Manning’s Equation Calculator (Open Channel Flow)

Open-channel velocity and discharge with Manning’s equation for rectangular, trapezoidal, triangular and part-full circular sections.

Z = 2 means 2H:1V. Each side rises 1 unit per Z units across.
Depth of water at the deepest point. For a full pipe, enter the diameter.
m/m (ft/ft)
Bed (energy) slope as a ratio: 0.5% = 0.005; 1 in 200 = 0.005.
FHWA HDS-4 Table B.2: smooth concrete 0.012, ordinary concrete 0.013, vitrified clay 0.015, earth channel in good condition 0.020, clean natural stream 0.025–0.033, weedy stream 0.050–0.080.
Discharge Q
2.056 m³/s
2.0561 m³/s = 72.610 ft³/s
Mean velocity V
1.371
Flow area A
1.50
Wetted perimeter P
4.2361
Hydraulic radius R = A/P
0.3541
Froude number
0.71
Subcritical (tranquil) flow

Estimate generated with SortedSums: https://sortedsums.com/mannings-equation-calculator/. For informational purposes only; verify before relying on it.

Estimate only. This tool is for informational and educational purposes. Results depend on your inputs and simplifying assumptions, and are not a substitute for professional engineering, design or financial advice. Always verify with a qualified professional and applicable codes before purchasing, building or making decisions.

How it’s calculated

Manning’s equation gives the mean velocity of steady, uniform open-channel flow from the channel’s hydraulic radius (flow area ÷ wetted perimeter), slope and roughness coefficient n. Discharge is velocity × area.

V = (Ku / n) × R^(2/3) × S^(1/2) Ku = 1 (SI), 1.49 (US units) Q = V × A R = A / P Trapezoid: A = By + Zy² P = B + 2y√(1 + Z²) Circle (depth y, diameter D): θ = 2 acos(1 − 2y/D), A = D²(θ − sin θ)/8, P = Dθ/2

Example (FHWA HDS-4, Example 4.1): a trapezoidal earth channel with B = 2 m, side slopes 1V:2H, S = 0.003, depth 0.5 m and n = 0.02. A = 2(0.5) + 2(0.5)² = 1.5 m², P = 2 + 2(0.5)√5 = 4.24 m, R = 0.354 m. V = (1/0.02)(0.354)^(2/3)(0.003)^(1/2) ≈ 1.37 m/s and Q ≈ 2.06 m³/s (HDS-4 rounds R to 0.35 m and reports 1.36 m/s and 2.0 m³/s).

The calculator works in SI internally, so mixed units are converted exactly; the 1.49 factor applies only if you solve the US-unit form by hand. Results assume uniform flow, where the water surface is parallel to the bed.

Frequently asked questions

What Manning’s n should I use?

Use a value for the lining: about 0.013 for concrete pipe or lined channels, 0.020 for a clean earth canal, and 0.03–0.05 or more for natural streams with stones and vegetation. Roughness dominates the answer, so pick conservatively.

Does a circular pipe carry most when it is full?

No. With Manning’s equation a circular pipe peaks at about 94% depth, because the wetted perimeter grows faster than area near the crown. Design usually uses full-flow capacity.

How do I find normal depth for a given flow?

Adjust the depth until the discharge matches your flow (trial and error, as in HDS-4 Example 4.2).

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Sources

Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.

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