Curve Number Calculator: Runoff Formula & Use

A Curve Number (CN) calculator estimates direct runoff depth from a storm using the USDA Soil Conservation Service (now NRCS) runoff equation. You input the curve number (a value from 40 to 98 representing soil type, land use, and antecedent moisture) and the storm rainfall depth; the calculator returns the runoff depth in inches or millimeters. This is a standard tool for hydrologic design, flood estimation, and stormwater management.

Formula

The NRCS (SCS) runoff curve number method uses the following equations:

Potential retention: S = (1000 / CN) – 10 (S in inches)

Initial abstraction: I_a = 0.2 * S

Runoff depth: Q = (P – I_a)² / (P – I_a + S) for P > I_a; otherwise Q = 0

Where:

• P = rainfall depth (inches)
• Q = direct runoff depth (inches)
• CN = curve number (dimensionless, 40–98)
• S = maximum potential retention after runoff begins (inches)
• I_a = initial abstraction (inches) – water trapped in depressions, intercepted by vegetation, and infiltrated before runoff starts

The method assumes that the ratio of actual runoff to potential runoff equals the ratio of actual infiltration to potential retention, leading to the above equation. The curve number itself is a lumped parameter that integrates soil type, land cover, and hydrologic condition.

Worked Example

Using the default values: CN = 75, rainfall P = 3.2 inches.

1. Compute S: S = (1000 / 75) – 10 = 13.333 – 10 = 3.333 inches
2. Compute initial abstraction: I_a = 0.2 * 3.333 = 0.667 inches
3. Check P > I_a: 3.2 > 0.667, so runoff occurs
4. Compute P – I_a: 3.2 – 0.667 = 2.533 inches
5. Compute Q = (2.533)² / (2.533 + 3.333) = 6.416 / 5.866 = 1.094 inches

The calculator rounds to two decimals, giving Q = 1.09 inches. This means about 1.09 inches of the 3.2-inch storm becomes direct runoff; the rest infiltrates, evaporates, or is stored.

How to Choose the Curve Number

Selecting the correct CN is the most critical step. The NRCS provides tables (e.g., in the National Engineering Handbook, Part 630, Chapter 9) that list CN values for combinations of land use, treatment, hydrologic condition, and soil group. The four hydrologic soil groups are:

• A – low runoff potential (deep sand, loamy sand), high infiltration
• B – moderate infiltration (sandy loam, silt loam)
• C – slow infiltration (clay loam, sandy clay loam)
• D – high runoff potential (clay, soils with high water table)

For example, a residential area with 1/8-acre lots on soil group B might have CN = 75 (good condition) or 80 (poor condition). A dense forest on group B could be CN = 55, while a paved parking lot is CN = 98 regardless of soil. The “hydrologic condition” refers to the density of vegetation and surface cover: good condition means dense, healthy cover that slows runoff.

If you don’t have a site-specific CN, use the NRCS tables or a local government stormwater design manual. Many engineering software packages include a CN lookup tool. The standard reference is the USDA NRCS National Engineering Handbook, Part 630, Chapter 9 (Hydrologic Soil-Cover Complexes).

Common Mistakes and Misconceptions

• Using the wrong units: The formula is in inches. If your rainfall is in millimeters, convert to inches (divide by 25.4) before using the equation. The CN is dimensionless and doesn’t change.
• Forgetting the initial abstraction: If P ≤ 0.2S, the runoff is zero. Many people try to compute a negative runoff; the correct result is zero.
• Applying CN to a single storm event vs. annual runoff: The method is designed for individual storm events, typically a 24-hour design storm. It is not accurate for continuous simulation without modifications.
• Ignoring antecedent moisture condition (AMC): The standard CN tables assume average antecedent moisture (AMC II). For dry (AMC I) or wet (AMC III) conditions, you must adjust the CN using conversion tables. A wet soil can have a CN 10–15 points higher.
• Using CN for snowmelt: The method does not account for snowmelt or frozen ground; those conditions require special treatment.

A common misconception is that the curve number is a measured physical property. In reality, it is a fitted parameter that best matches observed runoff for a given area. It varies with storm size and season, so it is not a universal constant.

Limitations and When to Use It

The CN method is best used for:

• Design of stormwater detention facilities (sizing ponds, culverts)
• Flood hydrograph estimation for small to medium watersheds (up to a few square miles)
• Comparing land-use change impacts on runoff
• Preliminary screening before using more complex models

It is not recommended for:

• Large watersheds (over ~10 mi² or 25 km²) where routing and timing become important
• Highly complex terrain with significant channel storage
• Continuous simulation (long-term water balance) without calibration
• Areas with substantial snowmelt or frozen ground

The method gives only total runoff depth, not the timing or peak flow. To get a hydrograph, you must combine it with a unit hydrograph or time-area method. It also assumes uniform rainfall distribution over the watershed, which may not hold for convective storms.

Alternatives to the Curve Number Method

Several other methods estimate runoff or infiltration:

• Rational Method: Q = CiA, used for peak flow from small urban watersheds (< 200 acres) where the time of concentration is short. It gives peak discharge, not runoff volume.
• Green-Ampt Infiltration Model: Physically based, uses soil hydraulic properties (saturated hydraulic conductivity, wetting front suction). More accurate for infiltration but requires more data.
• Snyder’s Unit Hydrograph: For generating a runoff hydrograph from rainfall; often used in conjunction with CN for loss rate.
• HEC-HMS / SWMM: Software models that can use CN or other loss methods, and simulate routing and water quality.
• USGS Regression Equations: Empirical formulas for peak flow based on watershed characteristics; useful for ungaged sites.

Each alternative has its own data requirements and accuracy. The CN method remains popular because it requires only one parameter and is well-documented in design manuals.

Frequently Asked Questions

What is a good curve number for a forest?

For a mature forest with good ground cover (leaf litter, dense understory), the CN on soil group B is typically 55 (good condition) to 70 (poor condition). For soil group A, it can be as low as 30. Check the NRCS tables for your specific forest type and condition.

How do I convert CN from AMC II to AMC III?

Use the standard conversion tables in the NRCS handbook. For example, a CN of 75 under AMC II becomes approximately 87 under AMC III (wet) and 58 under AMC I (dry). The exact values vary slightly, so use the official table.

Can I use the curve number method for a green roof?

Yes, but you need a CN that reflects the growing media and drainage layer. Some studies suggest CN values around 86–90 for intensive green roofs, but these are not standard in NRCS tables. It’s better to use a specialized model or measure runoff directly.

Why does my calculated runoff seem too low for a high CN?

Check your rainfall input. For a CN of 98, S = 0.204 inches and Ia = 0.041 inches, so even a small storm (e.g., 0.5 inches) produces runoff of about 0.42 inches. If you get zero, your rainfall is below 0.2S. Also verify that you are using inches consistently.

Is the curve number method the same as the SCS method?

Yes. The Curve Number method was developed by the Soil Conservation Service (SCS), now the Natural Resources Conservation Service (NRCS). It is often called the SCS Runoff Curve Number method or the NRCS CN method.

What is the difference between runoff depth and runoff volume?

Runoff depth (Q) is the depth of water over the entire watershed, in inches or mm. Runoff volume is the actual cubic feet or cubic meters of water, calculated by multiplying Q by the watershed area. For example, 1 inch of runoff over 1 acre equals 27,154 gallons (3,630 cubic feet).

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in cn | Curve Number | - | 75 | 40
in rain | Rainfall depth | in | 3.2 | 0
out runoff | Runoff depth | in | ((rain - 0.2 * (1000/cn - 10))^2) / (rain + 0.8 * (1000/cn - 10)) | 2
out S | Potential retention (S) | in | 1000/cn - 10 | 2
out Ia | Initial abstraction | in | 0.2 * (1000/cn - 10) | 2