Time of concentration is the travel time from the hydraulically remote part of a catchment to the design point. Many drainage methods use that time to choose a rainfall duration. TOOL-004 does not make that rainfall choice. It calculates one empirical channel-flow travel time and, under its stated single-segment assumption, reports that time as Tc.
What this estimate answers
The calculator answers a narrow question: given a flow length and a representative channel slope, what Kirpich channel travel time does the published equation return? It does not build a hydrograph, choose an IDF intensity, or decide that Kirpich is the method your jurisdiction requires.
FHWA HDS-2, the source registered for this tool, describes Kirpich as an empirical channel-flow relationship developed from small drainage basins of about 1–112 acres, and describes channel-flow use where gullying or engineered conveyance is evident in more than 10 percent of the primary watercourse. Those figures are applicability context, not hidden limits coded as a pass or fail.
Formula
The exponent on length is 0.77 and the exponent on slope is −0.385. A longer path increases the estimate. A steeper slope decreases it. The coefficient 0.0195 belongs to this SI form of the equation. Do not reuse it with a length that is still in feet.
- Flow length: the principal hydraulic path from the hydraulically remote point to the outlet.
- Slope: a representative main-channel slope along that path, entered as rise over run.
US inputs
The interface accepts SI or US length. A length in feet is multiplied by 0.3048 to reach metres before the equation runs. Slope in feet per foot is dimensionless, so the same numeric value is used as metres per metre. The engine then applies the SI equation above. Switching units does not change the equation.
Worked example: 300 metres at 2 percent
Illustrative inputs, not recommended defaults: L = 300 m and S = 0.02 m/m.
- Confirm that one channel-flow segment can represent the controlling path.
- Use the example length L = 300 m.
- Use the example slope S = 0.02 m/m.
- Substitute into Tc = 0.0195 × L^0.77 × S^-0.385.
Result: Tc ≈ 7.1043 minutes. That is the value the TOOL-004 methodology reports for these inputs, and it is the time the tool reports as Tc under the single-segment assumption. It is not a rainfall duration and not a peak flow.
Reproduce it in the time-of-concentration calculator by entering 300 m and 0.02.
When not to stop at this number
- Sheet flow or several segments control the path: add the applicable travel-time components with a method written for that path. This tool does not estimate sheet-flow roughness or shallow concentrated flow.
- The basin or watercourse sits outside the cited HDS-2 context: document why another travel-time method is required.
- You need intensity or runoff: Tc does not calculate either. The design-storm helper only records a supplied intensity, and the Rational Method guide shows how a supplied intensity enters Q = C i A.
How to use the result in a review
- Identify one channel-flow segment, or switch to a segmented method.
- Measure flow length along the principal path.
- Enter the main-channel slope for that path.
- Apply the SI Kirpich equation and check the units independently.
Keep the source label with the number: SRC-KIRPICH-FHWA-HDS2-TOOL004-001, FHWA Highway Hydrology (HDS-2), Third Edition. The calculator does not compute rainfall intensity, Rational Method runoff, channel velocity, detention routing, pipe capacity, or network hydraulics, and the result does not establish code or permit compliance.
Frequently asked questions
What equation does the Kirpich calculator use?
TOOL-004 uses Tc = 0.0195 × L^0.77 × S^-0.385, with L in metres, S in metres per metre, and Tc in minutes.
Which inputs are required?
A flow length along the principal hydraulic path and a representative main-channel slope.
Does the calculator include sheet flow?
No. This published version is a single-segment Kirpich channel-flow estimate, not a segmented sheet-flow, shallow-concentrated-flow, and channel-flow sum.
When is the Kirpich result treated as time of concentration?
Only when the controlling path can reasonably be represented by one channel-flow segment. Otherwise use a segmented travel-time method.
What applicability context does the page cite?
FHWA HDS-2 notes development from small drainage basins of about 1–112 acres and channel-flow use where gullying or engineered conveyance is evident in more than 10 percent of the primary watercourse.
Does the result select a rainfall intensity?
No. Rainfall intensity, Rational Method runoff, and pipe capacity are outside this calculator.
How are US inputs handled?
Length in feet is converted to metres with 0.3048 m/ft before the SI equation. A slope entered as feet per foot is already dimensionless and is used as metres per metre.
Does the estimate prove code compliance?
No. It is a preliminary travel-time estimate and does not establish local-code or permit compliance.
Estimate a single-segment Kirpich time
Enter flow length and main-channel slope in SI or US units.
Open the calculator