Time of Concentration Coefficients: Kirpich, Kerby, TR-55

Time of concentration coefficients

Each time of concentration formula carries a coefficient for the surface the water runs over. This page collects the four tables used by Delta Hydro Studio's time of concentration calculator: Kirpich adjustment factors, Kerby retardance coefficients, TR-55 sheet-flow Manning's n, and shallow concentrated flow velocity coefficients.

The tables below give the coefficient for each method, with the formula it belongs to in SI units (L in metres, S in m/m unless stated, times in minutes). The time of concentration calculator runs all of these methods side by side, and its guide compares them on one flow path.

Sheet flow: TR-55 Manning's n

Travel time for sheet flow over the first part of the flow path, from TR-55 with the 2-year, 24-hour rainfall depth P₂:

T_{t} = \frac{0.007 ( n L ) ^{0.8}}{P _{2}^{0.5} S ^{0.4}} (hours; L in ft, P_{2} in inches)

Surface	Manning's n for sheet flow
Smooth surfaces (concrete, asphalt)	0.011
Fallow (no residue)	0.050
Cultivated soil — residue cover ≤20%	0.060
Cultivated soil — residue cover >20%	0.170
Grass — short prairie	0.150
Grass — dense/tall	0.240
Bermuda grass	0.410
Range (natural)	0.130
Woods — light underbrush	0.400
Woods — dense underbrush	0.800

Grass covers include species such as weeping lovegrass, bluegrass, buffalo grass, blue grama and native grass mixtures. Woods n values assume cover to a height of about 30 mm (0.1 ft), the only part that obstructs sheet flow. Source: TR-55 Table 3-1.

Shallow concentrated flow: velocity coefficient k

After sheet flow, the water gathers into rills and shallow swales. HEC-22 gives the velocity as a function of slope:

V = k S_{p}^{0.5} (V in m/s, S_{p} slope in percent)

Land cover or flow regime	k (m/s)	k (ft/s)
Forest with heavy ground litter; hay meadow (overland flow)	0.076	0.25
Trash fallow or min. tillage; contour/strip cropped; woodland (overland flow)	0.152	0.50
Short grass pasture (overland flow)	0.213	0.70
Cultivated straight row (overland flow)	0.274	0.90
Nearly bare and untilled (overland flow); alluvial fans	0.305	1.00
Grassed waterway (shallow concentrated flow)	0.457	1.50
Unpaved (shallow concentrated flow)	0.491	1.61
Paved area; small upland gullies (shallow concentrated flow)	0.619	2.03

For example, 150 m of shallow flow over paving at 2 % runs at 0.619 × √2 = 0.88 m/s and takes 2.9 minutes. Unpaved ground at the same slope gives 0.69 m/s. The paved and unpaved rows reproduce the two TR-55 Figure 3-1 lines (V = 20.33 √S and 16.13 √S ft/s, S in ft/ft). Source: HEC-22 Table 3-3, after NEH-4.

Kirpich adjustment factor

t_{c} = 0.0195 k L^{0.77} S^{- 0.385}

Surface	Factor k	Note
Bare soil, roadside ditches, well-defined natural channel	1.0	No adjustment — the surface Kirpich was calibrated on
Overland flow on grass	2.0	Grassy overland surfaces retard flow, roughly doubling Tc
Overland flow on concrete or asphalt	0.4	Smooth impervious surfaces
Concrete-lined channel	0.2	Smooth lined channels
Natural channel with vegetation	1.0	Unimproved natural streams — practitioner extension, not in Chow
Channel with heavy brush	1.5	Heavily vegetated channels — practitioner extension, not in Chow

The 0.4 and 0.2 factors are from Chow et al. (1988), Table 15.1.2. Kirpich is reliable for small rural catchments with defined channels and slopes of 3 to 10 %; on flat or urban catchments it tends to underestimate t_c.

Kerby retardance coefficient

t_{c} = 1.44 (\frac{L r}{S ^{0.5}})^{0.467}

Surface	Retardance r
Smooth impervious (asphalt, concrete)	0.02
Smooth bare packed soil	0.10
Poor grass, cultivated row crops	0.20
Pasture or average grass	0.40
Deciduous forest	0.60
Dense grass, coniferous forest, deciduous forest with deep litter	0.80

Kerby's formula is for overland flow only. Combine it with a channel method (Kirpich, or Manning's equation for the channel velocity) for the rest of the flow path, as Texas DOT practice does in the Kerby–Kirpich method.

Which coefficient to trust

The coefficients are the least certain part of any t_c estimate, and the methods differ by a factor of two or more on the same flow path. Check the result against the travel time along the flow path using velocities you can defend, and use the rainfall intensity for the t_c you adopt in the Rational method. The Manning's n table covers channel roughness for the channel-flow segment.

Common questions

What Manning's n do I use for sheet flow?

The sheet-flow n values of TR-55 Table 3-1 are much larger than open-channel values because they include the effect of raindrop impact, drag over the surface and obstacles in very shallow flow. Smooth surfaces are 0.011, short prairie grass 0.15, and woods with dense underbrush up to 0.80. Do not use a channel n for sheet flow.

How long can sheet flow be?

TR-55 (1986) limits sheet flow to 300 ft (about 90 m); the 2010 NRCS revision (NEH Part 630, Chapter 15) reduced the maximum to 100 ft (about 30 m). Beyond that the flow concentrates into rills and becomes shallow concentrated flow. Many manuals use 50 to 100 m for well-graded, smooth surfaces such as car parks.

When should I use the Kirpich factor?

Kirpich (1940) calibrated his formula on small agricultural catchments in Tennessee with well-defined channels on steep slopes. Multiply the result by 0.4 for overland flow on concrete or asphalt and by 0.2 for concrete-lined channels, the adjustments Chow et al. (1988) give. A factor of about 2 for grassed overland flow is common in practice but is not in Chow.

What is the Kerby retardance coefficient?

Kerby's r describes how much the surface slows overland flow, from 0.02 for smooth pavement to 0.80 for dense grass or conifer forest. The Kerby formula applies to overland flow only, and practice limits it to overland lengths under about 365 m (1 200 ft); add a channel travel time for the rest of the flow path.

Sources

Kirpich, Z.P. (1940) Time of concentration of small agricultural watersheds. Civil Engineering, 10(6), 362.

Kerby, W.S. (1959) Time of concentration for overland flow. Civil Engineering, 29(3), 174.

USDA Soil Conservation Service (1986) Urban Hydrology for Small Watersheds, Technical Release 55 (TR-55), 2nd ed. Chapter 3 and Table 3-1.

USDA Natural Resources Conservation Service (2010) National Engineering Handbook, Part 630 Hydrology, Chapter 15: Time of Concentration.

Brown, S.A. et al. (2013) Urban Drainage Design Manual, Hydraulic Engineering Circular No. 22 (HEC-22), 3rd ed. FHWA-NHI-10-009. Federal Highway Administration. Tables 3-2 and 3-3.

Chow, V.T., Maidment, D.R. and Mays, L.W. (1988) Applied Hydrology. McGraw-Hill, New York. Table 15.1.2.

The values are the ones Delta Hydro Studio's calculators use. Last reviewed 9 October 2026. Check them against the design manual your project is reviewed under.