Manning Equation Calculator
Flow, normal depth, slope or pipe size for pipes and channels, with Chow’s n values.
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Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the Manning Equation Calculator
Work out uniform flow in a gravity pipe or an open channel by Manning’s equation, V = (1/n) R^(2/3) S^(1/2) (in SI units; 1.486/n in US customary units), Q = V A. Choose a part-full circular pipe, a rectangular, trapezoidal or triangular channel, and solve for the flow at a depth, the normal depth for a flow, the slope a flow needs, or the pipe diameter that carries a flow at a chosen depth ratio.
Every result comes with the velocity, flow area, wetted perimeter, hydraulic radius and top width, the Froude number and whether the flow is subcritical or supercritical, the critical depth and critical slope, the boundary shear stress, and for pipes the full-pipe capacity, the share of it in use and the largest gravity flow (at 93.8 % full). Pick the lining from 37 of Chow’s n values (with their ranges) or the sewer design value, or type your own; for sanitary sewers the page can check the Ten States Standards’ minimum velocity flowing full and its high-velocity limit. A cross-section drawing and a rating curve show the flow.
Without a pass, the free preview shows your inputs, the checks, the depth shares of the rating table’s first rows and watermarked drawings; the answer, the other figures, the working, Copy result and the CSV come with a Pro pass.
How to use it
- Choose what to work out — the flow from a depth, the normal depth for a flow, the slope for a flow, or the pipe size for a flow — and SI or US customary units (every box also has its own unit; changing a unit converts what you typed).
- Pick the shape and enter its size: the pipe’s inside diameter, or the channel’s bottom width and side slopes (horizontal per 1 vertical).
- Enter the slope (as %, m/m or ‰) and pick the lining for Manning’s n, or type your own n. Then the depth, the flow, or the flow and the largest depth ratio, depending on what you solve for.
- Read the answer, the Froude number, the critical depth and the pipe’s full capacity, the drawing and the rating table. Copy the result or download the CSV with a Pro pass, or after unlocking this result.
Examples
Circular pipe D = 300 mm, n = 0.013, slope 0.5 %, depth 150 mm
Q = 34.19 L/s at 0.967 m/s (half the full capacity of 68.38 L/s, at the same velocity); the largest gravity flow is 73.55 L/s at 93.8 % full. Froude number 0.90: subcritical.
Rectangular, 2 m wide, float-finished concrete (n = 0.015), slope 0.1 %, Q = 3 m³/s
Normal depth 1.096 m at 1.368 m/s; Froude number 0.42 (subcritical); critical depth 0.612 m, critical slope 0.49 %
Trapezoid, 3 m bottom, 2:1 banks, weathered earth (n = 0.022), slope 0.05 %, 1.2 m deep
A = 6.48 m², R = 0.775 m; V = 0.857 m/s, Q = 5.55 m³/s; Froude number 0.30
40 L/s at 0.5 % with n = 0.013
Flowing full it needs a 245 mm bore; kept to 75 % full, 254 mm. Pick the next standard size up.
203.2 mm (8 in) pipe at 0.40 %, n = 0.013
Flowing full: 0.667 m/s (2.19 ft/s), above the 0.6 m/s (2 ft/s) the standards ask for
Common uses
- Checking the capacity of a sewer, storm drain or culvert at its slope
- Finding the depth of flow in a channel, ditch or canal for a design flow
- Choosing a pipe diameter for a gravity flow, full or part full
- Finding the slope a flow needs, and whether the flow is subcritical or supercritical
- Open-channel hydraulics coursework, with each step of the working
Formulas
- Manning: V = (1/n) R^(2/3) S^(1/2) with R = A/P in metres (V = (1.486/n) R^(2/3) S^(1/2) in feet), Q = V A
- Circle part full: θ = 2 arccos(1 − 2y/D), A = D²(θ − sin θ)/8, P = Dθ/2, T = D sin(θ/2); half full has R = D/4, the same as full
- Rectangle: A = b y, P = b + 2y; trapezoid: A = (b + (z₁ + z₂)y/2) y, P = b + y(√(1 + z₁²) + √(1 + z₂²)), T = b + (z₁ + z₂) y; a triangle has b = 0
- Froude number: Fr = V ÷ √(g A/T); below 1 subcritical, above 1 supercritical
- Critical depth: Q² T ÷ (g A³) = 1; the critical slope makes the normal depth equal to it
- Boundary shear: τ = ρ g R S
- Largest pipe flow: at y/D = 0.938, about 1.076 times the full-pipe flow
Choosing n
The n values are Chow’s normal values, with his minimum and maximum, for clean, well-kept surfaces of each kind; older, damaged, weedy or debris-laden linings sit towards the maximum. For sanitary sewers, the Ten States Standards size pipes with n = 0.013 whatever the material, because a slime layer and the joints make every sewer rougher than new pipe.
Sources
- Manning, R., On the flow of water in open channels and pipes, Transactions of the Institution of Civil Engineers of Ireland
- Chow, V. T., Open-Channel Hydraulics, Table 5-6 (n values; its channel values are also reproduced in the USACE HEC-RAS Hydraulic Reference Manual)
- Recommended Standards for Wastewater Facilities (Ten States Standards), §33.41 (minimum velocity flowing full, n = 0.013, minimum slopes) and §33.45 (high-velocity protection)
Limitations
- Manning’s equation describes steady, uniform flow (the normal depth) in a long, straight reach of constant section and slope; near inlets, outlets, bends, junctions and changes of slope the depth differs (gradually varied flow).
- It assumes fully rough turbulent flow of water. For very smooth, small or slow flows, other liquids, or air-entrained flow on steep slopes, use the Darcy–Weisbach equation or specialist methods.
- A pipe that runs full under pressure (surcharged) follows its hydraulic grade, not Manning’s gravity flow; the page flags flows above the largest gravity flow.
- n values are typical; measure or use local guidance for real channels. Results are estimates, not a professional design — have a qualified engineer check anything that matters.
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Frequently asked questions
What do I get without a pass?
Without a pass, Manning Equation Calculator shows your inputs, the checks, the rating table’s first rows by depth and a watermarked section and curve, with the answer and every figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
What n value should I use for a concrete or PVC pipe?
New concrete pipe is about 0.011 to 0.013 and smooth plastic about 0.009, but sanitary sewers are usually designed with n = 0.013 whatever the material (the Ten States Standards do so), because slime, joints and manholes make them rougher in service. For channels, pick the lining from the list and move towards its maximum for weedy or poorly kept surfaces.
Why does a pipe carry the most water when it is not quite full?
Near the top of the pipe a little more depth adds very little area but a lot of wetted perimeter (the crown), so the hydraulic radius falls. The flow peaks at about 93.8 % of the diameter, about 7.6 % more than flowing full; the velocity peaks lower, near 81 % full.
What is the Froude number and why does it matter?
It compares the flow velocity with the speed of a surface wave, √(g A/T). Below 1 the flow is subcritical (deep and calm, controlled from downstream); above 1 it is supercritical (shallow and fast) and forms a hydraulic jump where it slows. Flow close to 1 has a wavy, unstable surface, so channels are designed to stay clear of it.
How fast should a sewer flow?
The Ten States Standards ask for a mean velocity of at least 0.6 m/s (2 ft/s) flowing full, based on n = 0.013, so solids do not settle — 0.9 m/s (3 ft/s) for sewers of 1,200 mm (48 in) and larger — and for protection against scour where the velocity exceeds 3 m/s (10 ft/s). Tick the sewer check to compare a pipe with both.
Is Manning’s equation dimensionally consistent?
No: n carries units, so the equation has a constant that depends on the unit system — 1 in metres and seconds, 1.486 in feet and seconds. The calculator works in SI internally and converts your inputs, so the same n works in both systems.