Scs Curve Number Calculator
Compute scs curve number using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
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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).
Last reviewed: December 2025
Worked Examples
Example 1: Urban Watershed Storm Analysis
Example 2: Agricultural Field Moderate Storm
Background & Theory
The Scs Curve Number Calculator applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) − 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0–12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1–10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5–7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 × exp(−Mgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.
History
The history behind the Scs Curve Number Calculator traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity — foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.
Frequently Asked Questions
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy