (CN)
Enter rainfall and curve number CN to compute potential retention S, initial abstraction Ia and runoff Q (SCS-CN method), estimating storm runoff.
Input Data
Results
At a glance:The SCS runoff curve number (CN) method estimates 'how much surface runoff a storm produces'. Developed by the US Natural Resources Conservation Service (formerly SCS, now NRCS), its simplicity, low data need and wide applicability make it the most used runoff-estimation method worldwide for soil conservation, drainage, urban storm and farmland planning. Core idea: after rain hits the ground, part is lost to interception, infiltration, depression storage and evaporation, and only the rest becomes surface runoff; a watershed's maximum capacity to 'hold' water can be summarized by one parameter related to soil, vegetation, land use and antecedent wetness — the curve number CN. CN is a dimensionless index from 30 to 100: larger means the land absorbs less (impervious pavement, clay soil, saturated wet) and runoff is more; smaller means better infiltration (loose sand, good vegetation, dry) and runoff less. CN is set by three things and looked up in standard tables: hydrologic soil group (A best infiltration to D worst), land use and cover (forest, grass, farmland, urban impervious etc.), and antecedent moisture condition (AMC). With CN, the model proceeds in two steps. Step 1 converts CN to the watershed's maximum potential retention S (upper limit of rainfall loss, mm): S = 25400/CN − 254 (metric; in inches S = 1000/CN − 10 then convert). CN = 100 gives S = 0 (all runs off), small CN gives large S (more absorption, less runoff). Step 2 computes runoff: before runoff starts there is an initial abstraction Ia (vegetation interception, depression storage, early infiltration) that eats the rain first, empirically Ia = 0.2S; only rainfall P beyond Ia can run off. Runoff Q follows the SCS equation: Q = (P − Ia)² ÷ (P + 0.8S), with P rainfall and Ia = 0.2S; if P ≤ Ia, Q = 0 (all rain consumed by initial loss, no runoff). Substituting Ia = 0.2S often writes Q = (P − 0.2S)² ÷ (P + 0.8S). Example: farmland CN = 80, storm P = 50 mm: S = 25400/80 − 254 = 317.5 − 254 = 63.5 mm, Ia = 0.2 × 63.5 = 12.7 mm, since P = 50 > Ia = 12.7, Q = (50 − 12.7)² ÷ (50 + 0.8 × 63.5) = 37.3² ÷ (50 + 50.8) = 1391.29 ÷ 100.8 ≈ 13.80 mm. So this 50 mm rain produces about 13.8 mm surface runoff, the rest ~36 mm intercepted/infiltrated. A light rain P = 10 mm gives Q = 0 (no runoff). Uses: multiply runoff depth Q (mm) by catchment area for runoff volume (1 mm × 1 ha = 10 m³) to design drainage, detention ponds, farmland return flow; compare land-use/cover changes (different CN) on runoff to assess urbanization, development and conservation measures (more infiltration, lower CN); and as the rainfall-loss basis for peak-flow estimation with unit hydrographs. Notes: it is an event-scale empirical model estimating total storm runoff, not the time process (peak needs a hydrograph method); CN is sensitive to antecedent wetness — standard tables give AMC II (average); very dry (I) or wet (III) need adjustment; Ia = 0.2S is a common value, some studies use 0.05S, strongly affecting small-rain runoff; be cautious extrapolating to tiny or extreme storms; use correct soil group and land-use classification to avoid systematic bias.
Formula
Potential retention: S = 25400 ÷ CN − 254 (mm).
Initial abstraction: Ia = 0.2 × S.
Runoff: if P > Ia, Q = (P − Ia)² ÷ (P + 0.8S), else Q = 0.
$$S = \dfrac{25400}{CN} - 254$$$$Q = \dfrac{(P - 0.2S)^2}{P + 0.8S}, \quad P > 0.2S$$How to Use
- Look up curve number CN from soil group, land use and antecedent moisture.
- Enter the total storm rainfall P.
- The tool returns S, initial abstraction Ia and runoff Q; multiply by catchment area for runoff volume for drainage design.
Curve number CN and runoff example
| Item | Value | Note |
|---|---|---|
| Curve number CN | 80 | Farmland / medium soil |
| Potential retention S | 63.5 mm | = 25400/80−254 |
| Initial abstraction Ia | 12.7 mm | = 0.2S |
| Rainfall P | 50 mm | Runoff only if P > Ia |
| Runoff Q | ≈ 13.80 mm | ≈ 138 m³/ha |
CN adjusts by AMC; Ia=0.2S is common, some studies use 0.05S.
Case Studies
Runoff from a storm on farmland
Farmland CN = 80, storm P = 50 mm.
S = 25400/80 − 254 = 63.5 mm, Ia = 12.7 mm; since P > Ia, Q = (50−12.7)²/(50+50.8) ≈ 13.80 mm.
On a 10 ha catchment, runoff volume ≈ 13.80 × 10 × 10 = 1,380 m³, used to size return ditches and detention capacity.
Urbanization raises runoff
Same 50 mm rain, but development raises CN from 80 to 92 via more impervious surface.
S = 25400/92 − 254 ≈ 22.1 mm, Ia ≈ 4.4 mm, Q = (50−4.4)²/(50+17.7) ≈ 30.7 mm.
Runoff rises from 13.8 to 30.7 mm, over double — showing development must pair detention and permeable facilities to lower CN.
FAQ
How do I look up the curve number CN?
CN is determined by three things from standard tables: hydrologic soil group (A best infiltration to D worst, by infiltration rate), land use and cover type (forest, grass, farmland, residential, commercial impervious etc.), and antecedent moisture condition AMC. NRCS manuals (e.g. TR-55) give CN for each combination. Standard tables usually give AMC II (average) CN; if the watershed was very dry or wet recently, adjust by AMC I or III.
What do S and initial abstraction Ia represent?
S is the 'maximum potential retention' — how much rain the watershed can at most 'hold' (infiltration, depression storage) in that state, from S = 25400/CN − 254; larger CN gives smaller S. Ia is the 'initial abstraction' — the rain first consumed by vegetation interception, surface depression and early infiltration before runoff starts, empirically Ia = 0.2S. Only rainfall beyond Ia can form runoff.
Why does a light rain give zero runoff?
Because the SCS-CN model assumes an initial abstraction Ia = 0.2S before runoff. When a storm P is ≤ Ia, the rain is not enough to fill initial losses (interception, depression, infiltration), all is absorbed and no surface runoff, so Q = 0. Here S = 63.5 mm, Ia = 12.7 mm; if rain is only 10 mm (< 12.7), runoff is 0; it must exceed 12.7 mm to start running off.
Is the computed runoff a depth or a volume?
Q is runoff depth (mm), the average runoff depth over the whole catchment. To get total runoff volume, multiply Q by catchment area: 1 mm depth × 1 ha = 10 m³. E.g. Q = 13.8 mm, area 10 ha → volume = 13.8 × 10 × 10 = 1,380 m³. This volume sizes detention ponds, drainage channels and farmland return-flow systems. For peak flow (m³/s) you also need a runoff hydrograph or time-distribution method.
What are the limits of the CN method?
It is an event-scale empirical model estimating total storm runoff, not the time variation (peak and recession need a unit hydrograph etc.). It is sensitive to antecedent wetness — the same place differs greatly dry vs wet. Ia = 0.2S is a common assumption; some regions and newer studies use 0.05S, strongly affecting small-rain runoff. Also be cautious extrapolating to very small or extreme storms and non-typical land use; wrong CN table classification causes systematic bias.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.