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
Reviewed by Daniel Agrici, Founder & Lead Developer
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.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy