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).

Drainage & Hydrology · TR-55 / Kirpich

Time of Concentration (T_c)

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 T_c, so an accurate T_c 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 T_c for urban and mixed-cover watersheds.

Kirpich Formula (Imperial)

T_c = 0.0078 × L^0.77 × S^−0.385 T_c in minutes L = channel length (ft) S = slope (ft/ft)

TR-55 Sheet Flow Travel Time (Imperial)

T_t = 0.007(nL)^0.8 / (P₂^0.5 · s^0.4) n = roughness L = length (ft, ≤300) P₂ = 2-yr 24-hr rainfall (in)

TR-55 Shallow Concentrated & Channel Flow

V = K_v × s^0.5 (paved K_v=16.13, unpaved K_v=9.04) V = (1.486/n) · R^2/3 · S^1/2 (channel, Manning's) T_t = L / (3600 × V) hours

Reference: NRCS TR-55 Urban Hydrology for Small Watersheds, 1986, Chapter 3; Kirpich, Z.P. (1940) Time of concentration of small agricultural watersheds, Civil Engineering, 10(6):362. P₂ from NOAA Atlas 14.