Engineering
USDA SCS Curve Number (TR-55) Stormwater Runoff Depth Formula
Calculate event runoff depth with the traditional TR-55 curve-number equation, including numeric input checks and the initial-abstraction threshold. Experiment with rainfall and curve number in a live worksheet.
What this worksheet estimates
This example uses the traditional TR-55 relationship Ia=0.2S. It estimates direct runoff depth for a rainfall event, not peak discharge, a hydrograph or a measured infiltration rate. S is potential maximum retention after runoff begins.
Curve number selection depends on hydrologic soil group, cover, treatment and hydrologic condition. The numbers below are illustrative inputs, not land-use classifications to copy into a drainage design. Do not substitute a different initial-abstraction ratio while retaining the same calibrated curve numbers without an appropriate method.
Set up the calculation
Enter dimensionless CN in B2 and total rainfall in inches in B3. B5 and B6 validate these inputs. B8 calculates S, B9 calculates Ia, and B10 calculates Q. The mathematical domain used here is 0<CN≤100 and P≥0; it is not a statement that every CN in that domain is appropriate for TR-55 field use.
=IF(B5<>"OK",B5,1000/B2-10)Apply the rainfall threshold before dividing
B10 returns zero when P≤Ia. Above that threshold it calculates (P−Ia)²/(P−Ia+S). A negative rainfall entry produces an error message rather than being treated as a dry storm.
The CN=100 boundary has S=Ia=0: positive rainfall gives Q=P, while P=0 gives Q=0 without division by zero. Zero predicted runoff is a model result, not evidence that all rainfall actually infiltrated.
=IF(B5<>"OK",B5,IF(B6<>"OK",B6,IF(B3<=B9,0,(B3-B9)^2/(B3-B9+B8))))Compare scenarios without rounding intermediate cells
At CN=80 and P=4 inches, S=2.5, Ia=0.5 and Q=2.0416667 inches. At CN=92 and the same rainfall, Q is approximately 3.1175523 inches. The helper and output cells retain their full numerical precision.
At CN=80, try P=0.4, 0.5 and 0.6. The first two give zero; the third gives approximately 0.00384615 inches. Try changing CN while leaving rainfall fixed, then change rainfall while keeping CN fixed.
If starting from millimetres, divide rainfall by 25.4 before entering B3; multiply the runoff result by 25.4 to convert it back. The constant 1000/CN−10 is specifically the inch form.
Interpret the result within the method
Use the source manual for curve-number selection and applicability. This small worksheet only implements the event runoff-depth equation; it does not perform watershed routing or select a design storm. Inspect input sensitivity before using the result in a broader analysis.
Try the example
Use the original values or change them to test your understanding.