What the curve number method does
The curve number method turns one storm depth into one runoff depth. It was developed by the Soil Conservation Service — now the Natural Resources Conservation Service — from rainfall-runoff records on small agricultural watersheds, and it is codified in Technical Release 55 and in Part 630 of the National Engineering Handbook. It is the default method for stormwater design in most of the United States, and reviewing agencies expect to see it.
Its appeal is that a single parameter carries all the catchment information. The curve number runs from 30 to 100 and rises with anything that makes a surface shed water: impervious cover, compacted or clayey soil, poor vegetative condition, steep slopes in some tabulations. A parking lot is 98. Woodland in good condition on sandy soil is 30. Everything a designer needs to know about a site's hydrologic behaviour is compressed into that one number, which is both the method's strength and the source of most of its errors.
What comes out is a volume, not a hydrograph. Runoff depth times area gives you the water that must be stored, treated or conveyed, which is what you need to size a detention basin or a water quality volume. Peak discharge is a separate calculation that needs the storm's time distribution and the catchment's time of concentration.
Where the equation comes from
The method starts from a proportionality assumption: once runoff begins, the ratio of actual retention to potential retention equals the ratio of actual runoff to potential runoff. Written out, F/S = Q/(P − Ia), where F is the water retained after runoff starts and S is the most the catchment could ever retain. Continuity says P = Q + Ia + F. Substitute and solve for Q and you get the equation on this page. It is not empirical curve-fitting dressed up; it follows from two statements you can argue about directly.
Potential maximum retention. S = 1000/CN − 10 in inches. This is simply the definition of the curve number — a rescaling chosen so that CN runs on a convenient 0-to-100 scale. CN = 100 gives S = 0, meaning every drop runs off. CN = 50 gives S = 10 inches. The relationship is strongly non-linear: moving from CN 90 to CN 95 halves S, while moving from CN 50 to 55 changes it by less than 2 inches. That is why small errors in curve number matter far more at the impervious end.
Initial abstraction. Rainfall is lost to interception by vegetation, to depression storage, and to infiltration before ponding, and none of it produces runoff. The original work set Ia = 0.2S from scattered data, and that ratio is baked into every published curve number. It behaves as a threshold: storms smaller than Ia produce no runoff at all.
The 0.05 alternative. Later re-analysis of event data by Hawkins and colleagues found 0.05 fits observations better than 0.2. You cannot simply substitute it, because the curve numbers themselves were calibrated at 0.2. The accepted approach transforms the retention instead: S₀.₀₅ = 1.33 · S₀.₂^1.15, then applies the same equation with λ = 0.05. This calculator does that transformation for you. Use 0.20 unless your agency has specifically adopted the alternative.
Composite curve numbers. Weight by area: CN = Σ(CNⱼAⱼ)/ΣAⱼ. This is an approximation, and it is a poor one when the sub-areas are hydrologically very different and the storm is small — averaging a parking lot with woodland can predict runoff where the woodland alone would produce none and the pavement alone would produce a lot. TR-55 advises computing runoff separately for markedly different areas and summing the volumes when accuracy matters.
Worked example: a 10-acre site, 60% paved, in a 4-inch storm
A 10-acre development has 6 acres of pavement and roof (CN 98) and 4 acres of maintained open space in good condition on hydrologic soil group C (CN 74). The design storm is the 4.0-inch 24-hour event. Antecedent condition is average, λ = 0.20.
- Composite curve number. (98 × 6 + 74 × 4) ÷ 10 = (588 + 296) ÷ 10 = 88.4.
- Potential maximum retention. S = 1000 ÷ 88.4 − 10 = 11.3122 − 10 = 1.3122 in.
- Initial abstraction. Ia = 0.2 × 1.3122 = 0.2624 in.
- Check the threshold. P = 4.0 in exceeds Ia, so runoff occurs.
- Runoff depth. Q = (4.0 − 0.2624)² ÷ (4.0 − 0.2624 + 1.3122) = 3.7376² ÷ 5.0498 = 13.9693 ÷ 5.0498 = 2.7663 in.
- Runoff volume. (2.7663 ÷ 12) × 10 acres × 43,560 ft²/acre = 0.23053 × 435,600 = 100,418 ft³.
- In other units. 2.3053 acre-feet, or 751,176 US gallons.
- Runoff share. 2.7663 ÷ 4.0 = 69.2% of the rainfall leaves as direct runoff.
Now change one thing. Redevelop so the paved area is 8 acres instead of 6: the composite rises to (98 × 8 + 74 × 2) ÷ 10 = 93.2, S falls to 0.7296 in, Ia falls to 0.1459 in, and Q rises to 3.8541² ÷ 4.5837 = 3.2404 in — a volume of 117,625 ft³. Two extra acres of pavement adds more than 17,000 cubic feet to the storm that has to go somewhere. That sensitivity, and not the absolute number, is what the method is best at showing.
How to read runoff depth and volume
Compare runoff depth against rainfall depth first. The ratio tells you what fraction of the storm the site sheds, and it is the clearest single statement of hydrologic impact. Under 25% is a lightly developed or well-infiltrating catchment; approaching 70% and above means the site behaves close to an impervious surface for this storm.
That ratio is not fixed for a site — it depends on the storm. Because the initial abstraction is a fixed depth, larger storms exceed it by proportionally more, so the runoff share rises with rainfall depth at any given curve number. The sweep table beneath the calculator shows this directly, and it is the reason a site can look benign in a 1-inch storm and severe in a 6-inch one. Design decisions made from one storm depth do not transfer to another.
Take the volume to the structure it sizes. Detention volume, water quality volume, first-flush capture and cistern sizing all start from a runoff volume for a specified storm. Note that many jurisdictions define the water quality event as a small storm — often around an inch — which is precisely the regime where the curve number method is least reliable, and several agencies specify a different small-storm method for that reason.
Finally, be honest about the precision. Curve numbers are read off tables that assign one integer to a whole cover class, and the underlying data scatter substantially around those values. A runoff depth quoted to three decimal places is arithmetic precision, not hydrologic accuracy. Where the answer is close to a design threshold, test the sensitivity by running the calculation at CN ± 5 and see whether your conclusion survives.
Runoff depth Q (inches) by curve number and storm depth
| CN | S (in) | P = 1 in | P = 2 in | P = 3 in | P = 4 in | P = 6 in |
|---|---|---|---|---|---|---|
| 60 | 6.667 | — | 0.06 | 0.33 | 0.76 | 1.92 |
| 70 | 4.286 | 0.00 | 0.24 | 0.71 | 1.33 | 2.81 |
| 75 | 3.333 | 0.03 | 0.38 | 0.96 | 1.67 | 3.28 |
| 80 | 2.500 | 0.08 | 0.56 | 1.25 | 2.04 | 3.78 |
| 85 | 1.765 | 0.17 | 0.80 | 1.59 | 2.46 | 4.30 |
| 90 | 1.111 | 0.32 | 1.09 | 1.98 | 2.92 | 4.85 |
| 95 | 0.526 | 0.56 | 1.48 | 2.45 | 3.43 | 5.41 |
| 98 | 0.204 | 0.79 | 1.77 | 2.77 | 3.77 | 5.76 |
Cells are produced by the same routine the calculator runs. Read across a row to see how the runoff share rises with storm depth, and down a column to see how sharply runoff responds to curve number in small storms compared with large ones.
Limits, assumptions and common errors
- It gives volume, not peak flow. Sizing a pipe or culvert needs a peak discharge, which requires the TR-55 graphical or tabular method with a rainfall distribution and a time of concentration. Runoff depth alone will not do it.
- It was calibrated on small agricultural watersheds. TR-55 itself restricts the graphical peak method to catchments with a time of concentration between 0.1 and 10 hours, and the method as a whole is weakest on very small, very large, very flat or snow-affected catchments.
- Small storms are the weak regime. Predicted runoff is highly sensitive to curve number when P is close to Ia, and observed data scatter widely there. Water-quality storms often sit in exactly this range.
- Averaging dissimilar sub-areas can mislead. Where impervious and pervious areas differ sharply and the storm is small, compute runoff separately for each and add the volumes rather than averaging the curve numbers.
- Connected versus disconnected impervious area matters. TR-55 provides adjustments for impervious area that drains to pervious ground rather than directly to the conveyance system. Treating a disconnected roof as directly connected overstates runoff.
- Do not adjust for antecedent condition casually. Published curve numbers are ARC II. Applying ARC III on top of a design storm that already embeds a return period can double-count conservatism, and many agencies prohibit it.
- The method has no time in it. A 4-inch storm over 24 hours and a 4-inch storm over 2 hours give identical runoff volume here, and behave completely differently on the ground.
Which documents govern
The runoff equation and the curve number tables come from the NRCS National Engineering Handbook, Part 630, Chapters 9 and 10. Technical Release 55, Urban Hydrology for Small Watersheds, packages them for urban design and adds the tabulated curve numbers for developed land uses, the connected-impervious adjustments, the time-of-concentration procedure and the peak-discharge methods. Rainfall depths for a given return period and duration come from NOAA Atlas 14 in most of the United States. Your local reviewing agency may specify a particular edition, a particular rainfall source, and its own curve number table for local soils — where it does, that governs over the national default.
Key terms
- Curve number
- A dimensionless index from 30 to 100 combining land cover, treatment, hydrologic condition and hydrologic soil group into a single runoff-potential parameter. Higher means more runoff.
- Hydrologic soil group
- A classification A through D describing infiltration capacity when thoroughly wet: A is deep sand with high infiltration, D is clay with very low infiltration. Group is looked up from the NRCS soil survey for the site.
- Potential maximum retention S
- The greatest depth of water the catchment could absorb after runoff begins, in inches. It is defined from the curve number by S = 1000/CN − 10.
- Initial abstraction
- Rainfall consumed by interception, surface depression storage and pre-ponding infiltration before any runoff occurs. Taken as 0.2S in standard practice.
- Antecedent runoff condition
- A three-level description of how wet the catchment was before the storm. Published curve numbers correspond to ARC II, the average condition.
- Direct runoff
- The portion of rainfall that reaches the drainage system as surface flow during and shortly after the storm, excluding baseflow.
What comes before and after this calculation
Before you can run the curve number method you need three things: the drainage boundary and the area inside it, the cover types and their areas, and the hydrologic soil group under each from the NRCS soil survey. Those three determine the composite curve number, and nothing downstream can be better than they are. Then you need a design rainfall depth for the required return period and duration, which in most of the United States comes from NOAA Atlas 14.
After it, the runoff volume feeds whatever structure the design requires. Detention and retention storage is sized from volume directly. Water quality volume is a specified small-storm runoff volume. On the beneficial-use side, the same arithmetic underlies rainwater harvesting yield, where a roof is simply a catchment with a curve number near 98 and the runoff is what you want to keep rather than dispose of.
If you need a peak flow rather than a volume, two routes are common. The TR-55 graphical peak discharge method uses the curve number, the time of concentration and a regional rainfall distribution. The Rational Method, Q = CiA, is the older alternative and is still permitted for small sites in many jurisdictions; its runoff coefficient C plays the same role as the curve number but is not interchangeable with it, and mixing the two methods in one design is a common review comment.
For the long-term water balance rather than single storms — irrigation demand, or how much of the annual rainfall is actually available — the relevant quantity is evapotranspiration rather than event runoff, which the reference ET calculator handles.