Culvert Flow Calculator
Calculate the full-flow discharge capacity of a circular culvert using Manning's equation. Used by drainage engineers to check whether an existing or proposed culvert can pass a design flood without overtopping.
Last updated: September 2026
Formula below · 2 sources (asce.org, Wikipedia) · Updated Sep 2026
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About this calculator
Manning's equation for open-channel or pipe flow is Q = (1.486/n) × A × R^(2/3) × S^(1/2), where Q is discharge (ft³/s), n is Manning's roughness coefficient, A is the cross-sectional flow area (ft²), R is the hydraulic radius (ft) equal to A divided by wetted perimeter P, and S is the slope (ft/ft). For a circular culvert of diameter D (inches) flowing full, A = π(D/24)² and P = π(D/12), giving R = D/48. For partial depth the full-flow result is multiplied by 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: 0.50 at half full, 0.91 at 75% full and 1.0 full. Manning's n for concrete culverts is typically 0.012–0.015 and for corrugated metal 0.022–0.027. Slope S is entered as a percentage and converted to ft/ft by dividing by 100.
How to use
Example: diameter D = 36 inches, slope S = 0.5% = 0.005 ft/ft, Manning's n = 0.013, flow depth ratio = 1.0 (full flow). Step 1 — A = π × (36/24)² = π × 2.25 = 7.069 ft². Step 2 — wetted perimeter P = π × (36/12) = π × 3 = 9.425 ft. Step 3 — R = A/P = 7.069 / 9.425 = 0.7499 ft. Step 4 — Q = (1.486 / 0.013) × 7.069 × (0.7499)^(2/3) × (0.005)^0.5 = 114.3 × 7.069 × 0.825 × 0.0707 ≈ 47.2 ft³/s. At full-flow capacity this 36-inch culvert can pass approximately 47 ft³/s (about 1.33 m³/s).
Frequently asked questions
What Manning's roughness coefficient should I use for culvert design?
The choice of Manning's n depends on the culvert material and its condition. Smooth concrete pipe culverts use n = 0.012–0.015. Corrugated steel or aluminium culverts range from n = 0.022–0.027 depending on the corrugation size and shape. HDPE smooth-bore culverts use about n = 0.010–0.012. For design purposes, it is conservative to use the upper end of the range to ensure the culvert is not undersized. State and local highway departments often prescribe specific n values for different culvert types in their drainage design manuals.
How does culvert slope affect the flow capacity and outlet velocity?
Slope drives the gravitational component of flow, so steeper slopes increase both discharge capacity and outlet velocity. Doubling the slope increases full-flow discharge by a factor of √2 ≈ 1.41. However, high outlet velocities can cause scour and erosion at the culvert outlet and in the receiving channel. When outlet velocity exceeds about 3 m/s (10 ft/s) for unprotected channels, energy dissipators, rip-rap aprons, or stilling basins are typically required. Very mild slopes risk sediment deposition inside the culvert, so a minimum slope of 0.3–0.5% is generally recommended.
When is a culvert flowing full versus partially full, and why does it matter?
A culvert flows partially full (open-channel flow) when the upstream headwater is low relative to the pipe diameter, and full (pressure flow) when the headwater submerges the inlet or tailwater fills the barrel. Manning’s equation applies to the open-channel case; pressure flow needs inlet and outlet loss analysis (FHWA HDS-5). The flow depth ratio here applies the exact circular-pipe geometry, so 75% depth carries about 91% of full-flow capacity and 50% depth carries half.