Manning's Equation Calculator
Calculate flow capacity in an open channel or ditch using Manning's equation, from channel width, depth, roughness, and slope.
How this calculator works
Manning’s equation is the standard way to estimate how much water an open channel can carry, whether that’s a drainage ditch, a roadside swale, or a culvert flowing partly full. It combines the size and shape of the water in the channel with how rough the channel surface is and how steep it slopes.
Formula: Manning’s equation for a rectangular channel: Q = (1.49/n) × A × R^(2/3) × S^(1/2), where A is channel cross-sectional area (width × depth), R is the hydraulic radius (area ÷ wetted perimeter), n is Manning’s roughness coefficient (about 0.013 for concrete, 0.03 for a natural earth channel), and S is slope as a decimal.
Worked example
A 4 ft wide, 1 ft deep concrete channel, n = 0.013, at 0.5% slope:
- Cross-sectional area: 4 × 1 = 4 sq ft
- Hydraulic radius: ≈ 0.667 ft
- Roughness coefficient: n = 0.013 (concrete)
- Slope: 0.5% (0.005)
- Flow capacity: ≈ 24.74 cfs
Notes
Hydraulic radius — area divided by wetted perimeter, the perimeter actually touching water rather than the open top edge — is what makes wide, shallow channels behave differently than narrow, deep ones even at the same cross-sectional area.
A rougher channel surface, like natural earth compared to smooth concrete, needs a steeper slope or a larger cross-section to carry the same flow, since a higher n value directly reduces capacity in the equation.
How to use
Enter the channel width and depth, pick or enter a roughness coefficient for the channel surface, and enter the slope. The calculator works out the area and hydraulic radius for you and returns the flow capacity in cubic feet per second, useful for sizing ditches, swales, and other open drainage channels.
A planning estimate using standard hydraulics formulas. For code-governed drainage or civil design, confirm with a licensed civil engineer.
Frequently asked questions
What is Manning's equation used for?
Manning's equation estimates how much water an open channel — a ditch, drainage swale, or culvert running partly full — can carry per second. It combines the channel's cross-sectional area, its shape, how rough the channel surface is, and how steep it slopes, into a single flow capacity figure used in drainage and civil design.
What is Manning's roughness coefficient, n?
Manning's n describes how much friction the channel surface adds to flowing water. A smooth surface like concrete has a low n, around 0.013, letting water move with less resistance. A rougher surface like a natural earth channel has a higher n, around 0.03, which slows the water and reduces how much the channel can carry at the same slope and size.
What is hydraulic radius, and why isn't it just the depth?
Hydraulic radius is the cross-sectional area of water divided by the wetted perimeter — the portion of the channel boundary actually in contact with water, not including the open top. It captures how efficiently a channel shape moves water: a wide, shallow channel and a narrow, deep one can have the same area but different hydraulic radii, and therefore different flow capacities.
Does this calculator work for non-rectangular channels?
This calculator is set up for rectangular channels, using width and depth to find area and wetted perimeter directly. Trapezoidal, circular, or irregular channel shapes use the same Manning's equation but require different area and wetted-perimeter formulas, so results for those shapes would need a calculator built for that specific geometry.
Estimates only. Verify quantities with your supplier before purchasing.