What's time of concentration used for?

T_c is the watershed hydrologic time step — the time required for runoff from the most distant point to reach the outlet. It selects rainfall intensity from IDF curves for the Rational Method, and sets time-to-peak for unit hydrograph methods.

Should I use Kirpich or NRCS lag?

NRCS lag (TR-55) is better for typical urban/suburban watersheds because it accounts for impervious cover via the curve number. Kirpich is best for small (<200 acre), steep, agricultural watersheds — its calibration data.

Is there a minimum T_c?

Most regulators impose a 5–10 minute minimum regardless of computed value. Even on a small lot, depression storage and surface roughness add a few minutes of lag. A computed 2-minute T_c isn't physically realistic.

What is the relationship between T_c and lag time T_L?

T_L = 0.6 × T_c (NRCS convention). Lag time is the delay between rainfall centroid and peak runoff. Time of concentration is the longer travel time from the most distant point. NRCS lag formula computes T_L directly; multiply by 1.67 to get T_c.

What is the SCS sheet/shallow/channel method?

The most rigorous T_c method splits the longest flow path into three regimes: sheet flow (≤ 100 ft, computed with TR-55 sheet flow equation), shallow concentrated flow (paved or unpaved, V from chart), and channel flow (Manning equation). T_c = sum of segment travel times.

What is the Kirpich formula?

Kirpich (1940): T_c = 0.0078·L^0.77·S^(-0.385), with T_c in minutes, L in feet, S as decimal slope. Originally calibrated on 7 small (<200 ac) Tennessee agricultural watersheds. Underestimates T_c for impervious or very flat ground.

How do I use Manning's kinematic wave for sheet flow?

TR-55 sheet flow: T_t = 0.007·(n·L)^0.8 / (P₂^0.5·S^0.4), where n is sheet-flow Manning's roughness (smooth surface 0.011, dense grass 0.24), L ≤ 100 ft, P₂ = 2-yr 24-hr rainfall (in), S = slope. Limited to first 100 ft of overland flow.

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Time of Concentration Calculator

Time required for runoff to travel from the hydraulically most distant point in a watershed to the outlet. Two of the most-cited methods, Kirpich (1940) and NRCS lag (TR-55), computed side by side so you can compare.

Units

Length of longest flow path, Lft

Average slope along path, Sm/m or ft/ft (dimensionless)

NRCS curve number, CN (NRCS only)—

Kirpich t_c—min

NRCS lag t_L—hr

NRCS t_c (= 1.67 t_L)—min

Defaults: 1500 ft hydraulic length, 2.5% slope, CN = 75 (suburban residential, average soils). Both methods are empirical US-customary (Kirpich 1940, NRCS TR-55); SI input is converted to feet internally.

Kirpich (US units, t_c in minutes):

$$ t_c = 0.0078 \, L^{0.77} \, S^{-0.385} $$

NRCS lag (TR-55, US units, t_L in hours):

$$ t_L = \frac{L^{0.8} \, (S' + 1)^{0.7}}{1900 \, Y^{0.5}} $$

where S' = 1000/CN − 10 (in inches), Y = average watershed slope as a percent.

t_c time of concentration · t_L watershed lag time (≈ 0.6 × t_c) · L hydraulic length of longest flow path · S slope along that path · CN NRCS curve number for the watershed.

Method comparison — when to use each

Time-of-concentration methods compared
Method	Best for	Inputs	Limits
Kirpich (1940)	Small steep agricultural	L, S	≤ 200 ac; not for flat or urban
NRCS lag (TR-55)	Urban / suburban	L, S, CN, Y	≤ 2000 ac; needs CN
SCS segmental (sheet/shallow/channel)	Mixed flow regimes (regulator preference)	L, S, n, P₂, channel geometry	Most rigorous; required by many state DOTs
FAA (1970)	Airport drainage, paved surfaces	L, S, C	Paved; uses Rational C
Velocity method (Manning)	Open-channel-only basins	L, S, n, R	Channel flow only
Bransby-Williams	British/AU, large watersheds	L, S, A	Less common in US

Sheet flow Manning's roughness coefficients (TR-55 Table 3-1)

For the segmental method's sheet-flow segment (max 100 ft per TR-55), use these surface-specific n-values (different from open-channel n!):

Manning's n for shallow sheet flow (TR-55 Table 3-1)
Surface description	Sheet-flow n
Smooth surfaces (concrete, asphalt, gravel, bare soil)	0.011
Fallow (no residue)	0.05
Cultivated soils, residue cover ≤ 20%	0.06
Cultivated soils, residue cover > 20%	0.17
Grass, short prairie	0.15
Grass, dense (typical lawn)	0.24
Grass, Bermuda	0.41
Range (natural)	0.13
Woods, light underbrush	0.40
Woods, dense underbrush	0.80

Shallow concentrated flow velocity (TR-55 Fig 3-1)

Velocity (ft/s) for shallow concentrated flow as function of slope
Slope (ft/ft)	V — paved (ft/s)	V — unpaved (ft/s)
0.005	1.4	1.1
0.010	2.0	1.6
0.020	2.9	2.3
0.040	4.1	3.2
0.060	5.0	3.9
0.080	5.8	4.5
0.100	6.4	5.0
0.150	7.9	6.2
0.200	9.1	7.1

Travel time T_t (sec) = L (ft) / V (ft/s). For mixed shallow flow, sum subsegments.

Worked examples

Example 1 — Small suburban watershed, two-method comparison

Given: L = 1500 ft, S = 0.025 (= 2.5%), CN = 75 (suburban residential).

Find: T_c by Kirpich and NRCS lag.

Kirpich: T_c = 0.0078·(1500)^0.77·(0.025)^−0.385 = 0.0078·343·3.51 = 9.4 min

NRCS lag: S′ = 1000/75 − 10 = 3.33 in; Y = 2.5%

T_L = (1500)^0.8·(3.33+1)^0.7 / (1900·√2.5) = 343·2.81 / 3004 = 0.321 hr

T_c = 1.67·0.321·60 = 32.2 min

Kirpich → 9.4 min · NRCS → 32 min. NRCS appropriate for suburban; Kirpich underpredicts.

Example 2 — Segmental method (sheet/shallow/channel)

Given: Suburban site. Sheet flow: L₁ = 100 ft on dense grass (n = 0.24), S₁ = 0.02, P₂ = 3.0 in. Shallow: L₂ = 400 ft, paved, S₂ = 0.015. Channel: L₃ = 1000 ft, V₃ from Manning = 4.5 ft/s.

Find: Total T_c.

Sheet: T₁ = 0.007·(0.24·100)^0.8 / (3.0^0.5·0.02^0.4) = 0.007·12.55/(1.732·0.208) = 0.244 hr = 14.6 min

Shallow: at S = 0.015 paved, V ≈ 2.5 ft/s; T₂ = 400/2.5/60 = 2.7 min

Channel: T₃ = 1000/4.5/60 = 3.7 min

T_c = 14.6 + 2.7 + 3.7 = 21.0 min

Why t_c matters

In the Rational Method (Q = CIA), t_c selects the rainfall intensity I to use. Shorter t_c → higher I → higher peak flow Q. Underestimating t_c oversizes pipes, culverts, and BMPs (conservative but expensive). Overestimating misses the peak and undersizes hydraulic infrastructure.

In NRCS hydrograph methods, t_c determines the time-to-peak and the unit hydrograph shape. Both peak flow and the volume of the rising limb are sensitive to t_c.

Practical minimums

Most stormwater regulatory agencies impose a 5- or 10-minute minimum t_c regardless of computed value. Even on a tiny lot, depression storage and surface roughness add at least a few minutes of lag, so a computed 2-minute t_c is not physically realistic.

Slope sensitivity

Both formulas have t_c ∝ S^-0.4 roughly. Doubling slope shortens t_c by ~25%. Halving slope adds ~33%. For very flat basins (S < 0.005 ft/ft), neither formula is reliable; use the segmental method.

Reference: USDA NRCS (1986). Urban Hydrology for Small Watersheds (TR-55). Original: Kirpich, Z.P. (1940). "Time of concentration of small agricultural watersheds." Civil Engineering, 10(6), 362.