Time of Concentration: Formulas & Worked Examples

Time of concentration (Tc) is the time runoff takes to travel from the hydraulically most distant point of a watershed to the outlet or design point. For most small sites, calculate it with the NRCS (TR-55) velocity method. Split the flow path into sheet flow, shallow concentrated flow and channel or pipe flow, compute each segment’s travel time, and add them:

Here Tc and Tt are in hours, L is the segment length in feet and V is its average velocity in ft/s (TR-55 Eqs. 3-1 and 3-2). Tc then sets the storm duration you use to read rainfall intensity from an IDF curve for the Rational Method. Many agencies apply a minimum Tc: 5 minutes in HEC-22 for inlet and storm-drain design, and 0.1 hour in TR-55.

Time of Concentration Formulas at a Glance

These are the equations most often used for Tc, in US customary and SI units. Each one is explained further down the page, with its variables, the range of data it was developed from, and its source.

Times are in hours for the TR-55 sheet-flow and NRCS lag equations and in minutes for the others. Convert a velocity to travel time with Tt = L/(3600V), in hours. S is slope in ft/ft (m/m) except where % is shown. The SI coefficients are the published values where a source gives them (TxDOT for Kirpich and Kerby, HEC-22 for the kinematic wave, ARR 1987 for Bransby-Williams); the rest are unit conversions of the US forms.

Which Method Should You Use?

• Your agency names one: use it. Most drainage criteria manuals specify the Tc method, the sheet-flow length limit and the minimum Tc.
• Urban or developing sites, storm drains, or any drainage you will change: use the NRCS velocity method. NEH Part 630 calls it “the best method for calculating time of concentration for an urbanizing watershed or if hydraulic changes to the watercourse are being considered.”
• Inlet spacing and gutter design: use sheet flow (TR-55 or the HEC-22 kinematic wave) plus gutter flow, with HEC-22’s 5-minute minimum.
• A whole rural watershed with little flow-path detail: use the NRCS watershed lag method (CN 50–95).
• Small rural watersheds with defined channels: use Kirpich. For Texas watersheds of 0.25 to 150 mi², TxDOT accepts its Kerby–Kirpich approach alongside the NRCS velocity method.
• Short overland planes: use Kerby, Izzard or FAA, within the range of each method’s data.

Empirical equations only apply within the range of the watersheds they were fitted to. NEH Part 630 warns that such regression equations “are for existing conditions and cannot be adapted to future conditions or urbanization changes that might occur in a watershed.” If two methods disagree widely, recheck the flow path and the inputs before choosing between them.

What Is Time of Concentration?

Time of concentration (Tc) is the time required for water to travel from the hydraulically most distant point in the watershed to the outlet. The hydraulically most distant point is the one with the longest travel time, which is not necessarily the one farthest away (NEH Part 630, Subpart F). The Rational Method assumes that when rainfall lasts at least as long as Tc, the entire watershed contributes runoff to the outlet, producing the maximum peak discharge.

Why Tc Matters

1. Rainfall Intensity Selection

In the Rational Method, Tc determines storm duration, which determines rainfall intensity:

The relationship:

• Longer Tc → Longer duration → Lower intensity → Lower peak flow
• Shorter Tc → Shorter duration → Higher intensity → Higher peak flow

2. Hydrograph Timing

In NRCS unit-hydrograph methods, Tc sets the watershed lag (L = 0.6 Tc) and, through it, the time to peak. See Tc, lag and time to peak below.

3. Design Storm Duration

Many regulations require storm duration = Tc for peak flow calculations.

The Segmented Flow Path Approach

The NRCS velocity method (TR-55; NEH Part 630, Subpart F) divides the flow path into segments with different flow types:

1. Sheet Flow

Shallow flow over plane surfaces (parking lots, lawns, roofs).

Characteristics:

• Very shallow depth (about 0.1 ft or less)
• Length limit: TR-55 (1986) says not to use its sheet-flow equation beyond 300 ft. The current NRCS guidance, NEH Part 630 Subpart F (2025), states that sheet flow typically lasts no more than 100 ft before it becomes shallow concentrated flow. HEC-22 notes that sheet flow rarely exceeds about 400 ft and may be less than 80 ft. Use the limit in your governing manual.
• Occurs at the top of the watershed, near the divide

NRCS Kinematic Wave Equation (TR-55 Eq. 3-3):

Where:

• Tt = Travel time (hours)
• n = Manning’s roughness coefficient for sheet flow (table below)
• L = Flow length (feet)
• P2 = 2-year, 24-hour rainfall (inches)
• S = Slope (ft/ft)

In SI units, with L in metres and P2 in millimetres, the coefficient becomes 0.0913 (Tt still in hours).

NEH Part 630 also gives the McCuen–Spiess criterion as an alternative to a fixed length. It limits sheet flow to the length at which nL/√S = 100 (L in feet):

For example, range land (n = 0.13) at 1% slope gives 77 ft, and woods with dense underbrush (n = 0.80) at 5% gives 28 ft.

Sheet Flow n Values (TR-55 Table 3-1):

¹ Includes weeping lovegrass, bluegrass, buffalo grass, blue grama grass and native grass mixtures. ² For woods, consider cover to a height of about 0.1 ft, the only part of the plant cover that obstructs sheet flow. HEC-22 Table 3-2 uses the same cover values and splits smooth surfaces further (for example, smooth asphalt 0.011 and smooth concrete 0.012).

2. Shallow Concentrated Flow

After sheet flow concentrates, but before it enters defined channels.

Characteristics:

• Depth typically 0.1-0.5 ft
• Flows in small rills, swales, or along curbs
• Velocity estimated from slope

NRCS Velocity Equations (TR-55 Appendix F):

For paved surfaces:

For unpaved surfaces:

Where V is in ft/s and S is slope in ft/ft. In SI units (V in m/s) the coefficients are 6.196 (paved) and 4.918 (unpaved). NEH Part 630 Subpart F (2025) adds equations for other covers, for example V = 6.962 S^0.5 for short-grass pasture and V = 2.516 S^0.5 for forest with heavy ground litter (ft/s).

Travel Time:

Where L is in feet and Tt is in hours.

3. Channel Flow

Flow in defined channels, pipes, or streams.

Use Manning’s Equation:

In SI units the constant is 1.0 instead of 1.49 (V in m/s, R in m). Take n from an open-channel or pipe table such as the Manning’s n reference, not the sheet-flow table above.

Then:

Alternative Tc Methods

These equations estimate Tc for a whole flow path or watershed in one step. Most are regressions on a small set of watersheds, so use them only within the range of their data.

NRCS Watershed Lag Method

Victor Mockus developed the lag method in 1961 from watershed data. NEH Part 630 gives lag (eq. 630.15-4a) and, with L = 0.6 Tc, time of concentration (eq. 630.15-4b):

Where:

• L = Lag (hours); Tc = Time of concentration (hours)
• ℓ = Flow length along the longest flow path (feet)
• Y = Average watershed land slope (%), not the slope of the flow path
• S = Maximum potential retention (inches)
• CN = Runoff curve number, used as a surrogate for the retardance factor

Because S + 1 = 1000/CN − 9, the SI form with ℓ in metres is Tc = ℓ^0.8(1000/CN − 9)^0.7 / (441 Y^0.5), still in hours.

Valid for: CN from 50 to 95; NEH says not to use values outside that range. The equation was developed from 24 watersheds of 1.3 acres to 9.2 mi², most of them smaller than 2,000 acres. Folmar and Miller (2000) found that a reasonable upper limit may be as much as 19 mi².

Example (NEH Part 630, Subpart F): Mawney Brook, Rhode Island, has ℓ = 3,865 ft, Y = 4.79% and CN = 63, so S = 1000/63 − 10 = 5.87 in.

NEH also notes that Folmar and Miller (2008) found both the lag and velocity methods tend to underestimate Tc on non-urban watersheds.

Kirpich Equation (1940)

Originally developed for small agricultural watersheds in Tennessee:

Where:

• Tc = Time of concentration (minutes)
• L = Length of main channel from headwater to outlet (feet)
• S = Average slope of that channel (ft/ft)

With L in metres the coefficient is 0.0195 (TxDOT Hydraulic Design Manual). NEH Part 630 prints the coefficient rounded to 0.007 (eq. 630.15-12); Kirpich’s 0.0078 is the value most manuals use.

Data range: seven rural watersheds on a Tennessee farm with well-defined channels and steep slopes, with drainage areas of 1.25 to 112 acres (NEH Part 630). Best for: Small rural watersheds with defined channels. Limitations: Doesn’t account for surface type. Chow, Maidment and Mays (1988) list multipliers of 0.4 for overland flow on concrete or asphalt and 0.2 for concrete channels.

FAA Method (1970)

Used for airport drainage:

Where:

• Tc = Time of concentration (minutes)
• C = Rational method runoff coefficient
• L = Length of overland flow (feet)
• S = Average slope (%)

With L in metres the coefficient is 3.26. The equation is printed on Figure 7, “Surface flow time curves”, of FAA Advisory Circular 150/5320-5B (1970). The chart covers slopes of 0.5% to 2.5% and distances up to 800 ft, and it says to use the formula for longer distances.

Best for: Overland flow on airfields and similar paved or turfed surfaces Limitations: Empirical; limited range of original data

Kerby-Hathaway Method

For overland flow (TxDOT Hydraulic Design Manual, Eq. 4-14):

Where:

• tov = Overland flow time of concentration (minutes)
• K = 0.828 with L in feet, or 1.44 with L in metres
• L = Overland flow length
• N = Kerby retardance coefficient (dimensionless; not Manning’s n)
• S = Slope (ft/ft or m/m)

Many references give Kerby’s original form, t = 0.83 (L N / √S)^0.467 with L in feet, which gives the same time to within about 1%.

Kerby N Values (TxDOT Hydraulic Design Manual, Table 4-5):

TxDOT says not to interpolate between these values. Kerby’s data included overland flow lengths of up to 1,200 ft (366 m), which TxDOT treats as an upper limit; NEH Part 630 notes that some references suggest keeping it below 1,000 ft. NEH also prints a different Kerby form that uses Manning’s n (eq. 630.15-13), so don’t mix N values into that equation.

Kerby–Kirpich Method

TxDOT’s Kerby–Kirpich approach (Hydraulic Design Manual, Eq. 4-13) adds a Kerby overland-flow time to a Kirpich channel-flow time:

Use the Kerby equation above for the overland part, and Kirpich for the main channel from the end of overland flow to the outlet (subtract the overland length from the channel length). TxDOT gives its range as watersheds of 0.25 to 150 mi², main channel lengths of 1 to 50 miles and main channel slopes of 0.002 to 0.02 ft/ft. TxDOT cites Roussel et al. (2005), who concluded that Kirpich-inclusive approaches, and Kerby–Kirpich in particular, are preferable for Texas watersheds.

Kinematic Wave Method (HEC-22)

HEC-22 (3rd ed., Eq. 3-3) estimates sheet-flow travel time from rainfall intensity:

Where:

• Tt = Sheet flow travel time (minutes)
• Ku = 0.933 in US units, 6.92 in SI
• n = Sheet flow roughness coefficient (HEC-22 Table 3-2)
• L = Flow length (ft or m)
• I = Rainfall intensity (in/h or mm/h)
• S = Surface slope (ft/ft or m/m)

Because I depends on Tc, the solution is iterative:

1. Assume a Tc for the whole path, including the downstream shallow and channel travel times.
2. Read I for that duration from the local IDF curve.
3. Compute the sheet-flow Tt and add the downstream times.
4. Repeat until the assumed and computed Tc agree.

HEC-22 Example 3-2 shows the process for 223 ft of Bermuda grass (n = 0.41) at 0.005 ft/ft, with 5.1 min of downstream travel. The equation reduces to Tt = 68.68 / I^0.4, and the intensities come from the example’s own IDF curve (HEC-22 Figure 3-1):

Using 47 min for the sheet flow, Tc = 47.0 + 3.7 + 1.4 = 52.1 min, so use 52 minutes.

HEC-22 also works the example in SI units. With L = 68 m and Ku = 6.92, the equation reduces to Tt = 249.8 / I^0.4 (I in mm/h). The IDF curve gives 90 mm/h for the first trial and 69 mm/h for the second, so Tt = 41.3 min and then 45.9 min. The next trial again gives 47 min, and Tc = 52 minutes.

Izzard Method

For shallow sheet flow over paved and turf surfaces:

Where Tc is in minutes, i is rainfall intensity (in/h), cr is a retardance coefficient, L is flow length (ft) and S is slope (ft/ft). The equation applies when i × L ≤ 500 (in/h × ft). In SI units (i in mm/h, L in m), the constants become 525 and 2.76 × 10⁻⁵, and the limit is i × L ≤ 3,870.

Izzard retardance coefficients (Izzard 1946):

Bransby-Williams Formula

Common in Australian practice for rural catchments. Australian Rainfall and Runoff (ARR 1987) gives it as:

Where Tc is in minutes, L is the main stream length to the catchment divide (km), A is the catchment area (km²) and Se is the equal-area slope of the main stream (m/km). In US units (L in miles, A in mi², S in ft/ft) the coefficient is 21.3. Bransby Williams (1922) developed it from catchments in India. Don’t use it for urban catchments.

Comparison of Methods

Step-by-Step NRCS Velocity Method Example

Given:

An 8-acre commercial site with:

• Sheet flow: 150 ft over parking lot (n = 0.011), 2% slope
• Shallow concentrated flow: 800 ft along curb line, 1.5% slope
• Channel flow: 1,200 ft in concrete pipe (n = 0.013), 0.5% slope, 36” diameter
• P2 = 3.5 inches

Solution:

Step 1: Sheet Flow

150 ft is within TR-55’s 300 ft limit and the McCuen–Spiess limit for this pavement (100 × √0.02 / 0.011 = 1,286 ft), but longer than NRCS’s current 100 ft guidance. If your reviewer applies 100 ft, treat the first 100 ft as sheet flow (1.2 min) and the last 50 ft as paved shallow concentrated flow at 2% (0.3 min). Tc then drops from 10.0 to 9.8 min.

Step 2: Shallow Concentrated Flow (Paved)

Velocity:

Travel time:

Step 3: Channel Flow (36” Concrete Pipe)

Assuming half-full conditions:

• A = 3.53 ft²
• R = 0.75 ft (D/4, the same as for full flow)
• n = 0.013

Velocity:

Travel time:

Step 4: Total Tc

Unrounded, the three segments sum to 9.95 min, so use Tc = 10 min. It is above HEC-22’s 5-minute and TR-55’s 0.1-hour (6-minute) minimums, so no minimum applies.

Step 5: Rainfall Intensity and Peak Flow

Use Tc = 10 min as the storm duration. Read the intensity for a 10-minute duration and your design return period from a local IDF curve, or from NOAA Atlas 14 in the US (see the IDF curves reference). NOAA’s precipitation frequency data server reports depths or intensities; to convert a depth, divide it by the duration. For illustration only, suppose the 10-year, 10-minute depth at the site is 1.00 in:

With C = 0.85 for a mostly paved commercial site (HEC-22 Table 3-1 gives 0.70–0.95 for downtown business areas and asphalt streets), the Rational Method peak flow is:

The 36-inch pipe’s full-flow capacity at 0.5% slope with n = 0.013 is 47.3 cfs, so it can carry this flow.

Tc, Lag and Time to Peak

These three timing terms are often confused. NEH Part 630 defines them as follows:

For the Mawney Brook example above, Tc = 1.14 h gives a lag of 0.6 × 1.14 = 0.69 h. NEH also notes that lag, and hence Tc, “is not a unique watershed characteristic and varies from storm to storm”. See Reading Hydrographs for how these times appear on a hydrograph.

Minimum Time of Concentration

Design manuals set a minimum Tc because very short durations give unrealistically high rainfall intensities, and IDF data rarely go below 5 minutes (the shortest duration in NOAA Atlas 14):

• HEC-22 (3rd ed., §7.2.2): “If the total time of concentration to the upstream inlet is less than five minutes, a minimum time of concentration of five minutes is used as the duration of rainfall.” FAA AC 150/5320-5D uses the same 5-minute minimum.
• TR-55 (1986, p. 3-4): “The minimum Tc used in TR-55 is 0.1 hour.” That is 6 minutes.
• Local manuals may set a different minimum, and the governing manual takes precedence.
• Application: Use the calculated Tc if it is longer than the minimum; otherwise use the minimum.

Effects of Development on Tc

Development typically reduces Tc:

TR-55 notes that Tc can also increase because of ponding behind small or inadequate drainage systems, such as storm drain inlets and road culverts.

Before and After Development

A typical site might have:

• Pre-development Tc: 45 minutes (grass, natural swales)
• Post-development Tc: 15 minutes (pavement, storm sewers)

On many IDF curves, cutting the storm duration from 45 to 15 minutes nearly doubles the rainfall intensity, and the peak flow rises accordingly.

Common Mistakes

1. Sheet Flow Length Too Long

NRCS now limits sheet flow to about 100 ft; the 1986 TR-55 allowed up to 300 ft. Use the limit in your governing manual, and model the rest of the path as shallow concentrated flow.

2. Using Wrong n Values

Sheet flow n values are NOT Manning’s equation n values. Kerby N and Izzard cr are different coefficients again. Use the table that goes with each equation.

3. Ignoring Minimum Tc

Don’t use calculated Tc values below 5 minutes without explicit approval.

4. Double-Counting Improvements

If pipes reduce Tc, don’t also use pre-development Tc elsewhere in the calculation.

5. Inconsistent Methods

Don’t combine unrelated methods for different parts of one flow path (for example, Kirpich for part and NRCS velocity for another). Use one consistent approach, or a combination that was developed as a pair, such as Kerby–Kirpich.

6. Forgetting Channel Entry/Exit

Include time to reach and exit channels, not just channel travel time.

Frequently Asked Questions

What is the formula for time of concentration?

There is no single formula. The most widely used is the NRCS (TR-55) velocity method: Tc is the sum of the travel times of the sheet-flow, shallow-concentrated-flow and channel segments of the flow path, and each travel time is flow length divided by velocity, Tt = L/(3600V) in hours with L in feet and V in ft/s. For a quick estimate on a small rural watershed with a defined channel, the Kirpich equation gives Tc = 0.0078 L^0.77 S^−0.385 in minutes, with L in feet and S in ft/ft.

What is the minimum time of concentration?

HEC-22 uses a minimum of 5 minutes for inlet and storm-drain design, and TR-55 states that the minimum Tc it uses is 0.1 hour (6 minutes). Local drainage manuals may set a different minimum, and the governing manual takes precedence. If the calculated Tc is shorter than the minimum, use the minimum.

How long can sheet flow be in a time of concentration calculation?

NRCS now states that sheet flow typically lasts no more than 100 feet before it becomes shallow concentrated flow (NEH Part 630, Subpart F). The 1986 TR-55 allowed its sheet-flow equation up to 300 feet, and HEC-22 notes that sheet flow rarely exceeds about 400 feet. Use the limit in your governing manual.

What is the difference between time of concentration and lag time?

Time of concentration is the travel time from the hydraulically most distant point of the watershed to the outlet. Lag is the time from the center of mass of rainfall excess to the peak of the runoff hydrograph. NRCS relates them as lag = 0.6 Tc, and time to peak = D/2 + lag, where D is the duration of rainfall excess.

Which time of concentration method should I use?

Use the method your reviewing agency specifies. Otherwise, use the NRCS velocity method for urban or developing sites and wherever the drainage system will change; the NRCS lag method for whole rural watersheds with curve numbers from 50 to 95; Kirpich for small rural watersheds with defined channels; and Kerby, Izzard or FAA only for overland flow within the range of the data each was developed from.

What are the SI forms of the Kirpich and Kerby equations?

With lengths in metres and time in minutes, Kirpich is Tc = 0.0195 L^0.77 S^−0.385 and Kerby is t = 1.44 (L N)^0.467 S^−0.235 (TxDOT Hydraulic Design Manual). The US forms use 0.0078 and 0.828 with lengths in feet. Slope S is dimensionless (m/m or ft/ft) in both.

Summary

Time of concentration is critical because:

• It determines design rainfall intensity
• It affects peak flow directly
• Errors propagate through all calculations

Key points:

• Use segmented approach (sheet → shallow → channel)
• Respect maximum sheet flow lengths
• Apply appropriate minimum Tc
• Consider effects of development
• Be consistent with chosen method

References

1. Natural Resources Conservation Service. (1986). Urban hydrology for small watersheds (Technical Release 55). U.S. Department of Agriculture.

2. Natural Resources Conservation Service. (2025). National engineering handbook, Part 630 Hydrology, Subpart F: Time of concentration (210-H-630, amended June 2025). U.S. Department of Agriculture.

3. Federal Highway Administration. (2013). Urban drainage design manual (3rd ed., Hydraulic Engineering Circular No. 22, FHWA-NHI-10-009). U.S. Department of Transportation.

4. Texas Department of Transportation. (2019). Hydraulic design manual, Chapter 4, Section 11: Time of concentration. TxDOT.

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

6. Federal Aviation Administration. (1970). Airport drainage (Advisory Circular 150/5320-5B), Figure 7. U.S. Department of Transportation.

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

8. Izzard, C. F. (1946). Hydraulics of runoff from developed surfaces. Highway Research Board Proceedings, 26, 129-150.

9. McCuen, R. H., & Spiess, J. M. (1995). Assessment of kinematic wave time of concentration. Journal of Hydraulic Engineering, 121(3), 256-266.

10. Bransby Williams, G. (1922). Flood discharge and the dimensions of spillways in India. The Engineer (London), 321-322.

11. Pilgrim, D. H. (Ed.). (1987). Australian rainfall and runoff: A guide to flood estimation. Institution of Engineers, Australia.

12. Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied hydrology. McGraw-Hill.

13. McCuen, R. H. (2016). Hydrologic analysis and design (4th ed.). Pearson.