Fluid Mechanics

Manning Equation Calculator

Calculate uniform open-channel discharge and average velocity from channel geometry, slope, and Manning roughness n.

Formula SI: Q = (1/n)AR^(2/3)S^(1/2); US: Q = (1.486/n)AR^(2/3)S^(1/2)Reviewed Sep 8, 2026

The Manning equation estimates steady, uniform flow in open channels such as concrete drains, roadside ditches, swales, canals, and partially full culverts. This calculator solves the practical capacity check: enter the channel shape, water depth, roughness coefficient n, and channel slope, then it returns discharge, velocity, hydraulic radius, and a Froude-number regime check. It is intentionally not a full stormwater design model; it gives a transparent first-pass flow estimate while calling out the assumptions that often control real designs.

Calculation Bench

Channel Shape

Roughness Preset

Presets are screening values only. Vegetation, bends, sediment, and channel condition can move n a lot.

Channel Geometry

01Bottom Width

b · Channel invert width. Rectangular/trapezoidal sections only.

02Flow Depth

y · Water depth in the channel, not total wall height or freeboard.

Roughness & Slope

01Manning Roughness

n · Typical concrete n is about 0.013; natural or vegetated channels are higher.

02Channel Slope

S · Friction slope for uniform flow. 0.001 means 0.1% grade.

Solution

Pick a channel shape, roughness n, slope, and water depth to calculate normal open-channel flow.

Q = (1.486/n) A R^(2/3) S^(1/2)

Manning flow assumes steady, uniform open-channel flow. It is not a culvert/backwater model, flood study, or pressurized pipe calculation; freeboard, outlet control, debris, erosion, and local stormwater criteria can govern the final design.

Formula Sheet

A = b y

A = y(b + z y)

P = b + 2y\sqrt{1+z^2}

R = \dfrac{A}{P}

Q = \dfrac{1}{n} A R^{2/3} S^{1/2}

Q = \dfrac{1.486}{n} A R^{2/3} S^{1/2}

Fr = \dfrac{V}{\sqrt{gD_h}}

QDischarge
VAverage Velocity
nManning Roughness
SSlope
RHydraulic Radius
AFlow Area
PWetted Perimeter

Typical Manning n roughness values for screening
Surface	Typical n	Use with caution
PVC / very smooth lining	0.009-0.011	Only for clean, smooth, manufactured sections.
Finished concrete	0.012-0.014	Good first-pass value for clean concrete channels.
Rough concrete	0.015-0.020	Use higher values for joints, aging, or rough finish.
Clean earth channel	0.020-0.025	Sensitive to erosion, sediment, and vegetation.
Grass-lined swale	0.030-0.050+	Can change a lot with mowing height and flow depth.
Natural stream	0.035-0.070+	Field survey and local hydraulic guidance are important.

Variables & Units

Symbol	Variable	Description	Common Units
Q	Discharge	Volumetric open-channel flow rate.	ft³/s, m³/s, US gpm
V	Average Velocity	Average section velocity predicted by Manning's equation.	ft/s, m/s
n	Manning Roughness	Empirical roughness coefficient representing lining material, vegetation, bends, and channel condition.	dimensionless
S	Slope	Friction slope used by the uniform-flow equation.	m/m, ft/ft, %
R	Hydraulic Radius	Flow area divided by wetted perimeter.	ft, m
A	Flow Area	Cross-sectional area occupied by water below the free surface.	m², ft²
P	Wetted Perimeter	Channel boundary length in contact with water.	m, ft

How to Use This Calculator

01Choose the channel shape. Use Rectangular for box channels or flat-sided flumes, Trapezoidal for ditches/swales with side slopes, and Custom A/P if you already know flow area and wetted perimeter.
02Enter the flow depth, not the total channel wall height. Freeboard should be checked separately above the calculated water surface.
03Select a roughness preset if you do not know Manning n. Smooth concrete is commonly around n = 0.013, while vegetated or natural channels can be much higher.
04Enter slope as m/m, ft/ft, or percent. For example, a 0.1% grade is 0.001 m/m or 0.001 ft/ft.
05For irregular natural channels, use Custom A/P only when flow area and wetted perimeter come from a survey or section drawing at the same water depth.
06The calculator converts units internally. If you hand-calculate in SI, use Q = (1/n)AR^(2/3)S^(1/2); if you hand-calculate in US customary ft/cfs units, use Q = (1.486/n)AR^(2/3)S^(1/2).
07Review both discharge and velocity. A channel may pass the required flow but still have erosion, sedimentation, or safety concerns if velocity is outside the acceptable range for its lining.
08Use the Froude-regime note as a stability cue. Near-critical or supercritical results deserve extra review because small depth changes, drops, or downstream controls can change flow behavior.

How the Formula Works

Manning's equation relates average velocity to channel roughness, hydraulic radius, and slope: V = (1/n) R^(2/3) S^(1/2) in SI units. In US customary units the coefficient is commonly written as 1.486/n. The hydraulic radius R is the flowing area divided by the wetted perimeter, R = A/P.

After velocity is calculated, discharge follows from Q = A × V. Rectangular and trapezoidal sections calculate A and P from the water depth and geometry; custom mode lets you enter A and P directly for irregular sections.

For rectangular and trapezoidal shapes the calculator also estimates Froude number using hydraulic depth D_h = A/T. That helps flag subcritical, near-critical, or supercritical open-channel behavior.

Worked Example 01

Rectangular concrete channel capacity

Known

Bottom width (b): 2 m
Flow depth (y): 1 m
Manning n: 0.013
Slope (S): 0.001 m/m

Formula

Q = (1/n) A R^(2/3) S^(1/2)

Substitution

A = 2 × 1 = 2 m²; P = 2 + 2 × 1 = 4 m; R = 0.5 m; Q = (1/0.013) × 2 × 0.5^(2/3) × 0.001^(1/2)

Result

Q ≈ 3.07 m³/s (about 108 ft³/s); V ≈ 1.53 m/s

The channel has enough hydraulic radius to carry roughly 3 cubic meters per second at a 0.1% grade. The velocity is moderate for a concrete-lined section, but final design still needs freeboard and downstream-control review.

Worked Example 02

Vegetated trapezoidal swale

Known

Bottom width (b): 3 m
Depth (y): 1 m
Side slope (z): 2H:1V
Manning n: 0.035
Slope: 0.08%

Formula

Q = (1/n) A R^(2/3) S^(1/2)

Substitution

A = 1 × (3 + 2 × 1) = 5 m²; P = 3 + 2 × 1 × √5 = 7.47 m; R = 0.669 m

Result

Q ≈ 3.09 m³/s (about 109 ft³/s); V ≈ 0.62 m/s

This is a slower, rougher channel than the concrete example. The capacity is still several cubic meters per second because the section is wide, but vegetation maintenance can materially change the result.

Applications

01Checking the approximate flow capacity of rectangular concrete drains
02Estimating ditch or swale flow from known depth, slope, side slopes, and roughness
03Comparing open-channel velocity against erosion or sedimentation screening limits
04Back-checking a survey cross-section when flow area and wetted perimeter are already known

Assumptions

01Flow is steady, uniform, and open to atmospheric pressure.
02The channel is prismatic enough that one representative cross-section describes the reach.
03Slope is a reasonable estimate of friction slope for the reach being checked.
04Manning n is selected from a reliable project reference or screening preset.

Where This Model Stops

01Does not solve normal depth from a target flow; it solves flow capacity from a known water depth.
02Does not model culvert inlet/outlet control, backwater, gradually varied flow, hydraulic jumps, bridges, weirs, debris, or tailwater.
03Does not check freeboard, erosion protection, sediment transport, storm recurrence interval, or local drainage criteria.
04Does not replace drainage-code, stormwater, floodplain, or erosion-control design checks.
05Roughness n can dominate the result; field condition, sediment, vegetation, bends, and maintenance condition should be reviewed by a qualified designer.

References

[1]
Manning Equation for Open Channel Flow
United States Geological Survey
Reference for the Manning equation variables and open-channel-flow use.
[2]
Hydraulic Design Series No. 4: Introduction to Highway Hydraulics
Federal Highway Administration
Highway-drainage reference covering open-channel flow, roughness, and practical hydraulic design context.

Frequently Asked Questions

What Manning n should I use?

Use project standards, local drainage manuals, or field-verified roughness where available. Presets are only screening values: finished concrete may be near 0.013, rough concrete around 0.017, clean earth around 0.022, and vegetated or natural channels can be 0.030 to 0.050 or higher.

Is this the same as the Flow Rate Calculator?

No. The Flow Rate Calculator uses Q = A × v when velocity is already known. This Manning Equation Calculator estimates that velocity from open-channel roughness, hydraulic radius, and slope before calculating Q.

Can I use Manning equation for a full pipe?

Manning's equation is commonly used for gravity sewer and partially full pipe flow when the pipe is acting as an open channel. It is not the right model for pressurized pipe flow; use pipe-flow or pressure-drop methods for full pipes under pressure.

Why does the calculator not ask for target flow and solve normal depth?

Normal-depth solving requires iteration and can have design-specific constraints. This first version is a capacity checker from known depth and geometry, which is easier to audit and less likely to hide an unstable design assumption.

What is the most sensitive input?

Manning n and flow depth often dominate the result. A small depth change changes area and hydraulic radius, while roughness can shift capacity materially between smooth concrete, grass, and natural-channel conditions.

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