Culvert Headwater & Control Calculator

Enter the culvert geometry, flow, and water-surface information to estimate upstream headwater depth and determine whether inlet or outlet control governs.

Geometry & Flow

This treats the box width and height equally.

Slope is positive when the outlet is lower than the inlet. Choose % or ft/ft.

Elevation drop over barrel = –

Hydraulics

Adjust Ke if you have a more specific value.

Using default weir/orifice coefficients for a square edge entrance.

Water Surface Data

Outlet invert (calculated) z₂ = –
Tailwater elevation: –

Enter the ratio your policy allows (example: 1.5 = “HW ≤ 1.5D”, 1.0 = “keep water below the crown”). The calculator will flag the result if the computed HW ÷ rise exceeds this limit.

Enter the allowable depth above the culvert crown (Example 19.12 uses 5 ft). This drives the sizing solver and the manual head-based iteration below.

Enter data and click “Compute Headwater” to view results.

Need a size? Enter HWallow and click “Solve culvert size” to get a suggested diameter/height.

How the calculator works

Inlet-control equations

Hw = [Q / (Cw · L)]2/3

Free-surface (weir) mode where L = span width. Depth is capped at the culvert rise to avoid unrealistic weir depths.

Ho = Q2 / [2g (Cd · A)2] + rise/2

Submerged (orifice) mode measured to the water surface at the inlet. The calculator takes the larger of Hw or Ho.

Remember: H is always the depth above the local invert (H = h1 − z1), so plug in the water-surface elevation h and subtract the invert elevation z.

Outlet-control energy balance

HWout = Δz + TW + he + hf + V2/(2g)

Δz is z₂ − z₁ (negative when the outlet is lower). TW is tailwater depth above the outlet invert.

he = Ke · V2/(2g)

hf = [((Q · n)/(1.486 · A · R2/3))2] · L

Those terms cover entrance, friction, and barrel velocity losses that must be overcome upstream.

Full-barrel capacity reference

Qfull = (1.486 / n) · A · R2/3 · S1/2

Shown in the results as the "capacity" line to show whether the flowing-full barrel can pass the design discharge at the supplied slope.

  • A = area of the chosen culvert shape (ft²)
  • R = A / wetted perimeter
  • S = barrel slope in ft/ft

USGS culvert flow types (WSP 233)

The six regimes describe how the inlet, tailwater, and barrel interact. Use them to sanity-check whether you expect inlet or outlet control.

Type Description Primary control
1 Inlet and outlet both unsubmerged with tailwater below the outlet invert (free outfall). Entrance/weir control.
2 Inlet unsubmerged but tailwater rises against the outlet (partial submergence or hydraulic jump). Still inlet driven but tailwater influences.
3 Inlet submerges while the outlet discharges freely (drawdown at exit). Entrance/orifice control.
4 Both inlet and tailwater partly submerged (tailwater between invert and crown). Mixed—entrance plus backwater.
5 Inlet and outlet submerged with tailwater over the crown but barrel not yet pressurized. Outlet + system losses.
6 Pressurized flow with the barrel flowing full from inlet to outlet. Outlet/total head.

Handbook logic checklist

  1. Assume a trial size. Start with the smallest span/rise that is practical in your context (the CERMs begins at 1.0 ft). Enter that trial dimension under Geometry & Flow.
  2. Calculate the head H. The total head is H = h1 − h3 plus the barrel slope term S·L. In this tool, supplying headwater, tailwater, length, and slope automatically computes H.
  3. Check the entrance mode. The calculator uses Eq. 19.106/19.100 variations to compute the weir/orifice depth and determine whether the trial is in entrance (case 5) or outlet (case 6/pressurized) control.
  4. Compute the barrel velocity. Manning’s equation (Eq. 19.100) is used with hf + keV²/2g to combine velocity head and friction loss. The reported velocity and hydraulic radius match the handbook quantities.
  5. Find discharge for the trial. Use Q = v·A. In the UI the “Flow Q” line shows the design discharge and the “Capacity check” line compares it to the calculated full-flow capacity; when the capacity is less than the design Q, increase the trial size.
  6. Repeat until adequate. Use “Solve culvert size” (which walks up in 0.5-ft increments per the CERMs iteration) or manually change the span/rise and recompute. Stop as soon as the calculated flow meets or exceeds the design Q and the HW/Rise and overtopping checks pass.

This mirrors Example 19.12 in the Civil Engineering Reference Manual: assume size → compute H → compute velocity/flow → check capacity → adjust size.

Sample problem (CERMs Example 19.12)

Given: square culvert, slope 0.01, length 250 ft, headwater 5 ft above the crown, free outlet, design flow 45 cfs, Manning n = 0.013, square-edge entrance (ke = 0.5). The handbook iterates through trial sizes until the discharge ≥ 45 cfs.

Trial 1 — 1 ft × 1 ft square

  • Area A = 1 ft², total head H = 6 ft
  • Velocity from Eq. 19.100 ≈ 9.9 ft/s (R ≈ 0.5 ft)
  • Q = vA ≈ 12.2 cfs → insufficient

Trial 2 — 2 ft × 2 ft square

  • A = 4 ft², H = 7 ft, R = 0.667 ft
  • Velocity from Manning ≈ 10.24 ft/s
  • Q ≈ 40.9 cfs (still < 45 cfs) → increase opening

Trial 3 — 2.5 ft × 2.5 ft square

  • A = 6.25 ft², H = 7.5 ft, hydraulic radius R = 0.5 ft (full barrel assumption)
  • Velocity: v = H / \sqrt{[(1+k_e)/(2g)] + [n²L/(2.21R^{4/3})]} ≈ 10.12 ft/s
  • Q = vA ≈ 63 cfs ≥ 45 cfs → acceptable; flow type 5/6
  • Critical depth dc ≈ 1.78 ft, normal depth dn ≈ 1.78 ft (supercritical, entrance assumption consistent)

Enter these trial sizes manually or use the “Solve culvert size” button to mimic the handbook iteration (it searches sizes in 0.5-ft increments). Setting the headwater limit above crown to 5 ft exposes the same V and Q calculations shown above.