Drainage & Hydrology
Time of Concentration
Time of concentration calculator using the Kirpich formula and the TR-55 three-segment method (sheet, shallow concentrated, channel flow).
Time of Concentration (Tc)
Time of concentration is the travel time for runoff to move from the hydraulically most remote point in a watershed to the design point. It is the critical link between the drainage area and the rainfall intensity used in the Rational Method — the rainfall duration is set equal to Tc, so an accurate Tc directly controls which intensity value is selected from the IDF curve.
Two methods are available. The Kirpich formula is best for small, homogeneous agricultural or rural watersheds where channel length and relief are the primary variables. The TR-55 three-segment method divides the flow path into sheet flow, shallow concentrated flow, and channel flow — providing a more detailed and defensible Tc for urban and mixed-cover watersheds.
Tc = 0.0078 × L0.77 × S−0.385
Tc in minutes L = channel length (ft) S = slope (ft/ft)
Tt = 0.007(nL)0.8 / (P₂0.5 · s0.4)
n = roughness L = length (ft, ≤300) P₂ = 2-yr 24-hr rainfall (in)
V = Kv × s0.5 (paved Kv=16.13, unpaved Kv=9.04)
V = (1.486/n) · R2/3 · S1/2 (channel, Manning's)
Tt = L / (3600 × V) hours
A 2,000-ft watercourse dropping 40 ft in elevation has an average slope of 2.0%. Plugging L and S into the Kirpich formula gives Tc = 0.0078 × 20000.77 × 0.02−0.385 ≈ 12.2 minutes (0.20 hours) — the storm duration to use when pulling a matching rainfall intensity from the local IDF curve for the Rational Method calculation.
Time of Concentration Calculator
Imperial units — feet, percent slope, minutes