Time of Concentration Calculator

Estimate a small catchment's time of concentration with the Kirpich equation.

What Is the Time of Concentration?

The time of concentration is the time water needs to travel from the hydraulically most remote point of a catchment to its outlet. The Rational Method uses it as the rainfall duration. This calculator applies the Kirpich (1940) equation.

tc = 0.0195 × L0.77 × S−0.385

  • tc: time of concentration (min)
  • L: length of the main flow path (m)
  • S: average slope of that path, elevation drop ΔH divided by L (m/m)

The equation was derived from seven small rural catchments in Tennessee with well-defined channels, slopes of about 3 to 10 % and areas of about 1 to 112 acres (0.4 to 45 ha). The constant 0.0195 is the metric form of the original 0.0078 for lengths in feet.

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Average Slope (S)

0.0000 m/m

Time of Concentration (tc)

0.00 min

Time of Concentration (tc)

0.000 h

L: m · ΔH: m · S = ΔH/L (m/m) · tc: minutes. Kirpich, Z.P. (1940), Civil Engineering 10(6), 362.

Worked example and limits

Worked example

For a catchment with a main flow path of L = 1000 m and an elevation drop ΔH = 20 m, the average slope is S = 20/1000 = 0.020. The equation gives tc = 0.0195 × 10000.77 × 0.020−0.385 = 17.95 min. With a drop of 50 m, S = 0.050 and tc = 12.62 min: over the same length, a steeper path brings the water to the outlet sooner. Values computed with the original English-unit form (coefficient 0.0078, L in feet) differ from these by less than 0.2 %.

How to find L and ΔH

Measure L on a map or digital elevation model along the main flow path from the most remote point of the catchment to the outlet. ΔH is the difference between the highest point of that path and the elevation at the outlet; both must come from the same elevation datum.

Using the result in the Rational Method

The tc you find is used as the rainfall duration t in the Rational Method: take the intensity for that duration from IDF data for the chosen return period. Rather than rounding the duration freely, interpret the result against the nearest duration the IDF curve is defined for, and state the choice in the report.

Assumptions and limits

  • The equation is empirical and was derived from small rural catchments; if catchment size, slope and land cover differ from that data set, the result may be unreliable.
  • L is measured along the main flow path, not as the straight distance between two points. The definition of slope varies between sources (flow-path slope or catchment slope); here the average slope of the flow path is used.
  • A single equation does not separate overland and channel flow; for mixed flow paths a segment-by-segment computation may be more suitable.
  • The Kirpich method is generally not suitable for catchments with very low slopes; different methods give different times, and the reason for the difference should be investigated.

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