Time of Concentration Calculator (Kirpich, Témez & Bransby-Williams)
Estimate a catchment’s time of concentration from the flow path length, elevation drop and area with the Kirpich, Témez and Bransby-Williams formulas — the storm duration used in the rational method.
How it works
Kirpich: tc = 0.0195 · L^0.77 · S^−0.385 (minutes, L in m, S in m/m) · Témez: tc = 0.3 · (L / S^0.25)^0.76 (hours, L in km) · Bransby-Williams: tc = 58.5 · L / (A^0.1 · S^0.2) (minutes, L in km, A in km², S in m/km) · S = elevation difference ÷ length.
The time of concentration is the time water takes to travel from the hydraulically most remote point of a catchment to its outlet. In the rational method (Q = CiA) the design storm lasts this long, so the whole catchment contributes at once and the peak flow is largest. Kirpich’s 1940 formula was fitted to small agricultural basins in Tennessee and is widely used in the US (it is the same as the California Culverts Practice formula); Témez’s formula is the standard in Spain’s Instrucción 5.2-IC and much of Latin America; Bransby-Williams is used in Australia and the UK for larger catchments. Different formulas often disagree by a factor of two, so comparing several is good practice.
Worked example
A catchment of 2 km² has a 1,500 m main flow path that falls 30 m (S = 0.02). Kirpich: tc = 0.0195 × 1,500^0.77 × 0.02^−0.385 = 24.5 min. Témez: 0.3 × (1.5/0.02^0.25)^0.76 = 0.86 h = 51.5 min. Bransby-Williams: 58.5 × 1.5/(2^0.1 × 20^0.2) = 45.0 min. The average of the three is 40.3 min.
Sources: Kirpich, Z. P. (1940). Time of concentration of small agricultural watersheds. Civil Engineering 10(6):362 · Ministerio de Transportes (España) — Instrucción 5.2-IC Drenaje superficial (fórmula de Témez)
Frequently asked questions
What is the time of concentration used for?
It sets the storm duration for the rational method: you read the rainfall intensity for a duration equal to tc from the local IDF curve, then Q = CiA. It is also an input to unit hydrographs such as the NRCS dimensionless hydrograph (lag ≈ 0.6 tc).
Which formula should I use?
Use the one your local design manual specifies. Kirpich suits small rural catchments with defined channels; Témez is required in Spain and common in Latin America; for urban areas the NRCS segmental method (sheet flow, shallow concentrated flow and channel flow) is preferred.
What is a minimum time of concentration?
Most agencies use a minimum of 5 to 10 minutes, because very short durations give unrealistically high intensities. For paved urban areas 5 minutes is common; for rural areas 10 minutes.
How do I measure the flow length and slope?
Trace the longest path water follows to the outlet on a topographic map or DEM, measure its length, and divide the elevation difference between its upper end and the outlet by that length for the average slope.
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This calculator is for educational purposes. Double-check important results before acting on them.