Time of Concentration: Formulas, Methods, and Common Pitfalls

Time of concentration (Tc) is the time it takes runoff to travel from the hydraulically most distant point of a catchment to the point you are designing for. It looks like a minor input — a number in minutes buried in the middle of a calculation — but in peak-flow methods like the Rational Method it directly sets the design rainfall intensity, so an error in Tc propagates straight into the design flow, the pipe size, and the culvert opening.

Why Tc controls the answer

Peak-flow methods assume the critical storm duration equals Tc: long enough for the whole catchment to contribute, short enough to keep the intensity high. Rainfall intensity falls steeply as duration increases — so underestimating Tc inflates the design flow, and overestimating it shrinks the flow. On short, steep urban catchments a 10-minute error in Tc can move the peak flow by 30% or more.

The two formulas used most in South African practice

Kirpich (1940)

Developed from small agricultural catchments in Tennessee, and still the most widely quoted Tc formula worldwide. In SI form:

Tc = 0.0195 · L⁰·⁷⁷ · S⁻⁰·³⁸⁵

where Tc is in minutes, L is the length of the flow path (m), and S is the average slope of that path (m/m). It suits defined channels on moderate to steep slopes — the conditions it was derived from.

SANRAL Drainage Manual — defined watercourse

The SANRAL Drainage Manual recommends, for reaches with a defined watercourse:

Tc = (0.87 · L² / (1000 · Sav))⁰·³⁸⁵

where Tc is in hours, L is the watercourse length (km), and Sav is the average slope (m/m). If the two formulas look related, they are: the SANRAL expression is the Kirpich relationship recast in these units, so both give essentially the same answer for the same inputs. The value of using the SANRAL form is that it is the version reviewers on road and municipal projects expect to see cited.

The Drainage Manual pairs this with a separate overland-flow formula (the Kerby relationship) for the upper, sheet-flow portion of the catchment; on real catchments Tc is the sum of the overland and defined-watercourse travel times, not one formula applied end-to-end.

You can compute both formulas side by side in our time of concentration calculator.

The pitfalls we see most often

• Slope in the wrong units. S must be a dimensionless gradient (m/m). Entering percent (2 instead of 0.02) makes the catchment look absurdly steep and collapses Tc. This is the most common single error in checked calculations.
• Slope taken as a straight line between endpoints. A river with waterfalls or a steep headwater and flat lower reach is poorly described by (drop ÷ length). Where the profile is irregular, use a weighted method — the Drainage Manual’s equal-area (10–85) slope approach — rather than the crude average.
• Applying a channel formula to sheet flow. Kirpich-type formulas assume concentrated flow in a defined channel. Applying them from the true catchment boundary — across what is actually slow overland flow — understates travel time. Split the flow path into overland and channel segments.
• Ignoring urbanisation. Piped and paved catchments deliver water far faster than the natural-catchment formulas assume. For developed areas, estimate travel time through the actual drainage network (velocity × length), not from a rural regression.
• No sanity floor. Very short computed Tc values (under about 15 minutes) push design intensities to extreme values; standard practice applies a minimum Tc rather than accepting a 4-minute response from a formula.
• False precision. Tc formulas are regressions from specific regions and catchment types, credible to perhaps ±25–30%. Quoting Tc to the second — or letting a design hinge on the difference between two formulas — misreads the tool. If the design is sensitive to Tc, test the sensitivity explicitly.

A worked example

A defined watercourse 2.4 km long falling 36 m along its length: Sav = 36 / 2400 = 0.015 m/m.

Tc = (0.87 × 2.4² / (1000 × 0.015))⁰·³⁸⁵ = (5.011 / 15)⁰·³⁸⁵ ≈ 0.66 h ≈ 40 minutes

That 40 minutes then sets the storm duration used to read the design rainfall intensity for the site — which is why the design rainfall estimate and Tc need to be treated as a linked pair, not independent inputs.

When it matters enough to check properly

For a single pipe on a small stand, a carefully applied formula is fine. For culvert design on a public road, a drainage system serving a township, or any flow estimate a reviewer will interrogate, the flow path segmentation, slope derivation, and formula choice should be documented and defensible — the level of rigour we apply in our hydrological studies.