Time of Concentration Calculator - Kirpich Scs
Our hydrology & water resources calculator computes time concentration kirpich scs accurately. Enter measurements for results with formulas and error
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Where Tc is time of concentration (min), L is flow length (ft), S is slope, tL is SCS lag time computed from flow length, Curve Number retention, and slope.
Last reviewed: December 2025
Worked Examples
Example 1: Urban Watershed Design
Example 2: Rural Agricultural Basin
Background & Theory
The Time of Concentration Calculator (kirpich Scs) 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 Time of Concentration Calculator (kirpich Scs) 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
Kirpich: Tc = 0.0078 * L^0.77 * S^-0.385; SCS: Tc = tL / 0.6
Where Tc is time of concentration (min), L is flow length (ft), S is slope, tL is SCS lag time computed from flow length, Curve Number retention, and slope.
Worked Examples
Example 1: Urban Watershed Design
Problem: Flow length 1500 m, elevation difference 45 m, CN = 85, slope = 3%.
Solution: Kirpich: Tc = 0.0078 x (4921)^0.77 x (0.03)^-0.385 = 28.4 min\nSCS: S = (1000/85)-10 = 1.76\ntL = (4921/5280)^0.8 x 2.76^0.7 / (1140 x 3^0.5) = 0.53 hr
Result: Kirpich: 28.4 min | SCS Lag: 31.8 min | Avg Tc: 30.1 min
Example 2: Rural Agricultural Basin
Problem: Flow length 3000 m, elevation 25 m, CN = 70, slope = 0.83%.
Solution: Kirpich: Tc = 0.0078 x (9843)^0.77 x (0.0083)^-0.385 = 72.5 min\nSCS: S = (1000/70)-10 = 4.29\ntL = (9843/5280)^0.8 x 5.29^0.7 / (1140 x 0.83^0.5)
Result: Kirpich: 72.5 min | SCS: longer | Rural response
Frequently Asked Questions
What is time of concentration in hydrology?
Time of concentration (Tc) is the time required for water to travel from the hydraulically most distant point in a watershed to the outlet. It represents the duration after which the entire watershed contributes to runoff at the outlet, producing the peak discharge. Tc is a critical parameter in the Rational Method and unit hydrograph methods because it determines the rainfall duration that produces the maximum peak flow. Shorter Tc values indicate flashier watersheds with higher peak flows.
How does the Kirpich formula estimate time of concentration?
The Kirpich (1940) formula is one of the oldest and simplest Tc equations: Tc = 0.0078 * L^0.77 * S^-0.385 where L is the maximum flow length in feet and S is the average watershed slope (H/L). It was developed from data on small agricultural watersheds in Tennessee with areas up to 0.5 square miles. The formula tends to underestimate Tc for flat terrain and overestimate for steep mountainous areas. It remains popular due to its simplicity and minimal data requirements.
What is the SCS lag method for time of concentration?
The SCS lag equation estimates watershed lag time (time from centroid of rainfall excess to peak discharge) as tL = (L^0.8 * (S+1)^0.7) / (1140 * Y^0.5) where L is hydraulic length in feet, S is the SCS potential retention ((1000/CN)-10), and Y is average slope in percent. Time of concentration is estimated as Tc = tL / 0.6 based on the assumption that lag equals 60 percent of Tc. This method incorporates land use effects through the Curve Number parameter.
Why is time of concentration important for drainage design?
Time of concentration determines the critical storm duration used in design because the peak discharge occurs when the storm duration equals Tc. Using a storm duration shorter than Tc means not all of the watershed contributes simultaneously, while using longer duration means the rainfall intensity is unnecessarily reduced. In the Rational Method, Tc is used to select the rainfall intensity from IDF curves. Underestimating Tc leads to over-design while overestimating leads to inadequate capacity.
What factors affect the time of concentration?
Tc depends on flow length (longer paths mean longer Tc), slope (steeper terrain means shorter Tc), surface roughness (rough surfaces slow flow increasing Tc), channel characteristics (smooth lined channels decrease Tc), and land use through its effect on infiltration and surface roughness. Urbanization typically reduces Tc by 30 to 50 percent through smooth impervious surfaces, gutters, and storm sewers that accelerate flow. Watershed shape also matters since elongated basins have longer Tc.
What is the relationship between lag time and time of concentration?
Lag time is the interval between the centroid (center of mass) of rainfall excess and the peak of the direct runoff hydrograph. The SCS empirically determined that lag time equals approximately 0.6 times the time of concentration for most watersheds. This relationship allows conversion between the two parameters. Some unit hydrograph methods use lag time directly while the Rational Method requires Tc. The 0.6 factor assumes a standard triangular unit hydrograph shape.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy