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Time Of Concentration Calculator

Time of concentration equals 0.0078 times travel length to the 0.77 power times slope to the negative 0.385 power

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Time of Concentration Equations

Time of concentration is how long runoff takes to travel from the most distant point in a watershed to the outlet.

tc = f(L, S, n, i, CN, ...)

How It Works

Time of concentration (tc) is how long runoff takes to travel from the most distant point in a watershed to the outlet. A shorter tc produces a higher peak flow rate for the same storm, which directly affects culvert, sewer, and detention basin sizing.

Example Problem

A small watershed has a maximum flow path of 2,000 ft and a slope of 0.04 (4%). Using the Kirpich formula, what is the time of concentration?

  1. Identify the knowns. Maximum flow path length L = 2,000 ft, watershed slope S = 0.04 (dimensionless, i.e., a 4% grade from the most distant point to the outlet).
  2. Identify what we're solving for. We want the time of concentration tc in minutes — how long it takes runoff from the hydraulically most distant point to reach the outlet.
  3. Write the Kirpich empirical formula in symbols: tc = 0.0078 × L^0.77 × S^(−0.385), with L in feet and S as a decimal slope.
  4. Substitute the known values: tc = 0.0078 × 2000^0.77 × 0.04^(−0.385).
  5. Simplify each power: 2000^0.77 ≈ 348.2 (since 2000 = 10^3.301 and 10^(3.301 × 0.77) ≈ 10^2.542 ≈ 348), and 0.04^(−0.385) ≈ 3.453 (since flipping the negative exponent gives 1 / 0.04^0.385 ≈ 1 / 0.2896).
  6. Multiply the three factors: 0.0078 × 348.2 × 3.453 ≈ 9.38. **tc ≈ 9.4 minutes** — a quick-responding small rural watershed.

When to Use Each Variable

  • Kirpich: Solve for tc — when you have a small rural watershed with a defined channel and know the flow path length and slope.
  • Kirpich: Solve for Travel Length — when you know the target tc and slope and need to find the maximum flow path length for a design.
  • Izzard: Solve for tc — when dealing with short overland sheet flow where rainfall intensity and surface retardance are known.
  • Kinematic Wave: Solve for tc — when you need to account for Manning roughness and rainfall intensity in an overland flow estimate.
  • NRCS: Solve for tc — when using the TR-55 method and you have the watershed lag time from the SCS curve number approach.
  • Bransby Williams: Solve for tc — when working with a channel-dominated watershed and you know the drainage area, length, and slope.

Key Concepts

Time of concentration (tc) is the time it takes for runoff to travel from the hydraulically most distant point in a watershed to the outlet. It determines the critical storm duration for design — shorter tc means higher peak flows for the same rainfall depth. Different empirical formulas apply to different watershed types: Kirpich for rural channels, Izzard/Kerby for sheet flow, Kinematic Wave for overland flow with known roughness, and NRCS/TR-55 for larger watersheds with SCS curve numbers.

Applications

  • Stormwater drainage design: selecting design rainfall intensity from IDF curves using tc as the storm duration
  • Culvert and bridge sizing: determining peak flow rates with the Rational Method (Q = CiA) where tc sets the rainfall intensity
  • Detention basin design: establishing the critical storm duration that produces the maximum required storage volume
  • Floodplain mapping: estimating peak discharges for different return periods as input to hydraulic models
  • Erosion control: timing sediment basin inflows during construction to size temporary BMPs

Common Mistakes

  • Using Kirpich for overland sheet flow — it was developed for small rural watersheds with defined channels, not parking lots or lawns
  • Applying a single tc formula across mixed land uses — composite watersheds often need segmented travel time calculations (sheet flow + shallow concentrated flow + channel flow)
  • Ignoring the effect of urbanization — impervious surfaces shorten tc dramatically, increasing peak flow by 50–200%
  • Confusing watershed lag time (tL) with time of concentration — NRCS defines tc ≈ 1.67 × tL, not tc = tL

Frequently Asked Questions

What is time of concentration used for?

It sets the duration for selecting rainfall intensity from IDF curves. In the Rational Method (Q = CiA), tc determines the design storm intensity, which drives peak flow calculations for drainage design.

When should I use each formula?

The Kirpich formula is best for small rural watersheds with defined channels. The Izzard and Kerby formulas apply to overland sheet flow on short slopes. The Kinematic Wave formula accounts for rainfall intensity and Manning roughness. The NRCS and Watershed Lag Time formulas are used in the TR-55 method for larger watersheds with known curve numbers. The Bransby Williams formula suits channel-dominated watersheds.

How does urbanization affect time of concentration?

Impervious surfaces reduce tc by increasing runoff velocity and eliminating infiltration. A 5-acre rural site might have tc of 20 minutes; the same site developed could drop to 8–10 minutes, significantly increasing peak flow.

What is a typical minimum tc value?

Most jurisdictions enforce a 5-minute or 10-minute minimum on tc for the Rational Method, regardless of what the formula produces. Below ~5 minutes the IDF intensities become extrapolations and overdesign drainage structures.

How is tc different from watershed lag time?

Lag time t_L is the centroid-to-centroid offset between rainfall and runoff hydrographs. NRCS defines tc ≈ 1.67 × t_L for unit-hydrograph methods. Using t_L where the Rational Method calls for tc underestimates intensity and undersizes drainage.

Why is tc raised to fractional powers in these formulas?

Empirical regressions on observed flow data produce non-integer exponents because tc depends on partially turbulent overland flow, Manning roughness, and slope in non-linear ways. The 0.77 exponent on length in Kirpich, for example, reflects the way travel velocity rises sub-linearly with reach length.

Can I add segment travel times to get a composite tc?

Yes — the TR-55 segmented approach computes sheet flow tc, shallow concentrated tc, and channel-flow tc separately and sums them. This is more accurate than a single empirical formula on mixed-cover watersheds, especially in suburban hydrology.

Worked Examples

Urban Storm Sewer Design

What is the Kirpich time of concentration for a 500 ft, 2% sloped urban subcatchment?

A municipal engineer is sizing a storm sewer inlet for a small commercial drainage area. The hydraulically longest flow path is 500 ft from the upstream divide to the inlet, with an average slope of 0.02 ft/ft (2%). What is the Kirpich time of concentration?

  • Knowns: L = 500 ft, S = 0.02 ft/ft
  • tc = 0.0078 × L^0.77 × S^(−0.385)
  • tc = 0.0078 × 500^0.77 × 0.02^(−0.385)
  • tc = 0.0078 × 119.7 × 4.509

tc ≈ 4.2 minutes

Kirpich is empirical and was originally calibrated for small (<200 acre) agricultural watersheds with well-defined channels. For paved urban subcatchments under 1 acre, kinematic-wave or a manual sheet-flow segment is often more appropriate, but Kirpich is widely used in routine storm-sewer design.

Highway Drainage

What is the time of concentration for a 1,500 ft, 5% sloped roadway watershed?

A state DOT culvert is being sized for a hilly mountain road. The drainage area's longest overland flow path is 1,500 ft with an average longitudinal slope of 0.05 ft/ft (5%). What is the Kirpich time of concentration used in the rational-method peak-flow estimate?

  • Knowns: L = 1,500 ft, S = 0.05 ft/ft
  • tc = 0.0078 × L^0.77 × S^(−0.385)
  • tc = 0.0078 × 1500^0.77 × 0.05^(−0.385)
  • tc = 0.0078 × 279.0 × 3.169

tc ≈ 6.9 minutes

Steeper slopes shorten tc and raise design rainfall intensity used in the rational method (Q = C × i × A), pushing culvert sizes upward — a key sensitivity in mountainous DOT projects.

Rural Watershed — Culvert Sizing

What is the time of concentration for a 3,000 ft, 1.5% sloped rural watershed?

A county-road bridge replacement is being sized for a rural watershed with a 3,000 ft hydraulic length and an average slope of 0.015 ft/ft (1.5% — typical for piedmont terrain). What is the Kirpich time of concentration used for the design-storm calculation?

  • Knowns: L = 3,000 ft, S = 0.015 ft/ft
  • tc = 0.0078 × L^0.77 × S^(−0.385)
  • tc = 0.0078 × 3000^0.77 × 0.015^(−0.385)
  • tc = 0.0078 × 475.5 × 5.039

tc ≈ 18.7 minutes

For watersheds larger than a few hundred acres or with significant overland-flow segments, NRCS lag-time or the SCS segmental method usually produces a more defensible tc; Kirpich is a quick rural screening estimate.

Time of Concentration Formulas

Six empirical equations are widely used in stormwater hydrology, each calibrated for a different flow regime — small rural channels, sheet flow, kinematic-wave overland flow, SCS curve-number basins, or channel-dominated catchments.

tc = 0.0078 × L^0.77 × S^(−0.385)Kirpich — small rural watersheds (tc in min, L in ft)
tc = [41 × L^(1/3) / i^(2/3)] × [(0.0007 × i + c_r) / S^(1/3)]Izzard — overland sheet flow with rainfall intensity
tc = 0.83 × (L × n × S^(−0.5))^0.467Kerby — overland sheet flow on short, mild slopes
tc = 0.93 × L^0.6 × N^0.6 / (i^0.4 × S^0.3)Kinematic wave — overland flow with Manning n
tc = 1.67 × t_L,   t_L = L^0.8 × (S + 1)^0.7 / (1900 × w_s^0.5)NRCS / TR-55 watershed lag (t_L and tc in hours)
tc = 21.3 × L / (A^0.1 × S^0.2)Bransby Williams — channel-dominated watersheds

Where:

  • tc — time of concentration (minutes in most formulas; hours for NRCS)
  • L — hydraulically longest flow path (feet for Kirpich, Izzard, Kerby, Kinematic; feet for NRCS; miles for Bransby Williams)
  • S — average slope along the flow path (decimal; inches of potential retention for NRCS)
  • i — rainfall intensity in inches per hour
  • c_r — Izzard surface retardance coefficient (dimensionless)
  • n, N — Manning roughness coefficient for overland flow
  • t_L — watershed lag time (NRCS, in hours)
  • w_s — average watershed slope as a percent (e.g., 2% enters as 2)
  • A — drainage area in square miles (Bransby Williams)

Each formula was calibrated against a different dataset of measured watersheds, which is why selecting the right one matters more than fine-tuning a single equation. Kirpich tends to under-predict tc for urban subcatchments because it ignores the overland-flow segment; TR-55 segmented travel time (sheet + shallow concentrated + channel) is preferred for mixed-cover, suburban watersheds.

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