Hydrology · Stormwater · Water Resources

SCS Curve Number Runoff Calculator

Estimate direct runoff depth and volume from a storm with the SCS-CN (NRCS curve number) method. Build a composite curve number from the complete TR-55 tables, adjust for dry or wet antecedent conditions, switch between Ia = 0.2S and 0.05S, and see how rainfall splits into initial abstraction, infiltration and runoff, with every step shown.

SI & US units Full TR-55 CN table AMC I / II / III λ = 0.2 or 0.05 Charts + steps

By Bimal Ghimire (PhD researcher, hydrology & remote sensing) · Free, no sign-up, runs in your browser.

Curve Number Runoff Calculator

Storm rainfall depth P (mm)Total depth for the design storm, e.g. 24-hour rainfall

Drainage area (optional)

For runoff volume; composite mode uses the sum of rows

Antecedent moistureNot sure? Use the 5-day rainfall helper

Initial abstraction ratio λ

Curve number CN (AMC II)

30 · forest, sand98 · pavement

Or click any value in the CN table below to add it.

Where the rain goes

Bold curve: your effective CN. Faint curves: CN 50–95 for reference. The dot is your storm. Runoff starts only after P exceeds Ia.

CN uncertainty of ±5 is typical when picking land-use and soil categories. Notice how strongly runoff responds, especially for small storms.

Switch to "Build composite CN" to see area-weighted results per land use.

5-day antecedent rainfall helper (AMC class)

Total rainfall in previous 5 days (mm)

Season

Thresholds from SCS (1972) as tabulated by Chow, Maidment & Mays (1988): dormant season < 12.7 mm (0.5 in) = AMC I, 12.7–27.9 mm = II, > 27.9 mm (1.1 in) = III; growing season < 35.6 mm (1.4 in) = I, 35.6–53.3 mm = II, > 53.3 mm (2.1 in) = III.

Lookup

Runoff Curve Number Table (TR-55, AMC II, Ia = 0.2S)

Complete Tables 2-2a (urban), 2-2b (cultivated agricultural) and 2-2c (other agricultural) from USDA TR-55 (1986). Search, then click any CN value to add that land use and soil group to the composite builder.

* Actual value is below 30; TR-55 says use CN = 30. Residential values assume the listed % impervious is directly connected and the pervious part is open space in good condition. Values for "Fair" open space use TR-55's 50–75% grass cover row.

Concept

What is the SCS Curve Number Method?

The SCS curve number (SCS-CN) method, now called the NRCS curve number method, estimates how much of a storm's rainfall becomes direct runoff. It was developed by the US Soil Conservation Service in the 1950s from small agricultural watershed records and is documented in the National Engineering Handbook, Part 630, and in Technical Release 55 (TR-55) for urban watersheds.

Its appeal is that one number, the curve number (CN), summarises land use, cover condition and soil infiltration capacity. CN runs from about 30 (deep sand under good forest, almost no runoff) to 98–100 (pavement and water, nearly all rain runs off). It is built into HEC-HMS, SWAT, TR-20, EPA SWMM and many GIS hydrology tools.

Input

Storm rainfall depth P, curve number CN, and optionally the area.

Output

Runoff depth Q and volume Q × A. Not a peak flow and not a hydrograph by itself.

Used for

Stormwater design, detention sizing, flood studies, watershed models, land-use change impact.

Runoff depth is half the story. To turn it into a flood hydrograph, combine it with a unit hydrograph (see our hydrograph guide). For small urban catchments where only the peak matters, the rational method Q = CiA is the usual alternative.

Mathematics

SCS-CN Runoff Equation and Where it Comes From

The method starts from a proportionality hypothesis: once runoff begins, the ratio of actual to potential retention equals the ratio of actual runoff to potential runoff.

1 · Water balance and proportionality

$$P = I_a + F + Q,\qquad \frac{F}{S}=\frac{Q}{P-I_a}$$

$I_a$ = initial abstraction (interception, depression storage, infiltration before runoff starts), $F$ = continuing abstraction after runoff begins, $S$ = potential maximum retention.

Substituting $F = P - I_a - Q$ into the proportionality and solving for $Q$:

2 · Runoff equation

$$Q=\begin{cases}\dfrac{(P-I_a)^2}{P-I_a+S} & P>I_a\\[6pt] 0 & P\le I_a\end{cases}\qquad I_a=\lambda S,\ \lambda=0.2\ \Rightarrow\ Q=\frac{(P-0.2S)^2}{P+0.8S}$$

3 · Retention from the curve number

$$S_{\text{in}}=\frac{1000}{CN}-10\qquad\qquad S_{\text{mm}}=\frac{25400}{CN}-254$$

CN is a dimensionless transform of S onto a 0–100 scale. CN = 100 gives S = 0 (all rain becomes runoff).

4 · Composite curve number

$$CN_c=\frac{\sum_i A_i\,CN_i}{\sum_i A_i}\qquad\text{or, more accurately,}\qquad Q_c=\frac{\sum_i A_i\,Q_i}{\sum_i A_i}$$

Because Q is non-linear in CN, averaging CN under-predicts runoff when sub-areas differ strongly (roofs at 98 next to lawns at 61). The calculator reports both.

Why the curve has that shape: as $P \to \infty$, $Q \approx P - I_a - S$: every extra millimetre of rain becomes runoff, and total losses approach S. That is why S is the "maximum" retention. Check it on the chart: all curves become parallel to the 1:1 line for large storms.

Soils

Hydrologic Soil Groups A, B, C and D

HSG	Runoff potential	Final infiltration rate	Typical soils
A	Low	> 7.6 mm/h (> 0.30 in/h)	Deep, well-drained sands and gravels
B	Moderately low	3.8–7.6 mm/h (0.15–0.30 in/h)	Moderately deep loams, silt loams
C	Moderately high	1.3–3.8 mm/h (0.05–0.15 in/h)	Sandy clay loams; soils with a layer that impedes drainage
D	High	< 1.3 mm/h (< 0.05 in/h)	Clays with high swelling potential, high water table, shallow soil over rock

In the US, look up the HSG of each soil map unit in the NRCS Web Soil Survey. Elsewhere, estimate it from texture, depth to an impeding layer and measured infiltration rates. Dual groups such as A/D mean "D when undrained, A when drained". For soil background, see floodplain soils.

Wetness

Antecedent Moisture Condition (AMC I, II, III)

The same field produces far more runoff after a wet week than after a dry month. Tabulated CNs represent average conditions (AMC II). For dry (I) or wet (III) conditions, a widely used conversion is:

$$CN_{I}=\frac{4.2\,CN_{II}}{10-0.058\,CN_{II}}\qquad\qquad CN_{III}=\frac{23\,CN_{II}}{10+0.13\,CN_{II}}$$

Example: CN_II = 80 gives CN_I = 62.7 and CN_III = 90.2. For a 100 mm storm, runoff ranges from about 23 mm (dry) to 74 mm (wet) instead of 51 mm.

Current NRCS documentation (NEH-630 Chapter 10) prefers the term antecedent runoff condition and treats AMC I/III as bounds of a distribution rather than strict classes tied to 5-day rainfall. In design, AMC II is the usual default; AMC III is sometimes required for conservative flood design or saturated, frozen or snowmelt conditions. State the choice in your report.

Current Research

Initial Abstraction: Ia = 0.2S or 0.05S?

The 0.2 ratio was an assumption based on limited data. Hawkins et al. (2002), analysing hundreds of small watersheds, found that most observed Ia/S ratios were well below 0.2 and that $\lambda = 0.05$ fits better. The catch: tabulated CNs were calibrated with 0.2, so you cannot just change λ. The retention must be converted:

$$S_{0.05}=1.33\,S_{0.2}^{\,1.15}\ \ (\text{inches}),\qquad Q=\frac{(P-0.05S_{0.05})^2}{P+0.95S_{0.05}}$$

The practical effect: with $\lambda = 0.05$, small storms and low-CN watersheds produce noticeably more runoff, while large storms on high-CN areas change little. TR-55 and most design manuals still use 0.2, so keep 0.2 for regulatory design unless your agency says otherwise, and use the 0.05 option to test sensitivity.

Practice

Worked Examples (SI and US)

Example 1 (SI): P = 100 mm, CN = 80, AMC II, λ = 0.2

$S = 25400/80 - 254 = 63.5$ mm
$I_a = 0.2 \times 63.5 = 12.7$ mm. Since P > Ia, runoff occurs.
$Q = (100 - 12.7)^2 / (100 - 12.7 + 63.5) = 7621.3 / 150.8 = 50.5$ mm
Runoff ratio $Q/P = 0.51$. Over 25 ha: $V = 0.0505 \text{ m} \times 250\,000 \text{ m}^2 \approx 12\,600$ m³.

Example 2 (US): P = 4.0 in, CN = 80

$S = 1000/80 - 10 = 2.50$ in, $I_a = 0.50$ in
$Q = (4.0 - 0.5)^2/(4.0 + 2.0) = 12.25/6.0 = 2.04$ in
With λ = 0.05: $S_{0.05} = 1.33 \times 2.5^{1.15} = 3.81$ in (equivalent CN 72.4), $Q = (4.0 - 0.19)^2/(4.0 + 3.62) = 1.90$ in.

Type these values into the calculator above to check every step.

Use With Care

Limitations of the Curve Number Method

No rainfall intensity

Only storm depth enters the equation. A 50 mm storm in 30 minutes and in 24 hours give the same Q.

Small runoff is unreliable

TR-55 advises another procedure when runoff is below about 0.5 in (13 mm), and when the weighted CN is below 40.

Calibrated on US data

Table values come from US watersheds. Elsewhere, calibrate CN against observed events where possible.

Not for snowmelt or frozen ground

The method describes rainfall runoff; snowmelt and rain on frozen soil need other approaches.

Event model only

No soil-moisture accounting between storms unless you add it (as SWAT does with daily CN updating).

Peak flow needs timing

Combine with a unit hydrograph or TR-55 graphical method to get a peak; see the rational method for small catchments.

Keep Learning

Related Tools and Guides

FAQ

Frequently Asked Questions

What is the SCS curve number runoff equation?

Q = (P − Ia)² / (P − Ia + S) for P > Ia, otherwise Q = 0. P is rainfall depth, Q is direct runoff depth, S is the potential maximum retention and Ia is the initial abstraction, usually Ia = 0.2S. S is found from the curve number: S = 1000/CN − 10 in inches, or S = 25400/CN − 254 in millimetres.

How do I calculate a composite curve number?

Multiply each sub-area by its curve number, add the products and divide by the total area: CNc = Σ(Ai × CNi) / ΣAi. When the curve numbers differ a lot (for example roofs at 98 and lawns at 61), it is more accurate to compute runoff for each land use separately and then area-weight the runoff depths. This calculator shows both.

What curve number should I use for impervious surfaces?

TR-55 uses CN = 98 for paved parking lots, roofs, driveways and paved streets with curbs and storm sewers. Gravel roads are 76–91 and dirt roads 72–89 depending on the hydrologic soil group.

What are AMC I, II and III?

Antecedent moisture condition describes how wet the watershed is before the storm. AMC II is average and is what the TR-55 tables give. AMC I is dry (lower CN, less runoff) and AMC III is wet (higher CN, more runoff). A common conversion is CN(I) = 4.2 CN(II) / (10 − 0.058 CN(II)) and CN(III) = 23 CN(II) / (10 + 0.13 CN(II)). Current NRCS guidance describes this as antecedent runoff condition.

Should I use Ia = 0.2S or Ia = 0.05S?

The tabulated curve numbers were developed with Ia = 0.2S, so use 0.2S unless your agency requires otherwise. Hawkins et al. (2002) found that 0.05S fits observed rainfall-runoff data better; if you switch, the curve number must be converted as well (S0.05 = 1.33 S0.2^1.15 in inches), not simply reused.

Can the curve number method give peak discharge?

No. The CN method gives runoff depth and volume for a storm. To get a peak flow you need a timing method: the TR-55 graphical peak discharge method, a unit hydrograph, or, for small urban catchments, the rational method Q = CiA.

Why does my calculation give zero runoff?

If the rainfall P is less than or equal to the initial abstraction Ia, all rain is retained by interception, depression storage and infiltration before runoff starts, so Q = 0. Low curve numbers and small storms produce this result.

Sources

References

USDA Soil Conservation Service (1986). Urban Hydrology for Small Watersheds, Technical Release 55 (TR-55), 2nd ed. Washington, DC.

USDA Natural Resources Conservation Service (2004). National Engineering Handbook, Part 630 Hydrology, Chapter 10: Estimation of Direct Runoff from Storm Rainfall.

USDA Natural Resources Conservation Service (2009). National Engineering Handbook, Part 630 Hydrology, Chapter 7: Hydrologic Soil Groups.

Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology, Section 5.5. McGraw-Hill, New York.

Ponce, V. M., & Hawkins, R. H. (1996). Runoff curve number: Has it reached maturity? Journal of Hydrologic Engineering, 1(1), 11–19.

Hawkins, R. H., Jiang, R., Woodward, D. E., Hjelmfelt, A. T., & Van Mullem, J. A. (2002). Runoff curve number method: examination of the initial abstraction ratio. Proceedings of the Second Federal Interagency Hydrologic Modeling Conference, Las Vegas.

Hawkins, R. H., Ward, T. J., Woodward, D. E., & Van Mullem, J. A. (2009). Curve Number Hydrology: State of the Practice. ASCE, Reston, VA.