As an affiliate, we may earn a commission from qualifying purchases. We get commissions for purchases made through links on this website from Amazon and other third parties.
A curve number does not convert to one fixed runoff coefficient. The two values come from different hydrology methods.
A practical way to create an event-based equivalent runoff coefficient is to use the curve number to calculate runoff depth for a specific storm, then divide runoff depth by rainfall depth:
[ C_{eq}=\frac{Q}{P} ]
where:
- (C_{eq}) = equivalent runoff coefficient
- (Q) = runoff depth
- (P) = rainfall depth
The important part is that you must choose a rainfall depth first. The same curve number will produce a different equivalent runoff coefficient for a 1-inch storm than for a 4-inch storm.
Why Curve Number and Runoff Coefficient Are Different
A curve number, often written as CN, is part of the Natural Resources Conservation Service rainfall-runoff method. It is used to estimate the total depth or volume of direct runoff from a storm.
CN normally ranges from 0 to 100. Higher numbers mean more runoff potential. Lower numbers mean more rainfall can be stored, infiltrated, or otherwise kept from becoming direct runoff.
The NRCS method uses total storm rainfall and does not use rainfall intensity as a direct input.
A runoff coefficient, often written as (C), is commonly used with the Rational Method:
[ q=CIA ]
where:
- (q) = peak runoff flow rate
- (C) = runoff coefficient
- (I) = rainfall intensity
- (A) = drainage area
The Rational Method is mainly a peak-flow method, while the curve number method first estimates storm runoff volume or depth. This is why there is no universal CN-to-(C) conversion.
How to Convert a Curve Number to an Equivalent Runoff Coefficient
For a rough event-based conversion, use four steps.
1. Choose the Curve Number
Use the CN that represents your drainage area.
The correct value depends on factors such as:
- soil type
- land cover
- vegetation
- pavement or other hard surfaces
- surface condition
- soil moisture conditions
Do not choose a CN simply because it produces the runoff result you want.
2. Calculate Maximum Potential Retention
If rainfall is measured in inches:
[ S=\frac{1000}{CN}-10 ]
where (S) is maximum potential retention in inches.
The NRCS defines CN as a transformation of this retention value.
If you are working in millimeters:
[ S=25.4\left(\frac{1000}{CN}-10\right) ]
Keep rainfall and (S) in the same units.
3. Calculate Runoff Depth
For the standard NRCS relationship:
[ I_a=0.2S ]
where (I_a), called initial abstraction, represents rainfall lost before runoff begins. This may include interception by plants, early infiltration, and water held in small surface depressions. NRCS notes that these losses can vary with soil moisture, rainfall conditions, and the ground surface.
If:
[ P\leq0.2S ]
then:
[ Q=0 ]
For a storm large enough to produce runoff:
[ Q=\frac{(P-0.2S)^2}{P+0.8S} ]
where:
- (Q) = direct runoff depth
- (P) = total storm rainfall
- (S) = maximum potential retention
This is the standard NRCS curve number runoff relationship.
4. Divide Runoff by Rainfall
Once you know (Q):
[ C_{eq}=\frac{Q}{P} ]
This gives the fraction of the storm rainfall predicted to become direct runoff.
You can also combine the equations:
[ C_{eq}= \frac{(P-0.2S)^2} {P(P+0.8S)} ]
for:
[ P>0.2S ]
Otherwise:
[ C_{eq}=0 ]
This is an equivalent storm runoff ratio, not a universal Rational Method coefficient.
Example: Convert CN 80 to a Runoff Coefficient
Suppose:
- Curve number = 80
- Storm rainfall = 2 inches
First calculate (S):
[ S=\frac{1000}{80}-10 ]
[ S=2.5\text{ inches} ]
Initial abstraction is:
[ I_a=0.2(2.5)=0.5\text{ inch} ]
Now calculate runoff:
[ Q=\frac{(2-0.5)^2}{2+0.8(2.5)} ]
[ Q=\frac{2.25}{4} ]
[ Q=0.5625\text{ inch} ]
Now divide runoff by rainfall:
[ C_{eq}=\frac{0.5625}{2} ]
[ C_{eq}\approx0.28 ]
Check estimating harvestable rainwater volume to verify long-term maintenance priorities for the installation.
For this specific 2-inch storm, CN 80 gives an equivalent runoff coefficient of about 0.28.
That does not mean CN 80 always equals (C=0.28).
How Storm Size Changes the Result
The table below shows why rainfall depth must be included in the conversion.
| Curve Number | 1-inch storm | 2-inch storm | 4-inch storm |
|---|---|---|---|
| 60 | 0.00 | 0.03 | 0.19 |
| 70 | 0.01 | 0.12 | 0.33 |
| 80 | 0.08 | 0.28 | 0.51 |
| 90 | 0.32 | 0.55 | 0.73 |
| 95 | 0.56 | 0.74 | 0.86 |
| 98 | 0.79 | 0.89 | 0.94 |
These values use the standard (I_a=0.2S) curve number equation.
Notice CN 80. Its equivalent coefficient changes from about 0.08 for a 1-inch storm to about 0.51 for a 4-inch storm.
That large change is why a simple conversion table such as "CN 80 = C 0.6" should not be treated as a general rule.
When This Conversion Is Useful
Calculating (Q/P) can be useful when you want to compare the runoff fraction from one storm event with another method.
For example, it can help with:
- simple watershed comparisons
- checking runoff-volume assumptions
- estimating what fraction of rainfall becomes runoff
- converting an NRCS runoff estimate into a dimensionless runoff ratio
- comparing different land-cover scenarios using the same design storm
Make sure all scenarios use the same rainfall depth if you want a fair comparison.
When You Should Not Use This Conversion
Do not automatically use (Q/P) as the (C) value in a Rational Method drainage calculation.
The Rational Method estimates peak flow, and rainfall intensity is a major part of the calculation. The NRCS curve number equation estimates runoff from total storm rainfall and does not directly account for rainfall intensity.
For culverts, storm drains, channels, detention structures, or other drainage works, use the method required by the applicable engineering manual or local authority.
A locally specified Rational Method coefficient may be based on:
- surface type
- slope
- rainfall frequency
- development density
- soil conditions
- drainage design standards
A calculated (Q/P) value should not replace those requirements without engineering justification.
What About Roof Runoff?
For rainwater harvesting from a roof, converting a curve number to a runoff coefficient is usually unnecessary.
Roof collection calculations are normally better handled with:
[ \text{Collected water}
\text{Rainfall} \times \text{Roof area} \times \text{Collection efficiency} ]
Actual collection can be reduced by first-flush diversion, gutter overflow, splash, leaks, debris screens, tank overflow, and other system losses.
Using CN 98 or CN 100 as a shortcut for a roof may not describe those real collection losses well.
For tank sizing, focus on the roof area, rainfall record, storage capacity, intended water use, and realistic system losses rather than trying to force a watershed CN into a roof collection coefficient.
Watch the Units
The ratio (Q/P) is dimensionless, so inches or millimeters give the same coefficient as long as both values use the same unit.
For example:
[ C=\frac{20\text{ mm runoff}}{50\text{ mm rainfall}}=0.40 ]
Do not calculate (Q) in inches and divide it by rainfall in millimeters.
A Simple Spreadsheet Formula
If:
- cell A2 contains CN
- cell B2 contains rainfall in inches
first calculate:
[ S=1000/A2-10 ]
Then the equivalent coefficient can be calculated conceptually as:
[ C_{eq}= \begin{cases} 0, & P\leq0.2S \ \dfrac{(P-0.2S)^2}{P(P+0.8S)}, & P>0.2S \end{cases} ]
The same approach works in metric units if (S) and rainfall are both converted to millimeters before calculating runoff.
The Main Rule to Remember
There is no single formula that changes a curve number into one permanent runoff coefficient.
Instead:
- Start with CN.
- Choose the storm rainfall depth.
- Calculate (S).
- Calculate runoff depth (Q).
- Divide (Q) by (P).
The result is an equivalent runoff coefficient for that storm.
If you need a coefficient specifically for a Rational Method peak-flow design, use the runoff coefficient required or recommended by the drainage standard you are following rather than assuming (Q/P) is interchangeable with it.
Frequently Asked Questions
Is there a direct conversion from curve number to runoff coefficient?
No. A curve number does not correspond to one fixed runoff coefficient. You need a rainfall depth before you can calculate an equivalent event runoff ratio.
What is the formula for converting CN to a runoff coefficient?
First calculate:
[ S=\frac{1000}{CN}-10 ]
Then calculate:
[ Q=\frac{(P-0.2S)^2}{P+0.8S} ]
when (P>0.2S). Finally:
[ C_{eq}=\frac{Q}{P} ]
Why does the runoff coefficient change with rainfall depth?
The curve number method includes rainfall losses before and during runoff. Those losses are a much larger fraction of a small storm than a large storm. As rainfall increases, a larger fraction can become runoff.
Does a higher curve number always mean a higher runoff coefficient?
For the same rainfall depth and the same curve number assumptions, a higher CN generally produces more runoff and therefore a higher (Q/P) ratio.
Can I use the calculated coefficient in the Rational Method?
Not automatically. (Q/P) is a storm-volume ratio, while the Rational Method coefficient is used to estimate peak runoff with rainfall intensity. Follow the coefficient guidance in the drainage standard used for your project.
Can I use this method in millimeters?
Yes. Keep all rainfall and retention values in millimeters. You can calculate retention with:
[ S=25.4\left(\frac{1000}{CN}-10\right) ]
Then use the same NRCS runoff equation.
Should I use curve numbers for rainwater harvesting from a roof?
Usually not. Roof rainwater collection is better estimated from rainfall, roof catchment area, and realistic collection losses. Curve numbers are mainly intended for rainfall-runoff estimates over drainage areas and watersheds.
