Time of Concentration Calculator (Kirpich)

Understanding the Kirpich time of concentration calculator — concept and principle

The time of concentration is how long rainwater takes to travel from the hydraulically most remote point of a catchment to its outlet. It sets the storm duration used in the rational method and controls how sharp a flood peak is. The Kirpich formula, one of the oldest and most widely quoted estimates, needs only the flow length and the average slope.

After 24.5 minutes of rain the whole catchment is feeding the outlet at once.

How it is calculated

t_c = 0.0195·L^0.77·S^−0.385, with t_c in minutes, L the longest flow path in metres and S the average slope along that path in m/m (elevation drop divided by L). This is the metric form; the original US form uses feet with a coefficient of 0.0078.

The principle

Travel time is length divided by velocity, and flow velocity rises with slope. Kirpich fitted data from small rural watersheds in Tennessee with well-defined channels and fairly steep slopes, and found that time grows a little less than proportionally with length (power 0.77, because longer paths gather more water and move faster) and falls with the slope to the power 0.385. Because these powers come from regression rather than physics, the formula is reliable only for conditions similar to the original data. For paved overland flow or concrete channels, practitioners often multiply the result by reduction factors such as 0.4 and 0.2.

Worked example

Inputs: L = 1,500 m, S = 0.02 m/m.
L^0.77 = 1500^0.77 = 278.99.
S^−0.385 = 0.02^−0.385 = 4.5092.
t_c = 0.0195 × 278.99 × 4.5092 = 24.53 minutes.

Each point is the calculator re-run with only “Flow length (m)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Flow length (m)	Time of concentration (min)
375	8.436108159
750	14.38584033
1,125	19.65737421
1,500	24.53173883
1,875	29.13057402
2,250	33.52112627
3,000	41.83323297

How to read the result

Use t_c as the rainfall duration when reading intensity from an IDF curve for the rational method. A shorter t_c means a higher intensity and a sharper peak; urbanisation usually shortens it by speeding up flow. Many design manuals set a minimum t_c of about 5 to 10 minutes for very small areas. If two methods give different values, compare them and justify the choice.

Common mistakes

Entering slope in percent (2) instead of m/m (0.02).
Using a straight-line distance rather than the actual longest flow path.
Using the US coefficient (0.0078) with metres, or the metric coefficient with feet.
Applying it to flat or urban catchments without adjustment.

Keep in mind: Kirpich is an empirical estimate for small, steep rural catchments. Results for flat, urban or large basins can be badly off. Use the methods required by your local drainage standards and have designs checked by a qualified engineer.

Frequently asked questions

How is the average slope defined?

Usually as the elevation difference between the remote point and the outlet divided by the flow length.

What other methods exist?

Velocity (segment) methods such as the NRCS TR-55 approach, the Kerby formula and the kinematic wave equation.

Does t_c change with rainfall intensity?

In reality yes, since faster flows travel quicker, but Kirpich treats it as fixed by geometry.

Sources: Z. P. Kirpich, Time of concentration of small agricultural watersheds, Civil Engineering, Vol. 10, No. 6, 1940 · V. T. Chow, D. R. Maidment and L. W. Mays, Applied Hydrology, McGraw-Hill, 1988

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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