Manning Equation Calculator

Inputs

Units SI (m, m³/s) US (ft, ft³/s)

US mode uses k = 1.486.

Solve for Discharge Q Velocity V Slope S Manning n

Choose an output; provide the needed inputs.

Channel shape Rectangular Trapezoidal Triangular Circular (partial/full)

Area and perimeter are computed from the shape.

Manning n

Typical: concrete 0.012–0.017, earth 0.02–0.035.

Slope S (m/m or ft/ft)

Bed slope; for mild slopes use small values.

Discharge Q (only for solving S or n)

Provide Q when solving for S or n.

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Geometry

Only the selected shape inputs are used.

Rectangular width b

Rectangular depth y

Trapezoid bottom width b

Trapezoid depth y

Side slope z (H:V)

Triangular depth y

Side slope z (H:V)

Diameter D

Flow depth y

Clamped between 0 and D.

Calculate Reset

Formula used

Manning’s equation estimates steady, uniform open-channel flow: Q = (k/n) · A · R^2/3 · S^1/2. Here, Q is discharge, A is flow area, R = A/P is hydraulic radius, P is wetted perimeter, S is energy slope, and n is roughness. Use k = 1.0 in SI or k = 1.486 in US units.

Velocity follows V = Q/A and also V = (k/n) · R^2/3 · S^1/2.

How to use this calculator

1. Select SI or US units for your project.
2. Choose the channel shape that matches your cross-section.
3. Enter geometry values to compute area and wetted perimeter.
4. Pick what you want to solve for: Q, V, S, or n.
5. Provide the required inputs for your chosen solve target.
6. Press Calculate to view results above the form.
7. Download CSV or PDF for documentation and sharing.

Example data table

Professional article

1) Where Manning’s equation fits in practice

Manning’s equation is a core method for estimating steady, uniform flow in open channels and partially full conduits. It is frequently used for preliminary sizing, capacity checks, and quick comparisons between alternative cross-sections when site data is limited.

2) Key variables and typical ranges

The main inputs are roughness n, slope S, flow area A, and hydraulic radius R. Typical n values are about 0.012–0.017 for finished concrete, 0.020–0.035 for earth channels, and 0.035–0.060 for dense vegetation. Practical slopes for drainage channels often range from 0.0002 to 0.01, depending on terrain and lining.

3) Geometry drives capacity

Discharge scales linearly with area, but only with R^2/3 for boundary effects. For the same area, sections that reduce wetted perimeter usually increase R and deliver higher capacity. This is why shape selection matters alongside width and depth.

4) Sensitivity to roughness and slope

Because Q ∝ 1/n, a 10% increase in roughness reduces discharge by roughly 9–10% if other terms stay fixed. Since Q ∝ √S, doubling slope increases discharge by about 41%. These relationships support quick “what-if” checks during design.

5) Interpreting the energy slope

In uniform flow, the energy slope is commonly approximated by bed slope. In backwater zones, near controls, or rapidly varied conditions, the energy slope may differ; use gradually varied flow calculations when water surface profiles are important.

6) Partially full circular sections

For pipes or culverts flowing partially full, area and wetted perimeter come from the circular segment defined by depth. The calculator computes the central angle and wetted arc length, enabling realistic capacity estimates below full depth without assuming a full-pipe condition.

7) Unit handling and the constant k

In SI mode, k = 1.0 with lengths in meters and discharge in cubic meters per second. Many US references use k = 1.486 with feet and cubic feet per second. Keeping a consistent unit system prevents hidden scaling errors.

8) Reporting, verification, and quality checks

Good documentation records geometry, n, S, computed A, R, and the final Q and V. Verify that flow depth is realistic, the slope is positive, and results align with field observations or prior designs before finalizing decisions.

FAQs

1) When should I use Manning’s equation?

Use it for steady, uniform open-channel flow and partially full conduits. It works best for quick capacity checks when geometry, slope, and roughness are known and flow is not rapidly varied.

2) What does hydraulic radius represent?

It is R = A/P. A larger hydraulic radius generally means less friction per unit area, increasing predicted velocity and discharge for the same slope and roughness.

3) Is slope the same as channel bed slope?

Often yes in uniform reaches. Near controls, backwater zones, or transitions, the energy slope can differ from bed slope. Use profile calculations when those effects matter.

4) How do I choose Manning n?

Start with published ranges for your lining, then adjust for vegetation, irregularity, bends, and joints. When uncertain, run a sensitivity range and document the selected value.

5) Why can similar areas yield different discharge?

Wetted perimeter changes R. For similar area, higher R increases R^2/3, raising velocity and discharge at the same n and S.

6) Can I use this for fully pressurized pipes?

Not usually. It is intended for open-channel or partially full flow. For fully pressurized pipes, use Darcy–Weisbach or another pressurized-flow method in your standard.

7) What should I export for my report?

Use CSV for spreadsheets and parametric checks. Use PDF for a quick summary attachment. Include geometry, n, S, and final Q and V for traceability.

Accurate flow estimates start with careful channel measurements daily.