How to Work Out Drain Slope from Invert Elevations
Why this matters
A drain line has two ends whose heights are fixed by things you cannot move: the fixture or cleanout at the top and the existing sewer at the bottom. Between them, the pipe has to fall at least the code minimum for its size, every foot of the way. Plumbing drawings state those two heights as invert elevations, and from them you can tell, before anyone saws a slab, whether the line can be built as drawn. When the numbers do not close, finding out at the desk costs a phone call. Finding out with the trench open costs a redesign while the crew stands there.
The terms
Invert elevation (IE). The height of the inside bottom of a pipe, which is the surface the water actually runs on. Not the top of the pipe, not the center line, not the rim of the cleanout or the floor drain grate. Plans commonly note inverts as "IE 96.85" at a cleanout, a connection or a change of direction. See related: Plumbing Plan Line Codes, Fixture Tags and Inverts.
Datum. The reference height every elevation on the drawing is measured from. Architectural and plumbing sets commonly set the level 1 finished floor at 100.00 ft (or 100'-0") as a project datum; civil and site drawings commonly use real elevations above sea level, such as 742.50 ft, with a note tying the two together ("FF 100'-0" = EL 742.50"). Two inverts can only be subtracted if they are on the same datum.
Above finished floor (AFF). A height measured up from the finished floor surface, used for fixtures, devices and pipe in walls. With the floor at 100.00, a height of 3 ft AFF is elevation 103.00, and an invert of 96.85 is 3.15 ft below the floor. Finished floor means the top of the flooring, which sits above the top of slab by the thickness of the finish.
Slope. The fall per unit of run, stated in plumbing as inches per foot (1/8 in per ft, 1/4 in per ft) or as a percent. The conversion: 1/4 in per ft is 0.25 / 12 = 2.08 percent, and 1/8 in per ft is 1.04 percent.
The worked calculation
A tenant improvement adds a 3 in sanitary line from a new cleanout, CO-1, to an existing building sewer. The plumbing plan gives IE 96.85 at CO-1 and IE 96.10 at the connection. The general notes state the level 1 floor is 100.00 ft. The route on the plan, following the pipe around a column, measures 42.0 ft of run.
RUN: 3 in SAN, CO-1 to existing building sewer
DATUM: FF LEVEL 1 = 100.00 ft (general notes)
Upstream IE (CO-1) 96.85 ft
Downstream IE (connection) 96.10 ft
Drop = 96.85 - 96.10 0.75 ft
Drop in inches = 0.75 x 12 9.0 in
Run, measured along route 42.0 ft
Slope = 9.0 / 42.0 0.214 in/ft
Check: 0.75 / 42.0 = 0.0179 ft per ft = 1.79 pct
1.79 pct x 12 / 100 = 0.214 in/ft
Code min, 3 in (IPC Table 704.1) 1/8 = 0.125 in/ft
Min drop = 42.0 x 0.125 5.25 in
Margin = 9.0 - 5.25 3.75 in
The steps below build that block, and each says what it protects against.
Step 1: Put both inverts on one datum
Find the datum note and confirm both inverts are referenced to it. They usually are when both appear on the same plumbing sheet. They often are not when one comes from the plumbing plan and the other from a civil sheet, a survey, or an old as-built.
What breaks if you skip it: subtract a civil elevation of 742.10 from a plumbing invert of 96.85 and you get nonsense, which is easy to spot. The dangerous case is two project-datum figures from two different projects, such as an invert on a 1990s as-built whose 100.00 was set at a different floor than today's set. The subtraction looks normal and is wrong by whatever the two floors differ.
Step 2: Confirm each figure is an invert
Read the label at each point. A rim elevation on a floor drain, a top-of-pipe shot from a survey, or a center-line elevation in a detail can all sit next to the invert and look like it. For a figure that is not an invert, convert it: a top-of-pipe elevation minus the pipe's outside diameter plus its wall thickness gives the invert, and both dimensions come from the pipe manufacturer's data for that material and schedule.
On the example, both are labeled IE. Converting the upstream invert to a depth for the field crew: 100.00 - 96.85 = 3.15 ft below finished floor, and 0.15 ft is 1.8 in, so about 3'-1 13/16" below the floor surface. See related: How to Convert Decimal Feet to Feet, Inches and Sixteenths.
Step 3: Measure the run along the pipe, not between the ends
Slope is fall over the length the pipe actually travels. Follow the route on the plan through every offset and change of direction. A straight line between CO-1 and the connection on the example would be shorter than the 42.0 ft route, and a shorter run makes the slope look steeper than it will be.
If the run is scaled rather than dimensioned, the length is an estimate, and so is the slope; see related: How to Scale a Dimension off a Print. For a close call, measure the route in the field.
What breaks if you skip it: a line that passes on paper by the straight-line distance and fails in the trench by the real one.
Step 4: Compute the drop and the slope two ways
Drop is upstream invert minus downstream invert: 96.85 - 96.10 = 0.75 ft, which is 0.75 x 12 = 9.0 in. Slope is drop over run: 9.0 in / 42.0 ft = 0.214 in per ft.
Then compute it the other way, in feet per foot: 0.75 / 42.0 = 0.0179, or 1.79 percent, and 1.79 percent of 12 in is 0.214 in per ft. The two agree. Doing it both ways catches the most common slip in this math, which is mixing feet and inches in one division (0.75 / 42 read directly as "inches per foot" gives 0.018, a slope twelve times too flat).
Step 5: Check it against the adopted code, for this pipe size
Minimum slope depends on the pipe size and on which plumbing code your jurisdiction has adopted, in which edition.
- Under the International Plumbing Code, Table 704.1 (2021 edition) sets minimum slopes of 1/4 in per ft for pipe 2 1/2 in and smaller, 1/8 in per ft for 3 in through 6 in, and 1/16 in per ft for 8 in and larger. The example's 3 in line at 0.214 in per ft clears the 0.125 minimum. Over 42.0 ft the minimum drop is 42.0 x 0.125 = 5.25 in against the 9.0 in available, a margin of 3.75 in.
- Under the Uniform Plumbing Code, Section 708 states in substance a general minimum of 1/4 in per ft, and permits a flatter slope down to 1/8 in per ft for pipe 4 in and larger only where the steeper slope is impractical and the authority having jurisdiction approves it first (check the current edition). The same 3 in line at 0.214 in per ft falls short of 0.25 there, and at 3 in it is below the size the flatter allowance reaches. In a UPC jurisdiction this line, as drawn, does not meet code.
California's plumbing code is based on the UPC, many other states adopt the IPC, and some states and cities adopt one with their own amendments. Find out which one governs your job before you call any slope a pass.
Also compare with the slope the drawing itself states, if it states one. A note reading "3 in SAN at 1/4 in per ft" over inverts that only produce 0.214 is a conflict in the documents even where the code is satisfied.
What breaks if you skip it: the right arithmetic checked against the wrong code. The same line passes in one state and fails in the next.
Step 6: Field-verify the end you cannot move
The connection to the existing sewer is the fixed point, and its invert on the drawing came from somewhere: a survey, an old as-built, or a guess. Before material is ordered or the slab is cut, shoot the existing invert with a laser level and a rod at the nearest accessible cleanout or the exposed pipe.
Opening an existing sanitary cleanout releases sewer gas, which can include hydrogen sulfide, and the pipe carries biological contamination. Open it slowly with your face away from the opening, ventilate the area, wear gloves and eye protection, and wash before eating or handling the truck cab. If you meet a strong rotten-egg odor and it fades, leave the area: hydrogen sulfide deadens the sense of smell at harmful levels, so a smell that stops is not an all-clear. Shoot the invert from the surface with the rod, then replace and tighten the cleanout plug before you leave, because an open cleanout vents sewer gas into the building. A manhole, sump or vault is a permit-required confined space under 29 CFR 1910.146 (general industry) or 29 CFR 1926 Subpart AA (construction), and nobody enters one to take this reading. In a trench, take the shot from outside unless the trench has a protective system where required, which under 29 CFR 1926.652 begins at 5 ft deep.
When the numbers do not close
Say the field shot finds the existing invert at 96.40, not 96.10. Re-run the block: drop 96.85 - 96.40 = 0.45 ft, which is 5.4 in. Slope 5.4 / 42.0 = 0.129 in per ft. Under the IPC that clears 0.125, but the margin is now 5.4 - 5.25 = 0.15 in over 42 ft, which is less than ordinary installation variation on hangers or bedding. On paper it passes. In practice, a line that close to minimum will have flat spots.
The options, roughly from cheapest:
- Shorten the route. A more direct path that cuts the run to 36 ft gives 5.4 / 36 = 0.150 in per ft, a minimum drop of 36 x 0.125 = 4.5 in, and a margin of 0.9 in.
- Lower the connection point. Tie in further downstream, where the existing sewer is lower, if the existing system allows.
- Raise the upstream invert. Usually the hardest, because the cleanout's invert is set by the fixtures above it and their trap arms, and raising it may push pipe up into a wall or a floor assembly that cannot take it.
None of these is your call to make silently. Each changes the design, so it goes to the engineer as an RFI with both elevations, the measured run and the computed slope, plus your proposed fix. See related: How to Write an RFI That Gets a Usable Answer.
References
- International Plumbing Code, as adopted by your jurisdiction: Table 704.1 (2021 edition), minimum slope of horizontal drainage piping
- Uniform Plumbing Code, as adopted by your jurisdiction: Section 708, horizontal drainage slope
- 29 CFR 1910.146 and 29 CFR 1926 Subpart AA (confined spaces); 29 CFR 1926.652 (excavation protective systems)
- See related: Plumbing Plan Line Codes, Fixture Tags and Inverts
- See related: How to Convert a Slope Spec into a Drop Over a Run