Kirpich vs NRCS: when time of concentration disagrees by a factor of two

TL;DR. Kirpich (1940) was calibrated on small steep agricultural watersheds in Tennessee — it underpredicts t_c for flat or urban basins. NRCS lag (TR-55) accounts for surface roughness via curve number — better for the typical urban / suburban work most stormwater engineers do. When they disagree by 2×, your watershed is outside Kirpich's calibration range. Use NRCS, or use the segmental sheet/shallow/channel method.

The setup

Time of concentration (t_c) is the time required for runoff to travel from the hydraulically most distant point in a watershed to the outlet. In the Rational Method, t_c selects which rainfall intensity I you read from the IDF curve — shorter t_c means higher I, which means higher peak flow Q. In NRCS hydrograph methods, t_c sets the time-to-peak and the unit hydrograph shape. It's load-bearing input.

The two formulas you'll see most often:

Kirpich (1940), US units, t_c in minutes, L in feet, S as ft/ft:

NRCS lag (TR-55, 1986), US units, t_L in hours, L in feet, S' = 1000/CN − 10 in inches, Y = slope in percent:

Why they disagree

Take a 1500-foot longest flow path with 2.5% slope, suburban residential (CN = 75):

Method	tc (min)	Implied design intensity (in/hr) at 25-yr
Kirpich	9.5	~6.5
NRCS lag	19.7	~5.0

Same watershed. Twice the t_c. The Rational Method peak Q from each: ~6.5/5.0 = 30% higher peak with Kirpich than with NRCS. That gap doesn't shrink for any reasonable basin slope or length — the methods are calibrated against different data sets.

Where each is calibrated

Kirpich

Kirpich (1940) fit his formula to data from six small agricultural watersheds in Tennessee — areas from 1.25 to 112 acres, slopes 3% to 10%, no urbanization. The formula is empirical and assumes:

• Steep terrain (S ≥ 0.005 ft/ft, prefers steeper)
• Bare or sparsely vegetated surface (rural agricultural runoff)
• Little to no impervious cover
• Channel-dominated flow (not sheet flow)

For watersheds matching that description, Kirpich is fine. For everything else — flat coastal plain, grassed urban catchments, suburban subdivisions with curb-and-gutter, parking lots — Kirpich systematically underestimates t_c, which produces overestimates of Q. Some agencies require Kirpich for forested mountain watersheds and forbid it elsewhere.

NRCS lag (TR-55)

NRCS lag is the lag-time formula from TR-55, calibrated against small US watersheds (under 2000 acres) across a wider range of land cover. The curve number term S' = 1000/CN − 10 represents potential maximum retention — high CN (impervious, urban) gives small S', short t_c; low CN (forest, sandy soils) gives large S', long t_c.

NRCS lag is appropriate for the vast majority of stormwater engineering work: urban/suburban subdivisions, mixed-use commercial sites, school campuses, anything with measured curve number. It's the default in HEC-HMS, SWMM, and HydroCAD.

The segmental method

For consequential designs where Tc materially drives the answer, neither single-formula method is enough. Use TR-55's segmental approach: split the longest flow path into three segments — sheet flow (max 100 ft), shallow concentrated, and channel flow. Compute travel time of each segment using its own physics:

• Sheet flow: $t = \frac{0.007 (n L)^{0.8}}{P_2^{0.5} \, S^{0.4}}$ where P₂ is the 2-year, 24-hour rainfall
• Shallow concentrated: empirical velocity vs slope relationships from TR-55 Figure 3-1
• Channel: Manning's equation with surveyed cross-section

Sum the three. Slower to set up, but defensible to a regulator, especially for designs near a code threshold.

Which method does your reviewer want?

State and county manuals vary. Some require NRCS lag for any urbanized basin; some require segmental for anything over 1 acre; a few still permit Kirpich for everything because that's how they did it in 1985. Read the local stormwater manual before you pick a method. If the manual specifies, follow it. If it doesn't:

• Use NRCS lag as your default.
• Use Kirpich only for watersheds that match its calibration: small, steep, mostly rural.
• Use the segmental method when t_c is load-bearing for the design — outlet sizing, FEMA submittal, anywhere a 30% swing in Q changes the answer.

Free Tc calculator that runs Kirpich and NRCS lag side by side: pe-calc.com/tools/time-of-concentration.html

— Michael Flynn, PE
Next issue: why your Manning's n estimate is probably wrong, and a worked example showing how a 15% roughness swing produces a 20%+ swing in computed channel capacity.