Time of Concentration Methods — Comparison
Time of concentration (Tc) is the time for runoff to travel from the hydraulically most distant point in the watershed to the design point. It controls the rainfall intensity used in the Rational Method (Q = CiA), and it sets the duration of the unit hydrograph in NRCS methods. Different methods make different assumptions about flow regime — the wrong choice can be off by 2× or more.
Decision matrix — pick the right method
| Watershed type | Recommended method | Why |
|---|---|---|
| Rural, single-flow-path, A < 200 ac, slope 3–10% | Kirpich (1940) | Calibrated on rural watersheds in this exact range. Reasonable for steep grass / row-crop terrain. |
| Rural with significant overland flow before defined channel | Kerby (overland) + Kirpich (channel) | Kirpich underestimates pre-channelized travel time. |
| Mixed urban / rural, mixed flow regimes | NRCS TR-55 segmental | Splits into sheet flow (≤ 100 ft), shallow concentrated flow, channel flow. The standard for SWMP work. |
| Whole watershed lumped, NRCS hydrology | NRCS Lag formula | Built into TR-20 / HEC-HMS NRCS unit hydrograph. Tc = TL / 0.6. |
| Airport, paved, very flat & short overland flow | FAA (1970) | Calibrated for runways. Short paved drainage paths. |
| Watershed too small or too large for any of the above | Don't use Tc — use a different model | For A < 5 ac use direct sheet-flow time; for A > 2,000 ac use a routing model. |
The equations, side-by-side (US units)
Kirpich (1940)
Tc (min) = 0.0078 · L0.77 · S−0.385
L = flow length (ft); S = average watershed slope (ft/ft). Multiply by 0.4 for paved overland flow, 0.2 for asphalt/concrete channels. Validity: 1 to 200 ac, slope 3–10%.
NRCS Lag (SCS)
TL (hr) = L0.8(S+1)0.7 / (1900 · Y0.5)
Tc = TL / 0.6
L = hydraulic length (ft); S = (1000/CN) − 10 (potential maximum retention, in); Y = average watershed slope (%). Validity: A < 2,000 ac, CN-based runoff hydrology.
TR-55 Segmental (3-segment travel time)
Sheet flow (≤ 100 ft, smooth surfaces only):
Tt,sheet = 0.007 · (n · L)0.8 / (P20.5 · S0.4)
Shallow concentrated flow: V = 16.1345·√S (unpaved), V = 20.3282·√S (paved); Tt = L / (3600·V)
Channel flow: Manning's equation V = (1.486/n) · R2/3 · S1/2; Tt = L / (3600·V)
Tc = Tt,sheet + Tt,shallow + Tt,channel
Kerby / Hathaway (overland)
Tc (min) = 0.83 · (L · n / √S)0.467
For overland flow only, L ≤ 1200 ft. n is a retardance coefficient (0.02 paved, 0.10 grass, 0.40 woods).
FAA
Tc (min) = 1.8 · (1.1 − C) · L0.5 / S0.333
C = rational-method runoff coefficient; L in ft; S in %.
Common mistakes
- Using Kirpich on urban watersheds. Kirpich was calibrated on rural Tennessee farmland. Apply the 0.4 / 0.2 multipliers if any portion is paved, or just switch to TR-55 segmental.
- Ignoring the 100-ft sheet-flow cap in TR-55. Sheet flow transitions to shallow concentrated flow within ~100 ft on natural terrain (50 ft on flat or vegetated terrain). Carrying sheet flow longer over-estimates Tc.
- Mixing methods on one path. If you start with Kirpich for a rural reach and then use TR-55 sheet-flow on the same upstream segment, you've double-counted. Pick one method per flow segment.
- Forgetting the lag-to-Tc conversion. NRCS lag (TL) is not Tc — it's 60% of it. Tc = TL / 0.6.
Sources: Kirpich, P.Z. (1940), Civil Engineering, Vol. 10, p. 362. NRCS TR-55 (1986). USDA NEH Part 630, Chapter 15. FAA AC 150/5320-5C. McCuen (2017), Hydrologic Analysis & Design, 4th ed.
Related cheat sheets
Once you have Tc and the design intensity, you'll need runoff coefficients for the Rational Method, and Manning's n for the channel-flow segment of the TR-55 method. For full event simulation including hydrograph routing, ponds, and BMP credit, see HydroComplete.