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.
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. A flow depth ratio adjusts capacity for partially full conditions — when the ratio equals 1, the culvert is analysed at full-flow capacity. 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 depth is low relative to the pipe diameter. It flows full (pressure flow) when the headwater submerges the inlet or the barrel runs full due to a tailwater condition. Capacity and velocity calculations differ between the two regimes — Manning's equation applies to open-channel flow, while pressure-flow culverts require additional inlet and outlet loss analysis. Most culverts are designed to flow partially full at design discharge to avoid surcharging. The flow depth ratio in this calculator lets you scale the Manning's full-flow result to approximate partially full conditions.