Civil Engineering

Manning Equation Calculator

Size a gravity sewer, culvert or open channel using the Manning equation. Enter the section shape and dimensions, the bed slope and the roughness coefficient, and this calculator returns the full-bore discharge capacity, the mean velocity, the hydraulic radius, the wetted perimeter, the Froude number and the minimum slope needed to hold the self-cleansing velocity. Circular, rectangular and trapezoidal sections are supported.

Manning equation · SI form, n in s/m^1/3 · full-bore uniform flow

This page covers gravity flow only. If your pipe is pressurised — pumped mains, rising mains, distribution networks, anything where the energy gradient comes from a pump rather than the bed slope — the Manning equation is the wrong tool. Use the pipe pressure drop calculator instead, which applies Darcy–Weisbach with a Colebrook friction factor.

🌊 Channel and Flow Inputs

Inputs convert when you switch. Results are always reported in SI — see the note under the results.

Section Shape

Internal Diameter D (mm)

Bed Slope S (m/m)

A slope of 1 in 200 is S = 0.005.

Manning Roughness n

0.013 for concrete sewer pipe. See the table below.

Design Flow Q_design (L/s)

The peak flow the section must carry. Set to 0 to skip the capacity check.

📊 Hydraulic Results

Press Calculate Flow to run the analysis.

ƒ Governing Formulae

Manning equation, SI form

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

Section properties

Circular, flowing full
A = πD²/4  P = πD  R = D/4

Rectangular
A = b·y  P = b + 2y  R = by/(b + 2y)

Trapezoidal
A = (b + zy)y  P = b + 2y√(1 + z²)

Derived checks

S_min = [ 0.6n / R^2/3 ]² (slope for v = 0.6 m/s)
Fr = v / √(g·y_eff) g = 9.81 m/s²

v — mean velocity of steady uniform flow, m/s

n — Manning roughness coefficient, dimensionally s/m^1/3

R — hydraulic radius, area divided by wetted perimeter, m

S — bed slope, m fall per m run; equals the friction slope under uniform flow

A, P — flow area and wetted perimeter

D — internal diameter of a circular section

b, y — bed width and flow depth of an open section

z — side slope, horizontal run per unit vertical rise

y_eff — depth used for the Froude number: the flow depth for open sections, the diameter for a full circular pipe

The 1/n coefficient is unit-bound. The form above is the SI version. In US customary units the same equation carries a leading 1.486, because the conversion is absorbed into the constant rather than into n — the roughness coefficient itself has the same numerical value in both systems. If you enter Imperial units on this page they are converted to SI before the calculation, so the SI form is always the one applied.

What this calculation does and does not do. It solves the full-section case: the capacity of the pipe or channel when flowing at the stated depth, which for a circular section means exactly full. It does not solve for normal depth — that is, it will not tell you how deep the water sits for a given discharge, which needs an iterative solution. It assumes steady uniform flow, so it does not cover backwater curves, hydraulic jumps, entry and exit losses or surcharged conditions. The Froude number for a full circular pipe is reported using the diameter as the effective depth; a pipe flowing exactly full has no free surface, so treat that figure as an indicator of how energetic the flow is rather than a strict free-surface Froude number.

📝 Worked Example 1 — 300 mm Concrete Foul Sewer

Given

A 300 mm internal diameter concrete sewer laid at 1 in 200, so S = 0.005, with a Manning roughness of n = 0.013. The peak design flow is 30 L/s.

Step 1 — section properties at full bore

A = π × 0.300² / 4 = 0.0707 m²
P = π × 0.300 = 0.942 m
R = A/P = D/4 = 0.0750 m

Step 2 — velocity from the Manning equation

R^2/3 = 0.0750^2/3 = 0.17785
S^1/2 = 0.005^1/2 = 0.07071
v = (1/0.013) × 0.17785 × 0.07071 = 76.923 × 0.012576 = 0.967 m/s

Step 3 — discharge capacity

Q = A × v = 0.070686 × 0.96737 = 0.068378 m³/s = 68.378 L/s
That is comfortably above the 30 L/s design flow, so the section has spare capacity.

Step 4 — self-cleansing and flow character

v = 0.967 m/s is above the 0.6 m/s self-cleansing minimum, so grit will stay in suspension.
S_min = [0.6 × 0.013 / 0.17785]² = 0.00192 m/m, roughly 1 in 520 — the flattest this pipe could be laid and still self-cleanse.
Fr = 0.967 / √(9.81 × 0.300) = 0.967 / 1.7155 = 0.564, subcritical.

Full-bore capacity 68.378 L/s against 30 L/s required — PASS

Velocity 0.967 m/s, above the 0.6 m/s self-cleansing minimum

Hydraulic radius 0.0750 m · Area 0.0707 m² · Wetted perimeter 0.942 m

Minimum self-cleansing slope 0.00192 m/m

Froude number 0.564 — subcritical

These are the calculator's default inputs. Press Calculate Flow without changing anything and you should get exactly these figures back. Note that the hydraulic radius of any circular pipe flowing full is simply D/4 — the diameter cancels out of the area-over-perimeter ratio, which is why the same R appears whatever size of pipe you enter.

⚠ Worked Example 2 — Enough Capacity, Wrong Answer

Given

The same 300 mm concrete sewer and the same n = 0.013, but laid much flatter at S = 0.0008, about 1 in 1250, to follow a level site. Design flow is 20 L/s.

The capacity check passes

v = (1/0.013) × 0.17785 × 0.0008^1/2 = 0.387 m/s
Q = 0.070686 × 0.38693 = 27.351 L/s, against 20 L/s required.
On capacity alone this section is adequate, with 37 percent to spare.

And the sewer will still silt up

At 0.387 m/s the flow is well below the 0.6 m/s needed to keep grit moving. Solids settle, the effective bore shrinks, roughness rises, velocity falls further, and the section blocks. The required slope is S_min = 0.00192 m/m — two and a half times the slope actually provided.

Capacity check 27.351 ≥ 20 L/s — passes

Velocity 0.387 m/s against 0.6 m/s required — FAILS

Verdict — not acceptable, and only the velocity check says so

What to do about it

Steepen the pipe to at least 1 in 520, or drop to a smaller diameter so the same flow occupies a greater proportion of the bore, or accept the flat gradient and add a pumping station. A smaller pipe is often the right answer and the least intuitive: reducing the diameter raises the velocity for a given flow even though it lowers the capacity.

This case is worth trying because the two checks pull in opposite directions. Capacity wants a big pipe on a flat grade; self-cleansing wants a small pipe on a steep one. Almost every gravity drainage problem is a negotiation between those two, and a design that satisfies only the first is the most common error in sewer sizing.

📏 Inputs, Units and Accepted Ranges

Input	SI unit	Imperial unit	Accepted	Notes
Section shape	—	—	circular, rectangular, trapezoidal	Sets which dimension fields apply
Diameter D	mm	in	> 0	Circular sections only; internal bore
Bed width b	m	ft	> 0	Rectangular and trapezoidal only
Flow depth y	m	ft	> 0	The depth analysed, not the channel height
Side slope z	—	—	≥ 0, typically 1.0 – 2.0	Trapezoidal only; horizontal per 1 vertical
Bed slope S	m/m	ft/ft	> 0	Dimensionless, so the same number in both systems
Manning n	—	—	> 0, typically 0.010 – 0.035	Same numerical value in SI and US customary
Design flow Q_design	L/s	gpm (US)	≥ 0	Enter 0 to skip the capacity comparison

📚 Reference Tables

Manning roughness coefficient n

Material	n, design	n, range	Notes
PVC, HDPE, GRP	0.011	0.009 – 0.012	Smooth bore; joints dominate the value
Vitrified clay	0.012	0.011 – 0.014	Traditional foul sewer material
Concrete pipe, precast	0.013	0.011 – 0.015	Standard design value for sewers
Concrete, cast in situ	0.014	0.012 – 0.017	Depends on formwork quality
Cast iron, ductile iron	0.013	0.011 – 0.015	Rises with tuberculation in old mains
Brickwork, well laid	0.015	0.012 – 0.018	Common in Victorian-era sewers
Corrugated metal	0.024	0.022 – 0.027	Strongly dependent on corrugation pitch
Earth channel, clean	0.022	0.018 – 0.025	Straight, uniform, no weed growth
Earth channel, weedy	0.030	0.025 – 0.035	Seasonal — check the summer condition
Natural stream, clean	0.030	0.025 – 0.040	Rises sharply with meanders and pools
Rock cut, jagged	0.040	0.035 – 0.050	Blasted section, irregular sides

Use the design value, not the best-case value. A new smooth pipe reaches its design roughness within a few years of service, and a design based on 0.011 for concrete has no margin left for the slime layer that will certainly form.

Full-bore capacity of circular concrete pipe at n = 0.013

D, mm	R = D/4, m	A, m²	Q at 1 in 200, L/s	Q at 1 in 500, L/s	v at 1 in 200, m/s
150	0.0375	0.0177	10.8	6.8	0.609
225	0.0563	0.0398	31.8	20.1	0.798
300	0.0750	0.0707	68.4	43.3	0.967
375	0.0938	0.1104	123.9	78.4	1.122
450	0.1125	0.1590	201.6	127.5	1.268
600	0.1500	0.2827	434.3	274.7	1.536
750	0.1875	0.4418	787.6	498.2	1.783
900	0.2250	0.6362	1281.9	810.8	2.015

Notice that a 150 mm pipe at 1 in 200 only just reaches the self-cleansing velocity. Small-diameter sewers on shallow gradients are where velocity, not capacity, governs.

Minimum self-cleansing slope for v = 0.6 m/s, concrete pipe at n = 0.013

D, mm	S_min, m/m	Expressed as
150	0.00485	1 in 206
225	0.00283	1 in 354
300	0.00192	1 in 520
375	0.00143	1 in 700
450	0.00112	1 in 893
600	0.00076	1 in 1316
900	0.00045	1 in 2247

These are full-bore figures. A sewer running part full at low flow reaches self-cleansing at a steeper gradient than this table suggests, which is why many authorities apply a 1 in D rule of thumb for small foul sewers.

Design velocity limits

Condition	Velocity, m/s	Consequence
Below self-cleansing	< 0.6	Grit and solids settle; progressive blockage
Self-cleansing minimum, foul	0.6	Standard design minimum
Self-cleansing minimum, combined	0.75	Higher grit load from road runoff
Normal design range	0.9 – 2.5	Comfortable operating band
Upper limit, concrete	3.0	Abrasion of the invert becomes significant
Supercritical, Fr > 1	varies	Hydraulic jump risk at any downstream control

❓ Frequently Asked Questions

What is the Manning equation and when is it used?

The Manning equation gives the mean velocity of steady uniform flow in an open channel as one over the roughness coefficient, times the hydraulic radius to the power two thirds, times the square root of the bed slope. It applies to gravity flow with a free surface, which covers sewers, culverts, drains and natural channels. It does not apply to pressurised pipe flow, where the Darcy-Weisbach equation should be used instead because the energy gradient is set by the pump rather than by the bed slope.

What Manning roughness coefficient should I use for a concrete pipe?

A value of 0.013 is the usual design figure for a concrete sewer pipe and is what most drainage codes assume. New smooth precast pipe can be as low as 0.011, but designing on that leaves no allowance for the slime layer, joint irregularity and minor deposits that develop in service. PVC and HDPE are commonly taken as 0.010 to 0.011, vitrified clay as 0.012, and corrugated metal from 0.022 upward depending on the corrugation profile.

What is the minimum velocity in a gravity sewer?

The usual self-cleansing requirement is 0.6 metres per second at full-bore or at the design peak flow, which is enough to keep grit and organic solids in suspension rather than letting them settle and build up. Some authorities require 0.75 metres per second for combined systems carrying road grit. This calculator flags any section falling below 0.6 metres per second and reports the minimum bed slope that would achieve it.

How do you calculate the hydraulic radius of a pipe flowing full?

Hydraulic radius is the flow area divided by the wetted perimeter. For a circular pipe flowing exactly full the area is pi D squared over four and the wetted perimeter is pi D, so the hydraulic radius simplifies to D over four regardless of the diameter. For a rectangular channel it is width times depth divided by width plus twice the depth, and for a trapezoidal channel the side slopes lengthen the wetted perimeter by twice the depth times the square root of one plus the side slope squared.

Why does a sewer carry more flow just below full than exactly full?

As the water surface rises above about ninety three percent of the diameter, the wetted perimeter grows faster than the flow area does, so the hydraulic radius falls and with it the velocity. Peak discharge in a circular pipe occurs at roughly ninety three or ninety four percent of full depth and is about seven percent higher than the exactly full value. Designing on the full-bore figure is therefore slightly conservative, which is why it remains standard practice.

🔗 Related Tools

← All Civil Engineering Calculators

Manning Equation Calculator — multicalci.com. Solves steady uniform full-section flow. Does not solve for normal depth, and makes no allowance for backwater effects, hydraulic jumps, entry and exit losses or surcharged conditions. Results are indicative and must be verified against the relevant drainage authority's design standard.