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 (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.

Kirpich Formula (Imperial)
Tc = 0.0078 × L0.77 × S−0.385 Tc in minutes   L = channel length (ft)   S = slope (ft/ft)
TR-55 Sheet Flow Travel Time (Imperial)
Tt = 0.007(nL)0.8 / (P₂0.5 · s0.4) n = roughness   L = length (ft, ≤300)   P₂ = 2-yr 24-hr rainfall (in)
TR-55 Shallow Concentrated & Channel Flow
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
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.
Worked Example

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.

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Time of Concentration Calculator

Imperial units — feet, percent slope, minutes

Longest watercourse from watershed divide to outlet
Total fall along L from upper end to outlet; S = H/L computed automatically
Time of Concentration Results
Total Tc
Average Channel Slope (S)
Tc (hours)
Use Tc to select rainfall intensity i from local IDF curves at the matching return period, then enter i into the Rational Method calculator. Requires PE review before use in any design document.

Flow-path diagram — updates live (Kirpich profile or TR-55 segments)

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