Drain Pipe Gradient Calculator: Slope from Invert Levels as a Percentage and 1 in N
The gradient of a drain or sewer pipe from the invert level at each end.
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How this calculator works
Enter the invert level at the upstream end and at the downstream end of the pipe, and the length between them. The invert is the inside bottom of the pipe, not the ground level.
The calculator gives the vertical fall, the gradient as a decimal, the percentage slope, the ratio 1 in N and the fall in millimetres for each metre.
Add the pipe diameter to check the full-pipe velocity and flow with Manning's equation against the minimum self-cleansing velocity.
Formulas used
- \text{Fall} = IL_{up} - IL_{down}
- S = \frac{\text{Fall}}{\text{Length}}
- S\% = S \times 100
- 1\ \text{in}\ N,\ N = \frac{1}{S}
- V = \frac{1}{n}R^{2/3}S^{1/2},\ R = \frac{D}{4}
Worked example
With the default numbers in the calculator above:
- Vertical fall: 0.60 m
- Gradient (as a decimal): 0.0100
- Percentage slope: 1.00 %
- Slope ratio: 1 in 100.00
- Fall for each metre of pipe: 10.00 mm per metre
- Angle of the pipe: 0.57 degrees
- Hydraulic radius of the full pipe: 0.0563 m
- Full-bore velocity (Manning): 1.13 m/s
- Full-bore flow: 44.90 L/s
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
How do I work out the slope of a drainage pipe?
Subtract the downstream invert from the upstream invert to get the fall, then divide the fall by the length. For a fall of 0.60 m over 60 m the gradient is 0.01, which is 1 per cent or 1 in 100.
What is an invert level?
The level of the inside bottom of the pipe. Use the invert levels, not the ground or the chamber lid levels, because the pipe is buried at a different depth at each end.
Is a gradient of 1 in 100 enough for every pipe?
No. The same gradient gives a different velocity and capacity in each pipe size. Check the velocity for the diameter you are using against the drainage code or the water authority minimum.
Why does the calculator check the velocity?
A pipe that is too flat lets solids settle, and one that is too steep can wear the pipe. The gradient alone does not show either, so the velocity check gives the next number to look at.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any hydraulics or civil drainage text (Manning's equation). In Australia, AS/NZS 3500.3 for stormwater drainage of buildings, and the water authority design manual for sewers.
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