Time of Concentration Calculator (Kirpich Formula, Tc)

Calculate time of concentration with the Kirpich formula from flow-path length and average slope or elevation drop, in feet or meters.

Time of Concentration Formula

Time of concentration describes travel time from the hydraulically most distant contributing point to an outlet: the controlling path has the greatest travel time, not necessarily the longest distance. This calculator evaluates the empirical Kirpich channel-flow relationship. A channel-segment estimate is not automatically the full watershed time of concentration: sheet flow, shallow concentrated flow, channels, and other relevant segments may require different methods and their travel times must be combined appropriately.

Tc = (0.0078 L0.77) / (S0.385)

This canonical form gives minutes for length L in feet and dimensionless slope S. The calculator converts meter inputs using exactly 1 foot = 0.3048 meter before applying the same model. The corresponding metric form is:

Tc = (Cm L0.77) / (S0.385)

For L in meters, C_m = 0.0078 ÷ 0.3048^0.77 ≈ 0.01947166465476015. A rounded coefficient such as 0.0195 is an approximation, not an exact unit conversion. In the formula, S is a dimensionless fall/run ratio. In the calculator, select Percent and enter 2 for 2%, or select Ratio and enter 0.02.

S = (elevation drop) / (horizontal run)

S = (slope %) / (100)

Variable Guide

Variable	Description	Practical Meaning
Tc	Time of concentration	The modeled channel travel time for the entered path; other flow segments may be needed for full watershed time of concentration.
L	Flow path length	The modeled channel path length along the controlling route, not a straight-line map distance. The full controlling route has the greatest travel time, which need not be the greatest distance.
S	Flow path slope	The positive average fall/run ratio; choose Ratio or Percent to match the entered number.

How to Use the Calculator

Identify the watershed outlet or discharge point.
Identify the hydraulically controlling route by travel time, then identify the channel path to model along that route.
Measure the total flow path length along that route.
Determine positive average slope from elevation drop divided by horizontal run. For the time solve, you can instead enter elevation drop and path length with their matching units.
Match the slope unit to the value: enter 2 with Percent, or 0.02 with Ratio, for a 2% slope.
Choose the time, length, or slope result, enter the required known values, and select Calculate. Length and drop support meters or feet independently; time supports minutes or hours.

The three solve modes rearrange the same mathematical relationship; choose the result explicitly rather than leaving an arbitrary field blank. Time, length, slope, and any entered elevation drop must be positive. A mathematically valid result does not establish that Kirpich is suitable for the site or that a drainage design is approved.

Example

Suppose a channel path is 500 feet long and has a 2% average slope. Choose the time solve, enter 500 with feet and 2 with Percent. The formula uses the equivalent ratio 0.02:

S = (2) / (100) = 0.02

Tc = (0.0078 (500)0.77) / ((0.02)0.385) ≈ 4.21 minutes

The Kirpich estimate for that entered channel path is about 4.211191 minutes, or 4.21 minutes to two decimal places. This is an empirical model result, not a measured arrival time or, by itself, a complete watershed routing or peak-flow prediction.

Why Time of Concentration Matters

Helps estimate how quickly a drainage area responds to rainfall.
Supports stormwater design decisions for ditches, culverts, channels, and inlets.
Improves peak runoff analysis by tying rainfall duration to watershed response time.
Provides a fast screening value when comparing alternative site layouts or grading plans.
Helps identify whether a basin behaves as a flashy system or a slower-draining one.

When the Kirpich Method Works Best

Check the governing drainage manual and site conditions before choosing this relationship. FHWA presents Kirpich as a channel-flow estimate and combines appropriate segment travel times to determine watershed time of concentration. Applicability depends on flow type and accepted local methods; the formula alone does not validate a site merely because it is small or rural.

Channel-flow segments within the applicability of the governing local method
Sites whose land cover and conveyance conditions have been assessed for the selected method
Defined swales, ditches, or channelized flow paths
Sites where average slope can be estimated with reasonable confidence

Sheet flow, pavement, shallow concentrated flow, storm sewers, detention, and very flat or steep terrain need appropriate engineering assessment. Urban conveyances are not categorically excluded, but a single Kirpich calculation does not represent all their routing or storage. This calculator uses the unadjusted relationship; it does not automatically add low-slope adjustments, surface factors, or travel times for other flow segments. Positive inputs outside a validated application range remain unvalidated estimates.

Solving for Another Variable

To solve for length, enter positive time and slope; to solve for slope, enter positive time and length. The forms below use time in minutes, length in feet, and slope as a ratio.

L = ((Tc S0.385) / (0.0078))(1) / (0.77)

S = ((0.0078 L0.77) / (Tc))(1) / (0.385)

The calculator handles the selected input and output units. For a hand calculation using meters, substitute the consistently derived metric coefficient C_m from above. Elevation-drop entry is available in the time solve; length and slope inverses use the known time and the other stated quantity.

Common Input Mistakes

Entering 2 as a Ratio when you mean 2%, or entering 0.02 with Percent when you mean a 0.02 ratio.
Using straight-line distance instead of the actual runoff travel path.
Choosing a unit that does not match the entered length, elevation drop, or time. The calculator converts the selected units; changing a unit converts its current quantity.
Using a zero or negative slope value.
Applying one empirical channel-flow estimate to a whole watershed or routed system without checking flow segments, storage, and governing method requirements.

FAQ

What does a smaller time of concentration mean?

A smaller modeled travel time indicates faster movement along the entered path under this relationship. It does not by itself determine watershed storage, runoff volume, or peak discharge; those require the rest of the hydrologic analysis.

Is time of concentration the same as total travel time?

Watershed time of concentration combines the relevant travel times along the hydraulically controlling path. Kirpich supplies a channel-flow estimate here; sheet flow, shallow concentrated flow, channels, and other segments may require their respective methods before their travel times are added.

Can I use percent slope directly?

Yes. Select Percent and enter 5 for 5%, or select Ratio and enter 0.05. The calculator converts either entry to the dimensionless ratio used in the equation.

What if my site has several different flow segments?

Choose an appropriate travel-time method for each distinct surface or conveyance segment, then combine the relevant segment times along the controlling path. This calculator does not perform that full segmented or routed analysis. When browser storage is available, it saves the last successful input snapshot and validates and recomputes it on return. Edits keep a marked previous result until Calculate is selected again; Reset clears this calculator’s saved state and returns numeric entries to blank.

Time of Concentration Calculator screenshot

time of concentration formula — Kirpich equation shown with time in minutes, length in feet, and slope as a dimensionless ratio.