What This Solves
Estimates total runoff depth from a rainfall event based on soil type, land cover, and antecedent moisture using the NRCS Curve Number method.
Best Used When
- You need to estimate runoff volume for pond or detention basin sizing
- You have mixed land uses and soil types across the drainage area
- You are working with hydrologic soil group (HSG) data and NRCS land cover classifications
Do NOT Use When
- You only need the peak flow rate, not the total runoff volume — Use Rational Method Calculator
- You have detailed site-specific runoff coefficients for impervious and pervious areas — Use Runoff Coefficient Calculator
Key Assumptions
- The rainfall event is a single storm of uniform intensity
- Initial abstraction (Ia) is a fixed ratio of maximum retention (typically 0.2S)
- Soil moisture conditions are uniform across the watershed
- The curve number adequately represents the combined effects of soil type, land use, and surface condition
- Antecedent moisture condition remains constant during the storm
Input Quality Notes
Curve numbers are empirical values that vary with antecedent moisture, season, and land management. Verify CN selections against local calibration data or NRCS tables for your region.
Try a Common Scenario
Click to pre-fill the calculator with realistic values.
Estimate the depth and volume of stormwater runoff generated by a design storm using the SCS (now NRCS) Curve Number method. Enter your rainfall depth and curve number to get runoff depth (Q), maximum retention (S) and initial abstraction (Iₐ), or weight multiple land uses into a single composite CN.
Calculation Mode
Runoff Calculation: Calculate runoff depth (Q) from rainfall depth (P) and curve number (CN) using the SCS equation.
SCS Curve Number Method Overview
The SCS (now NRCS) Curve Number method estimates direct runoff from storm rainfall. The basic equation is:
Where:
- Q = Runoff depth (in)
- P = Rainfall depth (in)
- Ia = Initial abstraction = 0.2S (in)
- S = Maximum retention = (1000/CN) - 10 (in)
Common Curve Number Values
| Land Use / Cover | Group A | Group B | Group C | Group D |
|---|---|---|---|---|
| Commercial (85% imp.) | 89 | 92 | 94 | 95 |
| Residential (1/4 acre) | 61 | 75 | 83 | 87 |
| Lawn (good condition) | 39 | 61 | 74 | 80 |
| Pasture (fair) | 49 | 69 | 79 | 84 |
| Woods (fair) | 36 | 60 | 73 | 79 |
| Paved (impervious) | 98 | 98 | 98 | 98 |
Source: USDA TR-55 (1986), Table 2-2. Values shown for AMC II (average conditions).
Antecedent Moisture Conditions
AMC I - Dry
Dormant season with less than 0.5" of rainfall in prior 5 days. Lowest runoff potential.
CNI = 4.2 CNII / (10 - 0.058 CNII)
AMC II - Average
Normal conditions. This is the standard condition used in TR-55 tables.
Standard CN values from tables
AMC III - Wet
Growing season with more than 2.1" of rainfall in prior 5 days. Highest runoff potential.
CNIII = 23 CNII / (10 + 0.13 CNII)
How the SCS Curve Number method works
The method estimates direct runoff depth (Q) from a single storm by treating the curve number as a measure of the watershed's runoff potential. The governing equation is:
The supporting relationships are:
S = (25400 / CN) − 254 (mm)
Where:
- Q = direct runoff depth (in or mm)
- P = total storm rainfall depth (in or mm)
- CN = runoff curve number (1–100), from cover type and hydrologic soil group
- S = potential maximum retention after runoff begins (in or mm)
- Ia = initial abstraction — losses before runoff begins, taken as λS
- λ = initial abstraction ratio (0.2 traditional, 0.05 revised)
For an antecedent moisture condition other than average (AMC II), the base curve number is adjusted before computing S: CNI = 4.2·CNII / (10 − 0.058·CNII) for dry conditions and CNIII = 23·CNII / (10 + 0.13·CNII) for wet conditions. If a drainage area is supplied, runoff volume is found from V = Q × A with the appropriate unit conversion (inch-acres to ft³, or mm-hectares to m³).
Sources: USDA TR-55 (1986), Urban Hydrology for Small Watersheds, Eqs. 2-1 to 2-3; NRCS National Engineering Handbook, Part 630, Chapter 10 (AMC conversions).
Curve numbers by cover type and soil group
Representative curve numbers for the average condition (AMC II), λ = 0.2. The four hydrologic soil groups run from A (sand/loamy sand, low runoff potential) to D (clay, high runoff potential). Use these to set CN directly or as a starting point for a composite calculation.
| Cover type / land use | A | B | C | D |
|---|---|---|---|---|
| Commercial / business (85% impervious) | 89 | 92 | 94 | 95 |
| Industrial (72% impervious) | 81 | 88 | 91 | 93 |
| Residential, 1/8-acre lots (65% impervious) | 77 | 85 | 90 | 92 |
| Residential, 1/4-acre lots (38% impervious) | 61 | 75 | 83 | 87 |
| Residential, 1-acre lots (20% impervious) | 51 | 68 | 79 | 84 |
| Open space / lawn, good condition (>75% cover) | 39 | 61 | 74 | 80 |
| Pasture / grassland, fair condition | 49 | 69 | 79 | 84 |
| Woods / forest, fair condition | 36 | 60 | 73 | 79 |
| Row crops, straight row, good condition | 67 | 78 | 85 | 89 |
| Paved or roof (impervious) | 98 | 98 | 98 | 98 |
Source: USDA TR-55 (1986), Table 2-2; NRCS National Engineering Handbook, Part 630, Ch. 9. Residential values are the composite CNs that combine impervious area with open-space lawn in good condition. Use the in-tool "Lookup" panel to pull a value for a specific cover, soil group and hydrologic condition.
Worked example (TR-55 Example 2-1)
A storm of P = 5.0 in falls on a watershed with CN = 75 (AMC II, λ = 0.2):
- Maximum retention S = (1000 ÷ 75) − 10 = 3.33 in
- Initial abstraction Ia = 0.2 × 3.33 = 0.67 in
- Since P (5.0) > Ia (0.67), runoff occurs
- Runoff depth Q = (5.0 − 0.67)² ÷ (5.0 − 0.67 + 3.33) = 2.47 in
- Runoff coefficient Q/P = 2.47 ÷ 5.0 = 0.49
Roughly half the rainfall becomes direct runoff for this moderately developed watershed, which matches the published TR-55 result.
Frequently asked questions
What is a curve number (CN)?
The runoff curve number is a dimensionless index from 1 to 100 that represents how much rainfall a surface converts to direct runoff. It bundles land cover and the hydrologic soil group (A–D) into a single value: low numbers (around 30–60) indicate pervious soils and dense vegetation that absorb most rainfall, while high numbers (90–98) indicate impervious surfaces such as pavement and rooftops, which produce almost pure runoff. Standard CN tables are published for the average antecedent moisture condition (AMC II) in USDA TR-55, Table 2-2.
How is runoff depth calculated from rainfall and CN?
The method first converts the curve number to a potential maximum retention S = (1000 / CN) − 10 inches (or (25400 / CN) − 254 mm). It then sets the initial abstraction Ia = 0.2S (the traditional ratio) and computes runoff as Q = (P − Ia)² / (P − Ia + S), where P is the total storm rainfall depth. If P is less than or equal to Ia, no runoff occurs (Q = 0). For example, P = 5.0 in with CN = 75 gives S = 3.33 in, Ia = 0.67 in, and Q ≈ 2.47 in, matching TR-55 Example 2-1.
What is the initial abstraction ratio (0.2 vs 0.05)?
Initial abstraction Ia is the rainfall lost to interception, depression storage, and infiltration before runoff begins. It is expressed as a fraction of S: Ia = λS. The traditional TR-55 value is λ = 0.2. More recent research (Hawkins et al.) found that λ ≈ 0.05 fits measured rainfall-runoff data better in many watersheds, producing more runoff for small storms. This calculator lets you choose either ratio, but note that CN tables were originally calibrated for λ = 0.2, so a CN value should be re-derived if a different λ is used.
How do I find the curve number for a watershed with mixed land use?
Use an area-weighted composite curve number: CN_composite = Σ(Aᵢ × CNᵢ) / Σ(Aᵢ). Break the drainage area into sub-areas of uniform cover and soil group, look up each CN, multiply by its area, sum the products, and divide by the total area. The "Composite CN" mode of this calculator performs this weighting automatically. For accuracy, weight by curve number rather than by percent impervious, especially when the area mixes very high and very low CN values.
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Last verified: February 2026