What is the culvert entrance loss coefficient Ke?

Ke is a dimensionless coefficient that gives the head lost at a culvert inlet under outlet-control flow: h_e = Ke·V²/(2g), where V is the barrel velocity. It depends on the inlet geometry — projecting, headwall, mitered, beveled, or tapered — and on the barrel material.

What is a typical Ke value?

Common values: square-edge inlet with headwall Ke = 0.5; groove/socket end of concrete pipe Ke = 0.2; projecting corrugated metal pipe Ke = 0.9; mitered to slope Ke = 0.7; beveled edges Ke = 0.2. Lower Ke means a more efficient, hydraulically smooth entrance.

When does Ke matter — inlet control or outlet control?

Ke is used in outlet-control headwater calculations, where the entrance loss is one term in the total head: HW = TW + (1 + Ke + 29n²L/R^1.33)·V²/2g − L·So. In inlet control the inlet geometry is captured instead by the inlet-control nomograph or polynomial coefficients, not Ke.

How do I reduce culvert headwater with the inlet?

Improve the inlet: replacing a square edge (Ke 0.5) with a beveled or groove end (Ke 0.2) cuts the entrance loss by ~60%. Side- or slope-tapered inlets reduce required headwater further and can avoid upsizing the barrel in inlet-controlled crossings.

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Culvert Entrance Loss Coefficients (K_e) — HDS-5

By Michael Flynn, PE · water resources & dam safety engineer · Last updated Oct 18, 2026

Entrance loss under outlet control: h_e = K_e·V²/(2g), with V the barrel velocity. K_e depends on inlet geometry and barrel material. Values are from FHWA HDS-5, Table 12 (Hydraulic Design of Highway Culverts).

Concrete Pipe

Inlet configuration	K_e
Projecting from fill, socket (groove) end	0.2
Projecting from fill, square-cut end	0.5
Headwall / headwall & wingwalls, socket end	0.2
Headwall / headwall & wingwalls, square edge	0.5
Headwall, rounded edge (radius ≈ 1/12 D)	0.2
Beveled edges (33.7° or 45° bevels)	0.2
Side- or slope-tapered inlet	0.2

In a SWMM model K_e is the culvert conduit’s entry loss. AquaSWMM sets it for every crossing in one table and runs the model on EPA’s own engine.

Corrugated Metal Pipe (CMP)

Inlet configuration	K_e
Projecting from fill (no headwall)	0.9
Mitered to conform to fill slope	0.7
Headwall or headwall & wingwalls, square edge	0.5
End section conforming to fill slope	0.5
Beveled edges (33.7° or 45° bevels)	0.25
Side- or slope-tapered inlet	0.2

Box Culvert (Reinforced Concrete)

Inlet configuration	K_e
Wingwalls 30°–75° to barrel, square edge at crown	0.4
Wingwalls 30°–75°, crown edge rounded (r ≈ 1/12 D)	0.2
Wingwalls 90° & 15° to barrel, square edge	0.5
Wingwalls parallel (extension of sides), square edge	0.7
Beveled edges on 3 sides	0.2

Outlet-control headwater.

HW = TW + H − L·S_o, H = (1 + K_e + 29n²L/R^1.33)·V²/(2g)

where H is total head loss (entrance + friction + exit), TW is tailwater depth, L barrel length, S_o barrel slope, R hydraulic radius. The "1" is the exit (velocity-head) loss. Design HW is the larger of the inlet-control and outlet-control results.

Source: FHWA, Hydraulic Design of Highway Culverts (HDS-5, Publication FHWA-HIF-12-026), Table 12. Inlet-control headwater uses the nomographs or the K, M, c, Y coefficients of HDS-5 Table 9 / Appendix A, not K_e.

Sizing a crossing? Open the culvert calculator → · Need the design flow first? NRCS runoff or Rational Method. · Want the whole set? Print all 38 cards →

Worked example: outlet-control headwater

48-in RCP, L = 100 ft, n = 0.012, S_o = 1%, Q = 100 cfs, tailwater 3.0 ft

Given A = 12.57 ft², R = D/4 = 1.0 ft, square-edge headwall (K_e = 0.5)

Find outlet-control headwater, and the effect of a groove-end inlet

V = 100/12.57 = 7.96 ft/s; V²/2g = 0.983 ft

Friction term: 29n²L/R^1.33 = 29 × 0.012² × 100 / 1.0 = 0.418

H = (1 + 0.5 + 0.418) × 0.983 = 1.89 ft

Tailwater (3.0 ft) is below the crown, so HDS-5 uses h_o = max(TW, (d_c + D)/2). Critical depth d_c = 3.03 ft, so h_o = (3.03 + 4.0)/2 = 3.51 ft

HW = h_o + H − L·S_o = 3.51 + 1.89 − 1.00 = 4.40 ft

With a groove-end headwall (K_e = 0.2): H = 1.59 ft, HW = 4.11 ft, about 0.3 ft lower

Compare this result against inlet control using the HDS-5 inlet coefficients. The design headwater is the larger of the two. A better entrance only helps when outlet control governs. When inlet control governs, a lower K_e changes nothing, and improving the inlet geometry itself, for example with a bevel or a tapered inlet, is the lever.

Common mistakes

Using tailwater as h_o when tailwater is below the crown. In this example that gives HW = 3.89 ft instead of 4.40 ft, an unconservative half-foot error.
Applying K_e to inlet control. K_e belongs only to the outlet-control energy equation. Inlet control uses the K, M, c and Y coefficients.
Taking the CMP value for a concrete pipe with a mitered end, or the reverse. The same geometry gives different K_e by material. A projecting CMP (0.9) loses nearly twice as much as a square-edge headwall (0.5).
Using the full-barrel equation when the barrel flows partly full. The H equation assumes a full barrel. For partly full outlet control, HDS-5 uses a backwater calculation through the barrel.

When this card doesn’t apply

The table is for the standard inlet types in HDS-5 Table 12. Debris-prone sites, culverts with fish-passage baffles, multi-barrel crossings with unequal inverts and culverts under a roadway that overtops all need more than one K_e. Where roadway overtopping or embankment safety is at stake, as at culverts through dam embankments, run the full HDS-5 procedure or HY-8 across the range of flows.

Related cheat sheets and tools

Pair K_e with the inlet-control constants K, M, c, Y, the culvert hydraulics tool and a barrel Manning's n. Get the design discharge from NRCS runoff or the Rational Method, and see the full inlet-vs-outlet worked example. For routing a crossing within a whole watershed model, see HydroComplete.