Scs Curve Number Calculator
Compute scs curve number using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
S = (25400/CN) - 254; Ia = lambda * S; Q = (P - Ia)^2 / (P - Ia + S)
Where S is maximum potential retention (mm), CN is the Curve Number, Ia is initial abstraction, lambda is the abstraction ratio, P is precipitation (mm), and Q is direct runoff depth (mm).
Worked Examples
Example 1: Urban Watershed Storm Analysis
Problem: A 10-hectare urban watershed has CN = 85 and receives 120 mm of rainfall over a 6-hour storm. Calculate runoff using lambda = 0.2.
Solution: S = (25400 / 85) - 254 = 44.82 mm\nIa = 0.2 x 44.82 = 8.96 mm\nQ = (120 - 8.96)^2 / (120 - 8.96 + 44.82) = 79.11 mm\nVolume = 79.11 x 10 x 10 = 7911 m3
Result: Runoff: 79.11 mm | Volume: 7,911 m3 | Peak Q: 27.4 m3/s
Example 2: Agricultural Field Moderate Storm
Problem: A 25-hectare field with CN = 65 receives 80 mm rainfall over 8 hours.
Solution: S = (25400 / 65) - 254 = 136.77 mm\nIa = 0.2 x 136.77 = 27.35 mm\nQ = (80 - 27.35)^2 / (80 - 27.35 + 136.77) = 14.63 mm\nInfiltration = 80 - 14.63 - 27.35 = 38.02 mm
Result: Runoff: 14.63 mm | Infiltration: 38.02 mm | Ratio: 18.3%
Frequently Asked Questions
What is the SCS Curve Number method?
The SCS Curve Number method, developed by the USDA Soil Conservation Service, is an empirical approach for estimating direct runoff volume from a rainfall event based on land use, soil type, and antecedent moisture conditions. The method uses a Curve Number (CN) from 0 to 100, where higher values indicate greater runoff potential. The equation calculates runoff depth as Q = (P - Ia)^2 / (P - Ia + S), where P is precipitation, Ia is initial abstraction, and S is maximum potential retention. It is one of the most widely used hydrologic models globally.
How is the maximum potential retention S calculated from the Curve Number?
The maximum potential retention S is inversely related to the Curve Number through S = (25400 / CN) - 254 in millimeters, or S = (1000 / CN) - 10 in inches. A CN of 100 gives S = 0 meaning all rainfall becomes runoff. A CN of 50 gives S = 254 mm indicating substantial soil storage. S represents the maximum water the soil and surface can absorb after runoff begins, including infiltration, depression storage, and interception. This parameter directly controls the shape of the rainfall-runoff relationship.
How do soil hydrologic groups affect Curve Number selection?
The USDA classifies soils into four Hydrologic Soil Groups (A through D) based on minimum infiltration rate when thoroughly wetted. Group A soils are deep sands and gravels with infiltration above 7.6 mm/hr producing the lowest CN values. Group B soils have moderate infiltration of 3.8 to 7.6 mm/hr. Group C soils have slow infiltration of 1.3 to 3.8 mm/hr due to restrictive layers. Group D soils are clay-rich with infiltration below 1.3 mm/hr producing the highest CN values. The same land use on Group A versus Group D can differ by 25 CN points.
What are the limitations of the SCS Curve Number method?
The CN method was developed for agricultural watersheds in the central United States and may not accurately represent arid or tropical regions. It does not account for rainfall intensity or temporal distribution, treating all storms with the same total depth identically. It tends to underestimate runoff for small storms and overestimate for very large events outside its calibration range. The method assumes a single-valued rainfall-runoff relationship, ignoring time-varying infiltration described by physically-based models like Green-Ampt.
How do you determine the Curve Number for urban areas?
For urban areas, CN values are determined using TR-55 tables accounting for impervious percentage and hydrologic soil group of the pervious portion. Fully impervious surfaces have CN = 98 regardless of soil type. The composite CN combines impervious and pervious area CN values weighted by their fractions. Connected impervious areas draining to storm sewers produce higher effective CN than disconnected areas draining onto pervious surfaces. A residential area with quarter-acre lots on Group B soil has composite CN of about 70, reflecting roughly 38 percent impervious cover.
What is the relationship between Curve Number and runoff depth?
The CN-runoff relationship is nonlinear and increasingly sensitive at higher CN values. For a given rainfall, small CN changes produce much larger runoff changes when CN exceeds 80 than below 60. At CN = 100, all rainfall becomes runoff. At CN = 50 with 100 mm rainfall, runoff is about 13 mm, while at CN = 90, runoff jumps to approximately 72 mm. This nonlinearity means accurate CN determination is most critical for developed watersheds where small errors translate to large runoff volume and peak flow errors.