Manning's Equation Calculator

Manning’s equation calculator: what it finds

A Manning’s equation calculator estimates the flow in an open channel, like a ditch or a concrete flume, from four inputs: channel width, flow depth, a roughness value called n, and the slope in percent. It reports flow in cubic feet per second, and in gallons per minute.

In US units the equation is Q = (1.49 ÷ n) × A × R^(2/3) × S^(1/2). Here A is the flow area in square feet, R is the hydraulic radius in feet, and S is the slope as a decimal. This tool takes the slope in percent and divides by 100.

The pieces in plain words

Flow area is the wet cross-section: width times depth. The wetted perimeter is the bottom plus the two sides the water touches, which is width + 2 × depth. The hydraulic radius is the area divided by that perimeter. It tells you how much water there is compared with how much wall drags on it.

A smoother wall, a steeper slope, or more water all push the flow up.

Worked examples

Example 1, the default concrete channel. Width 4 ft, depth 1 ft, n = 0.013, slope 0.5%.

• Area: 4 × 1 = 4.00 sq ft
• Wetted perimeter: 4 + 2 × 1 = 6 ft
• Hydraulic radius: 4 ÷ 6 = 0.667 ft
• Slope: 0.5 ÷ 100 = 0.005
• Flow: (1.49 ÷ 0.013) × 4 × 0.667^(2/3) × 0.005^0.5 = 24.74 cfs
• In gallons per minute: 24.74 × 448.831 = 11,104 GPM

Example 2, an earth ditch. Width 3 ft, depth 1.5 ft, n = 0.03, slope 1%.

• Area: 4.50 sq ft
• Hydraulic radius: 4.5 ÷ 6 = 0.750 ft
• Flow: 18.45 cfs, or 8,281 GPM

What changes the answer

These variations all start from the 4 ft wide, 1 ft deep channel in example 1.

Change	Flow (cfs)
Default: n = 0.013, slope 0.5%	24.74
Rough earth, n = 0.03	10.72
Steeper slope, 1%	34.99
Wider channel, 6 ft	40.14
Deeper flow, 2 ft	64.84

Switching from concrete to earth cuts capacity to about 43% of the concrete figure. Doubling the slope adds about 41%, since flow follows the square root of slope.

Typical roughness values

Surface	Typical n
Smooth plastic or very smooth concrete	around 0.010 to 0.013
Finished concrete	about 0.013
Earth, fairly clean	about 0.02 to 0.03
Earth with grass or weeds	0.03 and higher

Published tables give ranges and the sources differ a little, so pick a value from a reference you trust and keep it on the cautious side.

How to measure

Measure the width across the bottom of a rectangular channel and the depth of water you expect, not the full height of the wall. For slope, a string level or a laser level gives the drop over a measured length. A fall of 6 inches over 100 ft is 0.5 ft ÷ 100 ft = 0.5%. The drainage slope calculator does that conversion for you.

Limits of this tool

• It works for rectangular channels only.
• It gives the flow for a depth you choose. It does not find the depth for a given flow.
• It assumes steady, uniform flow, without drops, bends, or obstructions.
• It does not add freeboard, the extra wall height that keeps surges from spilling over.

Common mistakes

• Typing slope as a decimal, such as 0.005, when the box wants percent.
• Using the wall height as the depth.
• Choosing an n for new, clean concrete when the channel is old or silted.
• Applying the result to a pipe that flows full.

Checking the speed of the water

Flow divided by area gives velocity. In example 1, 24.74 cfs ÷ 4.00 sq ft = 6.19 ft per second. In example 2, 18.45 ÷ 4.50 = 4.10 ft per second. Fast water can scour a bare earth ditch and undercut the banks, so a channel that has enough capacity may still need lining, rock, or grass. Check your local erosion guidance.

Related calculators

For pipes and culverts, use the culvert calculator. The flow rate calculator converts between units, and the drainage slope calculator turns a measured drop into a percent. For stormwater that protects structures, a licensed engineer should confirm the numbers.