Pipe slope and invert level calculator

[Invert level](/en/glossary/invert-level) — invert elevation in US practice — is the height of the inside bottom of the pipe at a given point, quoted in the same datum as the ground level (m AOD in the UK, NAVD 88 in the US). Ground level minus invert level, less the outside diameter of the pipe, is the cover. On a long section the invert is resolved at every manhole and carried between them by a constant gradient over each reach.

One formula does the work: downstream invert = upstream invert − gradient × horizontal length. The gradient is dimensionless, so 1:200 goes in as 0.005 and 0.5% as 0.005 too.

Worked example. MH1 has an invert of 100.00 m AOD. The reach to MH2 is 30 m long and laid at 1 in 200. Then 100.00 − 0.005 × 30 = 99.85 m AOD, a fall of 150 mm. Read the other way: with both inverts known, the gradient is (100.00 − 99.85) ÷ 30 = 0.005, i.e. 1:200, 0.5%, 5 mm/m.

Two habits save rework. Length here is the horizontal length — the difference in chainage (station, in US practice), not the sloping length of the pipe; at sewer gradients the two barely differ, at a few percent they do. And DN is not the outside diameter: cover is measured over the crown, not over the invert.

UK drawings and specifications lead with the 1 in n ratio (a "fall of 1 in 80"); US plan-and-profile sheets normally use % or ft/ft; continental European standards write ‰, which is numerically the same as mm/m. The calculator shows all of them at once so nothing is lost in translation between a specification and a drawing.

The calculator flags a reach laid flatter than the 1-in-DN rule (known in the UK as Maguire’s Rule): the minimum gradient of a gravity public sewer is roughly 1:DN, so DN200 gets about 1:200 and DN300 about 1:300. It is a starting value for pre-dimensioning, not a verification.

Do not confuse these with the steep 1:40 and 1:80 falls of private and building drainage inside the plot (UK Approved Document H — roughly 1:40 for 100 mm and 1:80 for 150 mm pipes). Those runs rarely flow full, which is why they are graded harder; applying 1:80 to a DN400 trunk sewer would bury it needlessly deep.

The binding check under EN 752 is self-cleansing velocity at the design flow — on the order of 0.7 m/s (about 2.3 ft/s) at partial fill. In US practice the Ten State Standards (Recommended Standards for Wastewater Facilities) publish minimum slopes sized for 2.0 ft/s: 0.40% for 8 in, 0.28% for 10 in, 0.22% for 12 in, 0.15% for 15 in, 0.12% for 18 in, 0.10% for 21 in and 0.08% for 24 in. Confirm against the current edition of whichever applies to you.