Calculate full-flow circular culvert capacity from diameter, slope, and Manning roughness, or estimate the pipe diameter required for a target flow.

Barrel bed slope. Treated as the energy slope, which assumes steady uniform flow.

Typical Manning n for a clean barrel in good condition. Pick Custom to enter your own n.

Optional settings

Culvert Capacity Formula

Estimate theoretical full-barrel flow for a circular pipe or rectangular box culvert from size, slope and Manning roughness. For a supplied target flow, you can also estimate the theoretical pipe diameter or box opening. Both assume steady uniform flow. It does not calculate watershed runoff or perform inlet/outlet-control design.

Q = (1/n) × A × R(2/3) × √(S)
A = π×D2/4
R = D / 4
Q = (0.3117/n) × D(8/3) × √(S)
  • Q = culvert flow capacity, in cubic meters per second before conversion to cfs, L/s, and gpm
  • n = the entered Manning roughness coefficient for the actual barrel condition
  • A = full barrel cross-sectional area
  • R = hydraulic radius, equal to area divided by the wetted perimeter
  • S = energy slope as a decimal, such as 0.01 for 1%; it equals pipe-bed slope only for uniform flow
  • D = inside pipe diameter in meters

In full-barrel mode, choose a circular pipe or box culvert, enter its inside size and slope, and pick a barrel material (concrete, n = 0.013, by default) or Custom Manning n. The calculator uses SI internally and reports ft³/s (cfs), m³/s, L/s and US gpm. This is reference conveyance, not maximum actual culvert capacity.

D = (Q×n / (k×√(S)))(3/8), k = π/(4×4(2/3))

Supply a target flow from an appropriate hydrologic analysis. Diameter mode inverts the same full-barrel equation using your slope and n; there are no hidden rainfall, drainage-area or slope defaults. The next entry in an illustrative size list is shown only for comparison; confirm actual inside diameter and availability.

Estimate Box Culvert Size for a Target Flow

Choose Box size for a target flow. Enter the flow from your hydrologic analysis, the barrel slope, and the material or custom Manning roughness. For a fixed inside height, choose Known inside rise and enter that rise to solve for the span. If both dimensions can vary, choose Known span-to-rise ratio and enter inside width divided by inside height. A ratio of 2 gives a box twice as wide as it is tall.

A = b × h P = 2 × (b + h) R = A ÷ P Q = (1/n) × A × R(2/3) × √S

The formula above uses SI units. Enter span b and rise h in meters for hand calculation. The wetted perimeter P and hydraulic radius R are in meters, area A is in square meters, slope S is a decimal, and the resulting flow Q is in m³/s. The calculator converts customary inputs to SI and displays the flow in both m³/s and ft³/s. With a fixed rise, it adjusts the span until the Manning flow matches your target. With a fixed ratio b/h, flow varies with rise to the 8/3 power, so it solves for rise and then multiplies by the ratio to get the span.

This preliminary estimate covers barrel friction for one rectangular barrel flowing full. It uses the bed slope as the friction slope under the uniform-flow assumption. Check inlet and outlet control, headwater, tailwater, debris, erosion, overtopping and project requirements separately. To compare a supplier’s candidate size on the same basis, switch to Flow capacity (full barrel), select the box shape, and enter its actual inside dimensions.

Illustrative Manning Roughness Values

These optional preset values are illustrative starting assumptions from the earlier calculator, not universal material specifications. Roughness depends on profile, condition and installation; verify the n used for the actual barrel. The value remains editable and is shown in results.

Pipe material Manning n Effect on capacity
HDPE smooth / PVC 0.012 Higher flow for the same diameter and slope
Concrete, smooth 0.013 Common design value for smooth culverts
Corrugated HDPE 0.022 Lower capacity due to rougher wall
Corrugated metal pipe 0.024 Lowest listed capacity for the same size and slope

Example Culvert Capacity Calculations

Example 1: Capacity of an 18-inch concrete culvert

Suppose you have an 18-inch smooth concrete culvert at a 1% slope.

  • Diameter: 18 in = 0.457 m
  • Slope: 1% = 0.01
  • Manning n: 0.013
Q = (0.3117/0.013) × 0.457(8/3) × √(0.01)

The flow capacity is about 0.297 m³/s, or about 10.5 cfs.

Example 2: Theoretical diameter for a supplied target flow

For a target flow of 0.150 m³/s, n = 0.013 and an energy slope of 0.01, the inverse full-barrel equation gives an inside diameter of approximately 13.92 inches. The next entry in the example inch list is 15 inches. This is not a recommended design size: inlet/outlet control, headwater, tailwater and other project constraints still require analysis.

Culvert Capacity Calculator FAQ

Does a larger culvert always carry more water?

In this full-barrel Manning model, a larger diameter has more reference conveyance if energy slope and roughness stay the same. Actual culvert flow may be controlled by the inlet or downstream conditions. Diameter has a strong effect because the full-pipe Manning formula uses D raised to the 8/3 power. A small increase in diameter can produce a larger increase in flow capacity.

Why does pipe material change the result?

Pipe material changes the Manning roughness coefficient. A smooth pipe has a lower n value, so it offers less resistance to flow. Corrugated pipe has a higher n value, so the same diameter and slope will carry less water than a smooth pipe.

Are the estimated culvert dimensions final design sizes?

No. The result is a full-barrel uniform-flow estimate with a supplied target flow, not a completed culvert design or a runoff analysis. Actual culvert design may also need to account for inlet control, outlet control, headwater depth, tailwater, debris, erosion, road overtopping, local drainage rules, and the capacity of the upstream and downstream ditch or channel.