Manning’s Equation Calculator

Estimate open-channel flow using Manning’s equation. Solve for flow rate, velocity, or the required slope based on channel geometry and Manning roughness.

Configuration

Choose which quantity you want as the main result. All calculations are based on Manning’s open-channel flow equation.

Channel Properties

Provide the channel geometry and roughness. Use a consistent unit system (all metric or all US customary) for best results.

Results Summary

The main result is shown below, with quick stats for flow rate, velocity, and slope in both metric and US customary units.

Open Channel Flow Guide

Manning’s Equation Calculator: From Slope to Flow in One Place

Learn how to use Manning’s Equation to size ditches, culverts, storm sewers, and channels with confidence. This guide walks through the core variables, common methods, worked examples, and practical checks that pair directly with the Manning’s Equation Calculator above.

10–15 min read Updated 2025

Quick Start: Using the Manning’s Equation Calculator

Manning’s Equation is the workhorse for open channel flow. The calculator above wraps the algebra and unit conversions so you can quickly solve for discharge \(Q\), velocity \(V\), or slope \(S\) with consistent units.

  1. 1 Choose what you want to solve for: discharge \(Q\), mean velocity \(V\), normal depth \(y\), or required slope \(S\), depending on the options provided in the calculator.
  2. 2 Select the channel shape or configuration (e.g., circular pipe, rectangular channel, trapezoidal ditch) if the calculator supports multiple geometries.
  3. 3 Enter the geometry inputs: flow depth, bottom width or diameter, side slopes, and length units (m, ft, mm, in) as required by the selected mode.
  4. 4 Pick an appropriate Manning roughness coefficient \(n\) for the channel material and condition (e.g., finished concrete, grass-lined earth, riprap).
  5. 5 Enter the longitudinal slope \(S\) (channel bed slope or energy grade line, in m/m or ft/ft), or leave it as the unknown if you are solving for required slope.
  6. 6 Check your units (SI or US customary) and run the calculation. Review the main result plus any quick stats such as \(Q\), \(V\), hydraulic radius \(R\), and flow area \(A\).
  7. 7 Use the Calculation Steps section (if enabled) to see the full path from input geometry to area, hydraulic radius, and Manning’s Equation — useful for reports and QA/QC.

Tip: Start with a reasonable guess for \(n\) and slope based on design standards. Once you see velocity from the calculator, adjust to stay within recommended ranges for erosion and sediment control.

Common mistake: Mixing units. If geometry is in mm and slope is in %, convert properly before applying Manning’s Equation. The calculator will help, but your inputs must be consistent.

Choosing Your Method: Design vs. Check vs. Back-Calculation

Manning’s Equation appears simple, but in practice you apply it in different ways depending on whether you are designing a new channel, checking an existing one, or interpreting field data. The calculator can mirror these workflows through different solve-for options and modes.

Method A — Design for Capacity (Solve for Flow \(Q\))

Use this when you know the channel geometry, slope, and material and need to estimate how much flow it can carry at normal depth.

  • Direct link to hydrology results (design discharge vs. capacity).
  • Ideal early in design to size ditches, culverts, and storm sewers.
  • Works well with standard channel templates and typical roughness values.
  • Assumes uniform flow and that normal depth is equal to flow depth.
  • Does not directly flag supercritical vs. subcritical flow without further checks.
Capacity: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \]

Method B — Check Velocity (Solve for \(V\))

Use this when you know the expected discharge and want to verify that channel velocities are within acceptable limits.

  • Direct check against allowable erosion and deposition criteria.
  • Helps tune side slopes, linings, and roughness treatments.
  • Good for retrofit evaluations where geometry is fixed.
  • Requires a known or assumed discharge \(Q\).
  • Still assumes uniform flow; transitions and backwater effects are ignored.
Mean velocity: \[ V = \frac{1}{n} R^{2/3} S^{1/2} \quad ; \quad Q = V A \]

Method C — Back-Calculate Roughness or Slope

Use this in calibration and forensic work when you measure flow and depth in the field and want to estimate \(n\) or check whether the assumed slope is realistic.

  • Supports calibration of models and verification of as-built performance.
  • Helps align textbook \(n\) values with real-world conditions.
  • Highly sensitive to measurement error in depth and discharge.
  • Non-uniform flow, backwater, or local losses can distort the result.
Rearranged for roughness: \[ n = \frac{A R^{2/3} S^{1/2}}{Q} \]

What Moves the Number: Key Drivers in Manning’s Equation

Manning’s Equation is often written as \[ Q = \frac{1}{n} A R^{2/3} S^{1/2}. \] Every term has clear physical meaning and design leverage. Understanding what moves the number helps you use the calculator intelligently rather than blindly.

Roughness coefficient \(n\)

Represents resistance from surface texture, vegetation, joints, and alignment. Lower \(n\) (smooth concrete) means higher flow capacity; higher \(n\) (natural streams with vegetation) reduces capacity and velocity.

Hydraulic radius \(R = A/P\)

The ratio of flow area \(A\) to wetted perimeter \(P\). For a given area, shapes that minimize wetted perimeter (more compact sections) increase \(R\) and therefore increase both velocity and capacity.

Slope \(S\)

Typically the channel bed slope or energy grade line. Steeper slopes increase the available energy, boosting velocity roughly with \(S^{1/2}\). Very mild slopes lead to low velocities and possible sedimentation.

Flow area \(A\)

Directly scales discharge. Larger depth or width increases area, but also changes \(R\) and sometimes roughness (e.g., if water reaches rough side slopes or overbank).

Unit system and consistency

Manning’s Equation is empirical. Whether you use SI (m, m³/s) or US customary (ft, cfs), all inputs must be in a consistent system or your results will be meaningless. The calculator handles conversions but depends on clean input.

Flow regime & depth assumptions

Manning assumes steady, uniform flow at normal depth. If your depth is controlled by backwater, culvert control, or rapidly varied flow, the equation still gives numbers but the physical interpretation can be wrong.

Worked Examples

Example 1 — Trapezoidal Roadside Ditch (Solve for \(Q\) and \(V\))

Design a grass-lined roadside ditch that can carry a design storm flow at normal depth without causing erosion.

  • Shape: Trapezoidal open channel
  • Bottom width \(b\): 1.0 m
  • Side slopes: 3H:1V (i.e., \(z = 3\))
  • Flow depth \(y\): 0.5 m
  • Slope \(S\): 0.005 (0.5% grade)
  • Manning \(n\): 0.035 (dense grass)
1
Compute area \(A\): \[ A = y \left(b + z y\right) = 0.5 \left(1.0 + 3 \times 0.5\right) = 0.5 (1.0 + 1.5) = 1.25\ \text{m}^2 \]
2
Compute wetted perimeter \(P\): \[ P = b + 2 y \sqrt{1 + z^2} = 1.0 + 2 (0.5) \sqrt{1 + 3^2} = 1.0 + 1.0 \sqrt{10} \approx 4.16\ \text{m} \]
3
Hydraulic radius \(R\): \[ R = \frac{A}{P} = \frac{1.25}{4.16} \approx 0.30\ \text{m} \]
4
Apply Manning’s Equation: \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} = \frac{1}{0.035} (1.25) (0.30)^{2/3} (0.005)^{1/2} \] The calculator will evaluate this numerically, giving \(Q\) in m³/s.
5
Mean velocity \(V\): \[ V = \frac{Q}{A} \] Check that \(V\) is within acceptable limits for grass-lined channels (typically ~0.6–2.0 m/s depending on guidance).

Example 2 — Full Circular Storm Sewer (Solve for Required Slope)

Suppose you have a proposed storm sewer that must convey a design flow and you want to determine the minimum slope using Manning’s Equation.

  • Shape: Circular pipe, flowing full
  • Diameter \(D\): 900 mm (0.9 m)
  • Design discharge \(Q\): 0.7 m³/s
  • Material: Reinforced concrete pipe
  • Manning \(n\): 0.013
  • Unknown: Required slope \(S\)
1
Geometry at full flow: \[ A = \frac{\pi D^2}{4} = \frac{\pi (0.9)^2}{4} \approx 0.636\ \text{m}^2 \] \[ P = \pi D = \pi (0.9) \approx 2.83\ \text{m} \] \[ R = \frac{A}{P} \approx \frac{0.636}{2.83} \approx 0.225\ \text{m} \]
2
Rearrange Manning’s Equation for \(S\): \[ Q = \frac{1}{n} A R^{2/3} S^{1/2} \Rightarrow S = \left(\frac{Q n}{A R^{2/3}}\right)^2 \]
3
Substitute values: \[ S = \left( \frac{0.7 \times 0.013}{0.636 \times 0.225^{2/3}} \right)^2 \] The calculator handles the exponent and squaring to deliver the required slope (m/m).
4
Convert to % or ‰ if needed: \[ S_{\%} = 100 \times S, \quad S_{\text{‰}} = 1000 \times S. \] Compare the result with constructability limits and minimum self-cleansing velocity requirements.

Common Layouts & Variations

Manning’s Equation is used across many channel types. Geometry, lining, and flow condition all affect which simplifications you can safely make.

ConfigurationTypical UseNotes for Manning’s Equation
Rectangular channelLab flumes, some canals, channels cast against retaining walls Easy geometry; \(A = b y\), \(P = b + 2y\). Works well in uniform sections with consistent lining and slope.
Trapezoidal ditchRoadside ditches, drainage swales Use \(A = y (b + z y)\) and \(P = b + 2 y \sqrt{1 + z^2}\). Side slopes and vegetation drive \(n\) and flooding behavior.
Circular pipe (full)Storm sewers, culverts, sanitary sewers Use full-flow formulas for \(A\) and \(P\). Only valid when flowing essentially full; otherwise use partial-flow relationships or reference charts.
Partially full circular pipeStorm sewers under variable depth \(A\) and \(P\) depend on depth ratio. Many calculators or tables use dimensionless curves; Manning still applies but with more geometry work.
Natural channelStreams, rivers, grass or rock-lined channels \(n\) is uncertain and may vary with stage. Use ranges and calibrate to gauged data when possible; account for meanders and vegetation.
Composite sectionFloodplains with main channel + overbank Often analyzed with subsections: compute \(Q\) for each subsection (with its own \(n\)) and sum. The calculator may provide a single equivalent \(n\) for simplified checks.
  • Confirm that the section you model matches the actual field geometry.
  • Check that linings, joints, and fittings match the chosen roughness value.
  • Compare calculated velocities with allowable ranges from design manuals.
  • Consider backwater and control structures; Manning assumes uniform flow.
  • Use conservative \(n\) values when there is high uncertainty or risk.
  • Document assumptions (shape, \(n\), slope) for future reviewers.

Specs, Logistics & Sanity Checks

Manning’s Equation is just one piece of a complete design. The calculator gives you fast hydraulic numbers; you still need to ensure they make sense for constructability, maintenance, and safety.

Design Specs & Criteria

  • Check minimum and maximum velocities from relevant codes or design manuals.
  • Verify freeboard and maximum depth against roadway, embankment, or bank elevations.
  • Use appropriate return periods for storm design (e.g., 10-year roadside ditch vs. 100-year culvert).
  • Consider erosion control measures if velocities are high (linings, riprap, vegetation).

Field & Construction Realities

  • Actual slopes may vary from plan due to construction tolerances.
  • Long-term sediment deposition can reduce effective area and change roughness.
  • Vegetation growth, debris, and trash racks increase effective resistance.
  • Thermal or settlement cracking in lining can change friction over time.

Sanity Checks with the Calculator

  • Run a low \(n\) case (smooth) and a high \(n\) case (rough) to bracket behavior.
  • Slightly vary slope and depth to see how sensitive \(Q\) and \(V\) are.
  • Compare Manning-based results with other methods or historic data where available.
  • Use the steps output to confirm geometry, \(R\), and unit conversions are as expected.

A good Manning’s Equation Calculator makes these checks quick, so you can iterate on geometry and materials instead of fighting with algebra and units.

Frequently Asked Questions

What is Manning’s Equation and when should I use it?
Manning’s Equation is an empirical formula for steady, uniform flow in open channels and non-pressurized conduits. It relates discharge \(Q\) to cross-sectional area \(A\), hydraulic radius \(R\), channel slope \(S\), and roughness coefficient \(n\). Use it for ditches, canals, storm sewers flowing partly full, and natural channels where energy slope and bed slope are similar.
Can I use Manning’s Equation for pressurized pipes?
Manning’s Equation is not intended for fully pressurized pipe flow with significant pressure gradients or pump-driven systems. It can be used when a circular pipe flows by gravity and behaves like an open channel (partially full or just full) with slope-driven flow. For general pressurized pipe networks, use energy equations with head losses (Darcy–Weisbach or Hazen–Williams) instead.
Which units does the Manning’s Equation Calculator use?
The calculator typically supports both SI and US customary units. You might enter geometry in meters and discharge in m³/s, or in feet and cfs. Internally, the tool converts everything to a consistent system before applying Manning’s Equation, but you must choose the correct unit options for each input so the conversions are correct.
How do I choose an appropriate Manning roughness \(n\)?
Start from published tables for typical materials (e.g., smooth concrete, corrugated metal, natural streams). Then adjust based on channel condition, vegetation, alignment, and debris. If the project is critical or data is available, calibrate \(n\) by comparing measured flows and water surface profiles against model predictions.
Should I use bed slope or energy slope for \(S\)?
Manning’s Equation technically uses the energy grade line slope. In long, uniform reaches with mild slopes and small losses, it is common practice to approximate this with the bed slope. Where there are significant expansions, contractions, drops, or junctions, energy slope may differ from bed slope and a more detailed hydraulic analysis is warranted.
What are the main limitations of Manning’s Equation?
It assumes steady, uniform flow, prismatic channels, and a constant roughness coefficient. It does not account for rapidly varied flow, hydraulic jumps, strong backwater, or highly non-uniform geometry. In these cases, gradually varied flow profiles or full dynamic models are more appropriate, with Manning’s Equation only supplying local resistance terms.
How can I document results from the Manning’s Equation Calculator?
Most engineers capture the input set (shape, dimensions, \(n\), slope), the calculated \(A\), \(P\), \(R\), and the resulting \(Q\) and \(V\). The step-by-step equations shown in the calculator’s solution section are ideal for copying into design notes or reports, ensuring future reviewers can trace every assumption and numerical step.
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