Culvert Design Calculator
Size a circular or box culvert to pass a design stormwater discharge using Manning's equation. Essential for highway engineers, drainage designers, and land developers ensuring roads stay clear during storm events.
Last updated: September 2026
Formula below · 2 sources (asce.org, Wikipedia) · Updated Sep 2026
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About this calculator
Culvert sizing here uses Manning’s equation, Q = (1/n)·A·R^(2/3)·S^(1/2) in SI units. For a circular pipe flowing full, A = πD²/4 and R = D/4, so Q_full = 0.3117·D^(8/3)·√S / n. At a partial depth y/D the flow is Q = Q_full × (A/A_full) × (R/R_full)^(2/3), with θ = 2·acos(1 − 2·y/D), A/A_full = (θ − sin θ)/(2π) and R/R_full = 1 − sin θ/θ; for example the ratio is 0.50 at half depth and 0.91 at 75% depth. Solving for the diameter gives D = [Q·n / (0.3117·√S·ratio)]^(3/8). For the rectangular option the calculator sizes a square box of side D flowing at depth y·D (A = y·D², wetted perimeter D·(1 + 2y)). The arch option uses the circular relation as an approximation. Q is the design discharge (m³/s), n is Manning’s roughness, S is the slope (m/m). This is a barrel-capacity check only: culverts must also be checked for inlet control and headwater (FHWA HDS-5), which often governs.
How to use
Design a circular concrete culvert (n = 0.012) for Q = 1.5 m³/s, slope S = 0.005 m/m, flow-depth ratio y/D = 0.85. Step 1 — partial-flow ratio at 0.85 depth: θ = 2·acos(1 − 1.7) = 4.692 rad; A/A_full = 0.906 and R/R_full = 1.212, so Q/Q_full = 0.906 × 1.212^(2/3) ≈ 1.03. Step 2 — Q·n = 1.5 × 0.012 = 0.018. Step 3 — 0.3117 × √0.005 × 1.03 = 0.02270. Step 4 — D = (0.018 / 0.02270)^0.375 = 0.793^0.375 ≈ 0.917 m. Select the next standard size, 1.0 m, and check inlet-control headwater. The defaults (5 m³/s, 0.005, n = 0.012, circular, 0.75 depth) give about 1.51 m.
Frequently asked questions
What Manning's roughness coefficient should I use for culvert design?
The correct Manning's n depends on the culvert material and condition. Smooth precast concrete pipe typically uses n = 0.011–0.013; cast-in-place concrete is n = 0.013–0.015; corrugated metal pipe ranges from n = 0.021–0.027 depending on corrugation size; high-density polyethylene (HDPE) smooth-lined pipe is around n = 0.010–0.012. For design purposes, it is prudent to use the higher end of the range to add conservatism, since roughness increases with age, sediment deposition, and joint misalignment.
How do I determine the design discharge for culvert sizing?
Design discharge is usually calculated using the Rational Method (Q = C·i·A) for small catchments or statistical flood-frequency analysis for larger ones. The return period — often 10-year for minor roads, 50-year for major highways, and 100-year for critical infrastructure — is set by the relevant design standard or local authority. Accurate inputs such as catchment area, runoff coefficient, and rainfall intensity from intensity-duration-frequency (IDF) curves are essential. Undersizing a culvert risks road overtopping and structural damage during storms.
What is the difference between inlet control and outlet control in culvert hydraulics?
In inlet control, the culvert capacity is limited by the inlet geometry — the flow contracts at the entrance and the barrel flows only partially full. The headwater depth depends on inlet shape, edge condition, and discharge but not on culvert length or slope. In outlet control, the full barrel length, slope, roughness, and tailwater level all govern capacity, and the barrel typically flows full. Most culvert design procedures check both conditions and use the one that gives the higher required headwater as the governing case, ensuring safe operation under all scenarios.