Time of Concentration Calculator

TR-55 segments

Tc is the sum of the travel times of sheet flow, shallow concentrated flow and channel flow along the hydraulically most distant path. Sheet flow: T_t = 0.007 (nL)^0.8 / (P₂^0.5 s^0.4) hours (TR-55 Eq. 3-3). Shallow concentrated flow: V = k s^0.5. Channel flow: Manning’s equation with the bankfull hydraulic radius (Eq. 3-4). Each T_t = L / (3600 V).

Sheet flow length

TR-55 (1986) allows sheet flow up to 300 ft; NRCS NEH Part 630 Chapter 15 (2010) recommends no more than 100 ft. Lengths over 100 ft carry a warning and over 300 ft are refused.

2-year rainfall

P₂ is the 2-year, 24-hour rainfall. Type it, or look it up for a Texas location from NOAA Atlas 14 (the same value as the Atlas 14 IDF Calculator).

Kirpich and Kerby-Kirpich

Kirpich (1940): t_ch = 0.0078 L^0.77 S^−0.385 minutes for the main channel. Kerby (1959): t_ov = 0.828 (L N)^0.467 S^−0.235 minutes for overland flow of 1,200 ft or less. The TxDOT Hydraulic Design Manual (Chapter 4, Section 11, Eqs. 4-14 and 4-15) adds the two, with the overland length taken off the main channel length. On low slopes the TxDOT HDM uses an adjusted slope, S + 0.0005, in both equations: below 0.002 ft/ft it should be used, and 0.002–0.003 ft/ft is transitional (Cleveland et al. 2012). The calculator applies it below 0.002 by default and reports the slope used; you can force it on or off.

NRCS lag

NEH Part 630 Chapter 15: L = ℓ^0.8 (S + 1)^0.7 / (1900 Y^0.5) hours with S = 1000/CN − 10 and Y the average watershed slope in percent; T_c = L / 0.6 (Eq. 15-4b).

No minimum here

The calculator reports Tc as computed. A minimum duration for rainfall intensity (TxDOT uses 10 minutes) is applied in the Rational Method Calculator.

Sheet flow: Manning’s n (NRCS TR-55 Table 3-1)

Shallow concentrated flow: V = k s^0.5 (TR-55 Figure 3-1; NEH 630 Chapter 15 Table 15-3)

Overland flow: Kerby retardance N (TxDOT HDM Chapter 4)

The calculator is tested against the cases below every time its code changes.

Travel times are compared with the published worked examples — NRCS TR-55 Example 3-1, NEH 630 Chapter 15, FHWA HEC-22 Example 4.2 and the TxDOT Kerby-Kirpich example — to the precision each prints; the rest are hand calculations of the published equations.

• One flow path. Choosing the hydraulically most distant path, and the lengths and slopes along it, is the user’s.
• Channel velocity uses a bankfull hydraulic radius; pipe and gutter segments are not modeled separately (use the Pipe Flow Calculator for a pipe velocity and enter it as a channel segment’s travel time by hand).
• Methods give different results for the same watershed. Your city, county or TxDOT criteria may set which method to use.
• The low-slope adjustment is TxDOT guidance. In the transitional band (0.002–0.003 ft/ft) the calculator does not decide for you; other agencies may handle flat watersheds differently.

What is the time of concentration?

The time it takes runoff to travel from the hydraulically most distant point of the watershed to the outlet. It sets the rainfall duration in the Rational Method and the peak timing in NRCS methods.

Which method should I use?

TR-55 segments follow the flow path piece by piece and are common for small urban and rural watersheds. Kirpich was developed on small agricultural watersheds; TxDOT combines Kerby for overland flow with Kirpich for channels. Local criteria manuals often name the method.

Why limit sheet flow to 100 feet?

True sheet flow rarely stays shallow and uniform for long before it concentrates into rills. NRCS NEH Part 630 Chapter 15 (2010) recommends 100 ft as the limit; TR-55 (1986) allowed up to 300 ft.

Can I attach the calculation sheet to a design report?

You can print it and include it as a supporting calculation that you have checked. It is a calculation aid, not a sealed engineering document: the engineer of record reviews it and is responsible for the design, and the criteria of the reviewing agency decide which methods and values apply.

Topic	Reference
TR-55 segments	USDA NRCS (1986). Urban Hydrology for Small Watersheds, Technical Release 55, 2nd ed., Chapter 3 and Appendix F.
Time of concentration	USDA NRCS (2010). National Engineering Handbook Part 630, Chapter 15: Time of Concentration.
Kirpich	Kirpich, Z.P. (1940). Time of concentration of small agricultural watersheds. Civil Engineering, 10(6), 362.
Kerby	Kerby, W.S. (1959). Time of concentration for overland flow. Civil Engineering, 29(3), 174.
Texas practice	TxDOT Hydraulic Design Manual, Chapter 4, Section 11 — Time of Concentration.