SCS/NRCS Curve Number Method Explained

The Curve Number (CN) method, developed by the USDA Soil Conservation Service (now Natural Resources Conservation Service), is one of the most widely used methods for estimating storm runoff volume. Unlike the Rational Method, which gives only peak flow, the CN method provides runoff depth that can be used with unit hydrograph procedures to develop complete hydrographs.

History and Development

The CN method was developed by the SCS in the 1950s based on analysis of rainfall-runoff data from small agricultural watersheds. The method was published in National Engineering Handbook Section 4 (NEH-4) in 1954 and later refined in Technical Release 55 (TR-55) in 1986.

The Fundamental Concept

The CN method is based on the water balance equation:

Where:

• P = Total rainfall (inches)
• Ia = Initial abstraction (losses before runoff begins)
• F = Continuing abstraction (infiltration after runoff begins)
• Q = Runoff (inches)

The key insight is the proportionality assumption:

Where S is the potential maximum retention (the maximum amount of water the soil can absorb after runoff begins).

The Runoff Equation

Combining the water balance with the proportionality assumption yields:

Where:

• Q = Runoff depth (inches)
• P = Rainfall depth (inches)
• Ia = Initial abstraction (inches)
• S = Potential maximum retention (inches)

Initial Abstraction

The original SCS relationship assumes:

Substituting this into the runoff equation:

Runoff Only Occurs When P > Ia

If P ≤ Ia, all rainfall is abstracted and Q = 0. This threshold is why small storms may produce little or no runoff.

The Curve Number

The Curve Number converts the potential maximum retention (S) to a more intuitive scale from 0 to 100:

Or rearranged:

Interpreting CN values:

• CN = 100: Impervious surface, no retention (S = 0)
• CN = 0: Infinite retention, no runoff (theoretical only)
• Higher CN: More runoff
• Lower CN: More retention, less runoff

Selecting Curve Numbers

CN selection depends on three factors:

1. Hydrologic soil group
2. Cover type (land use)
3. Hydrologic condition

Hydrologic Soil Groups

Learn more: Hydrologic Soil Groups Guide →

Standard CN Tables

Urban Areas

Agricultural Areas

Hydrologic Condition Definitions

• Good: >75% ground cover, lightly grazed, no compaction
• Fair: 50-75% ground cover, moderately grazed
• Poor: <50% ground cover, heavily grazed or compacted

Composite Curve Number

For mixed land use, calculate an area-weighted CN:

Worked Example

Site breakdown:

Antecedent Moisture Conditions

The standard CN tables are for Average Antecedent Moisture Condition (AMC II). Adjustments can be made for dry or wet conditions:

Adjustment Equations

To convert CN(II) to other conditions:

Step-by-Step Calculation

Step 1: Determine Soil Group

Use NRCS Web Soil Survey or local soil data to identify the hydrologic soil group.

Step 2: Identify Land Use and Condition

Categorize each distinct area by cover type and hydrologic condition.

Step 3: Select CN for Each Area

Use the appropriate table to find CN for each combination of soil group, cover, and condition.

Step 4: Calculate Composite CN

Weight by area for the overall watershed CN.

Step 5: Calculate S and Ia

Step 6: Calculate Runoff Depth

For each rainfall depth P:

Complete Worked Example

Given:

• Composite CN = 80
• Design rainfall (24-hour): 5.0 inches

Solution:

1. Calculate S:

2. Calculate Ia:

3. Since P (5.0”) > Ia (0.5”), runoff occurs:

4. Runoff volume for a 10-acre site:

Try the SCS Curve Number Calculator →

Converting Runoff Depth to Peak Flow

The CN method gives runoff depth, not peak flow. To get peak flow, use:

1. Graphical Peak Discharge Method (TR-55)

Where:

• Qp = Peak discharge (cfs)
• qu = Unit peak discharge (csm/in)
• A = Drainage area (mi²)
• Q = Runoff depth (inches)
• Fp = Pond/swamp adjustment factor

2. SCS Unit Hydrograph Method

Develop a complete hydrograph using:

• Runoff depth from CN method
• Time of concentration
• SCS dimensionless unit hydrograph

Try the SCS Unit Hydrograph Calculator →

Rational Method vs. CN Method

Common Mistakes

1. Using Wrong Tables

Agricultural CN tables don’t apply to urban lawns. Urban “open space” CNs account for compaction from construction.

2. Interpolating Between Soil Groups

Don’t interpolate (e.g., average B and C for “BC” soil). Use the actual dual soil group designation from the soil survey.

3. Ignoring Small Rainfall Threshold

If P ≤ Ia, runoff is zero. Don’t apply the equation for storms smaller than the initial abstraction.

4. Confusing Runoff Depth with Peak Flow

CN method gives inches of runoff, not flow rate. Additional steps are needed to convert to peak flow.

5. Not Checking Ia Assumption

If using Ia = 0.05S instead of 0.2S, the runoff equation changes:

Summary

The CN method is powerful because it:

• Provides runoff volume for detention design
• Accounts for soil type through soil groups
• Includes land use and condition effects
• Works for any watershed size
• Integrates with unit hydrograph methods

Remember:

• Select CN from appropriate tables
• Check which Ia assumption is required
• Output is runoff depth, not peak flow
• Use with unit hydrograph for complete analysis

References

1. Natural Resources Conservation Service. (1986). Urban hydrology for small watersheds (Technical Release 55). U.S. Department of Agriculture.

2. Natural Resources Conservation Service. (2004). National Engineering Handbook, Part 630: Hydrology, Chapter 9: Hydrologic Soil-Cover Complexes. U.S. Department of Agriculture.

3. Hawkins, R. H., Ward, T. J., Woodward, D. E., & Van Mullem, J. A. (2009). Curve number hydrology: State of the practice. ASCE Press.

4. Woodward, D. E., Hawkins, R. H., Jiang, R., Hjelmfelt, A. T., Van Mullem, J. A., & Quan, Q. D. (2003). Runoff curve number method: Examination of the initial abstraction ratio. World Water & Environmental Resources Congress 2003, 1-10.

5. Soil Conservation Service. (1972). National Engineering Handbook, Section 4: Hydrology. U.S. Department of Agriculture.