Manning Equation Calculator (Open Channel Flow)

How to use the Manning equation calculator

Enter the roughness coefficient n, the channel bottom width, the flow depth and the slope. You get the flow area, wetted perimeter, hydraulic radius, mean velocity and flow rate. To find the normal depth for a known flow, clear the depth and enter the flow.

Manning equation (SI)

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

Rectangular channel: A = b·y  ·  P = b + 2y  ·  R = A ÷ P

Example

Concrete channel (n = 0.013), 2 m wide, 0.5 m deep, slope 0.1%:

• A = 1 m², P = 3 m, R = 0.3333 m
• V = (1/0.013) × 0.3333^2/3 × √0.001 = 1.169 m/s
• Q = 1.169 × 1 = 1.169 m³/s (4,210 m³/h)

Flow vs depth (same channel)

Depth	Velocity	Flow
0.1 m	0.492 m/s	0.098 m³/s
0.25 m	0.832 m/s	0.416 m³/s
0.5 m	1.169 m/s	1.169 m³/s
0.75 m	1.383 m/s	2.074 m³/s
1 m	1.532 m/s	3.065 m³/s
1.5 m	1.730 m/s	5.191 m³/s

Typical Manning n values

Surface	n
PVC / HDPE pipe	0.009–0.011
Finished concrete	0.012–0.014
Unfinished concrete	0.014–0.017
Corrugated metal	0.022–0.026
Earth channel, clean	0.018–0.025
Natural stream, some weeds and stones	0.030–0.040

Notes

• Manning assumes steady, uniform, fully turbulent flow; it is not valid near weirs, gates or sudden changes.
• For flow measurement, use a calibrated structure such as a weir or flume — see the weir flow calculator.

Frequently asked questions

What is the Manning equation?

In SI units V = (1/n) R^(2/3) S^(1/2), where V is mean velocity in m/s, R the hydraulic radius in m, S the slope and n the roughness coefficient. Flow Q = V × A.

What is the hydraulic radius?

Flow area divided by wetted perimeter. For a rectangular channel of width b and depth y, R = b·y ÷ (b + 2y).

How do I use Manning in US units?

The US form includes a factor 1.486, V = (1.486/n) R^(2/3) S^(1/2) with feet. This calculator works internally in SI, so you can switch display units freely.

Can I find the normal depth for a given flow?

Yes. Clear the depth, enter the flow rate and calculate — the depth is solved numerically.

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