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Time Of Concentration Calculator

Time of concentration equals 0.0078 times travel length to the 0.77 power times slope to the negative 0.385 power

Solution

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Time of Concentration Equations

Time of concentration is how long runoff takes to travel from the most distant point in a watershed to the outlet.

tc = f(L, S, n, i, CN, ...)

How It Works

Time of concentration (tc) is how long runoff takes to travel from the most distant point in a watershed to the outlet. A shorter tc produces a higher peak flow rate for the same storm, which directly affects culvert, sewer, and detention basin sizing.

Example Problem

A small watershed has a maximum flow path of 2,000 ft and a slope of 0.04 (4%). Using the Kirpich formula, what is the time of concentration?

  1. tc = 0.0078 × 2000^0.77 × 0.04^-0.385
  2. tc = 0.0078 × 417.5 × 4.217
  3. tc ≈ 13.7 minutes

When to Use Each Variable

  • Kirpich: Solve for tc — when you have a small rural watershed with a defined channel and know the flow path length and slope.
  • Kirpich: Solve for Travel Length — when you know the target tc and slope and need to find the maximum flow path length for a design.
  • Izzard: Solve for tc — when dealing with short overland sheet flow where rainfall intensity and surface retardance are known.
  • Kinematic Wave: Solve for tc — when you need to account for Manning roughness and rainfall intensity in an overland flow estimate.
  • NRCS: Solve for tc — when using the TR-55 method and you have the watershed lag time from the SCS curve number approach.
  • Bransby Williams: Solve for tc — when working with a channel-dominated watershed and you know the drainage area, length, and slope.

Key Concepts

Time of concentration (tc) is the time it takes for runoff to travel from the hydraulically most distant point in a watershed to the outlet. It determines the critical storm duration for design — shorter tc means higher peak flows for the same rainfall depth. Different empirical formulas apply to different watershed types: Kirpich for rural channels, Izzard/Kerby for sheet flow, Kinematic Wave for overland flow with known roughness, and NRCS/TR-55 for larger watersheds with SCS curve numbers.

Applications

  • Stormwater drainage design: selecting design rainfall intensity from IDF curves using tc as the storm duration
  • Culvert and bridge sizing: determining peak flow rates with the Rational Method (Q = CiA) where tc sets the rainfall intensity
  • Detention basin design: establishing the critical storm duration that produces the maximum required storage volume
  • Floodplain mapping: estimating peak discharges for different return periods as input to hydraulic models
  • Erosion control: timing sediment basin inflows during construction to size temporary BMPs

Common Mistakes

  • Using Kirpich for overland sheet flow — it was developed for small rural watersheds with defined channels, not parking lots or lawns
  • Applying a single tc formula across mixed land uses — composite watersheds often need segmented travel time calculations (sheet flow + shallow concentrated flow + channel flow)
  • Ignoring the effect of urbanization — impervious surfaces shorten tc dramatically, increasing peak flow by 50–200%
  • Confusing watershed lag time (tL) with time of concentration — NRCS defines tc ≈ 1.67 × tL, not tc = tL

Frequently Asked Questions

What is time of concentration used for?

It sets the duration for selecting rainfall intensity from IDF curves. In the Rational Method (Q = CiA), tc determines the design storm intensity, which drives peak flow calculations for drainage design.

When should I use each formula?

The Kirpich formula is best for small rural watersheds with defined channels. The Izzard and Kerby formulas apply to overland sheet flow on short slopes. The Kinematic Wave formula accounts for rainfall intensity and Manning roughness. The NRCS and Watershed Lag Time formulas are used in the TR-55 method for larger watersheds with known curve numbers. The Bransby Williams formula suits channel-dominated watersheds.

How does urbanization affect time of concentration?

Impervious surfaces reduce tc by increasing runoff velocity and eliminating infiltration. A 5-acre rural site might have tc of 20 minutes; the same site developed could drop to 8–10 minutes, significantly increasing peak flow.

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