How to Convert a Slope Spec into a Drop Over a Run

Why this matters

A slope spec on a drawing or in a code book is a rate. What the crew needs on the job is two elevations: where the pipe, swale or slab starts and where it has to end. The conversion between them is one multiplication, and it still goes wrong often enough to cost a dig-up: a drain that holds water in its middle third, a patio that pitches toward the house, a sewer that arrives at the main too low to connect. Every one of those started as a correct spec turned into a wrong number of inches.

The whole method is drop = run x slope, with the slope written in the same length units as the run. The rest of this card is about getting the slope into those units, measuring the run you actually have, and proving the result on the ground before anything is backfilled or poured.

Step 1: Rewrite the spec as inches per foot

Specs arrive in four costumes: inches per foot, a percent, a ratio like 1:48, or degrees. Convert to inches per foot first, because a tape reads inches and a run is measured in feet, so inches per foot multiplies straight into an answer you can mark.

• Inches per foot: already there. 1/4 in per ft is 0.25 in per ft.
• Percent: multiply the decimal by 12. 2 percent is 0.02 x 12 = 0.24 in per ft. 5 percent is 0.05 x 12 = 0.60 in per ft.
• Ratio 1:N: divide 12 by N. 1:48 is 12 / 48 = 0.25 in per ft. 1:12 is 1.0 in per ft.
• Degrees: take the tangent and multiply by 12. 2 degrees is tan(2) x 12 = 0.0349 x 12 = 0.42 in per ft.

Write the converted figure on the ticket next to the original spec, not instead of it. If somebody later asks where 0.24 came from, "2 percent per site plan sheet C-2" answers it.

Why this step comes first: every later error is easier to see in inches per foot. A number like 0.6 in per ft is obviously steep for a drain and obviously gentle for a lawn; 5 percent does not trigger the same reflex in most people. See related: Slope Four Ways: Percent, Ratio, Inches Per Foot and Degrees, which owns the full conversion table.

What breaks if you skip it: the commonest slip is multiplying a percent by a run in feet and reading the answer as inches. 2 percent of 40 ft is 0.8 ft. Read as 0.8 in, the line gets about a twelfth of the fall it needs.

Step 2: Measure the run horizontally, between the two points the spec governs

The run is the horizontal distance over which the slope applies, and it is measured level, not along the pipe or the ground. At drainage slopes the difference is negligible: 40 ft of pipe at 1/4 in per ft has a horizontal run of 39.99 ft. On a steep yard, measuring along the ground does start to matter, and the habit of measuring level costs nothing.

Measure between the points that actually bound the slope:

• A drain: from the fixture's trap arm or the upstream cleanout to where the line enters the stack, the building drain or the sewer connection, along the route the pipe will take. A route with a dogleg is longer than the straight-line distance between its ends, and the slope applies to every foot of it.
• Grade away from a foundation: from the face of the wall out to the distance the spec names.
• A slab or walk: from the high edge to the drain or the low edge, in the direction the water is meant to travel.

What breaks if you skip it: measuring the straight line between the ends of a routed drain understates the run, so the computed fall is too small and the far end comes in high. On a fixed-elevation connection that is the difference between meeting the sewer and missing it.

Step 3: Multiply, and keep the units on the line

Drop in inches = run in feet x slope in inches per foot. The feet cancel and inches remain.

For the line in the worked example below: 40 ft x 0.25 in per ft = 10 in.

Round only at the end, and round toward more fall where the spec is a minimum. A minimum slope is a floor; landing on it exactly leaves no room for a sag in the pipe or a high spot in the bedding. See related: Write the Calculation Down: The Field Math Habit, and Units Carried Through Every Line of a Calculation.

Run it backward when the ends are fixed. On a lot of real jobs the start and end elevations are already set by something you cannot move: an existing sewer tap, a floor level, a footing. Then the question is not how much drop to build but whether the available drop meets the spec. Available slope = available drop / run. If the sewer tap is 9 in lower than the start of a 40 ft run, the slope available is 9 / 40 = 0.225 in per ft, which is under 1/4 in per ft. On a pipe that needs 1/4, the route, the start elevation or the design has to change before anyone digs.

Step 4: Set a datum and write every elevation against it

A datum is a fixed reference you measure from: a string line pulled level, a laser plane, a mark on a wall. Write the start elevation and the end elevation as distances below the datum, and add intermediate marks so a sag in the middle of the run shows up.

Measure to the same surface every time. For a pipe that is the invert, the inside bottom of the pipe, because that is the surface water flows on. On site it is easier to measure to the top of the pipe, which works as long as the pipe size does not change along the run. Change pipe size and the top of pipe stops tracking the invert, so measure to invert or correct for the difference.

What breaks if you skip it: checking slope with a level at a few spots catches local slope but not cumulative error. Five sections each a little flat add up to an end elevation that is an inch high, and no single level reading looked wrong.

Step 5: Prove it with a level and a measured block

Set a block of known thickness under the downhill end of a level, so that when the pipe or form has the right slope, the bubble reads level. The block thickness is the slope times the level's length.

• On a 4 ft level at 1/4 in per ft: 4 x 0.25 = 1 in block.
• On a 2 ft level at 1/4 in per ft: 2 x 0.25 = 0.5 in block.
• On a 4 ft level at 1/8 in per ft: 4 x 0.125 = 0.5 in block.

Check the level itself first: set it on a flat surface, mark where it sits, read the bubble, then turn it end for end in the same spot. If the bubble does not read the same both ways, the level is out, and every slope check with it is out by the same amount.

The level and block check local slope. The datum readings check cumulative fall. Do both, and do them before backfill, before cover, and before any concrete is placed, because once the pipe is buried or the slab is poured, the check is a dig-up.

Worked example: a 40 ft drain and a strip of grade

The drain. A 2 in drain runs 40 ft along the route from a cleanout to the point where it ties into the building drain. The spec is 1/4 in per ft, which for that size is the common minimum in the plumbing codes, as adopted by your jurisdiction (the IPC states it in Table 704.1; check the edition your jurisdiction has adopted, because the UPC words its slope rule differently). A string line is pulled level along the trench as the datum.

DRAIN LAYOUT, TOP OF PIPE BELOW A LEVEL STRING
-----------------------------------------------
spec          1/4 in per ft = 0.25 in/ft
run           40 ft, measured level along route
drop          40 ft x 0.25 in/ft = 10.0 in

station   distance   fall so far    below string
-------   --------   -----------    ------------
start       0 ft      0.0 in          18.0 in
  A        10 ft      2.5 in          20.5 in
  B        20 ft      5.0 in          23.0 in
  C        30 ft      7.5 in          25.5 in
end        40 ft     10.0 in          28.0 in

check     28.0 - 18.0 = 10.0 in   matches drop
level     4 ft level, 1 in block, downhill end
-----------------------------------------------

Every station's fall is its distance times 0.25 in per ft, and every "below string" figure is 18.0 in plus that fall. The last line is the check that the station list and the drop agree.

On the job, the crew hits all five stations within 1/8 in except station B, which reads 22.5 in below the string, 1/2 in high. The level with its 1 in block reads level across A and across C, so the local slope near those stations looked fine. The datum reading found what the level did not: a high spot in the bedding between A and C. That section comes up, the bedding is trimmed, and B is reread at 23.0 in before backfill.

The strip of grade. The same house needs the soil re-graded along the back wall after the trench is closed. The IRC requires, in substance, that the grade fall at least 6 in within the first 10 ft from the foundation (IRC R401.3, as adopted by your jurisdiction; check the current edition). Where lot lines, walls, slopes or other physical barriers prohibit that fall, drains or swales must carry the water away instead, and a swale within 10 ft of the foundation must slope at least 2 percent. Separately, impervious surfaces within 10 ft of the foundation must slope at least 2 percent away. The barrier has to actually exist on the site; the exception is not a choice.

Convert the main rule the same way: 6 in over 10 ft is 6 / 10 = 0.6 in per ft, which is 0.6 / 12 = 0.05, so 5 percent. With a stake at the wall face and a stake at 10 ft, and a string pulled level between them, the soil at the wall must sit at least 6 in higher than the soil at the 10 ft stake. Measured down from the string: 4 in at the wall and 11 in at the stake gives 11 - 4 = 7 in of fall, which passes.

What changes the answer

• The pipe size or the code changes the slope, not the method. Larger drains commonly carry a smaller minimum slope, 1/8 in per ft in the IPC's table for 3 in through 6 in. Rerun the drain above at 1/8 in per ft: 40 ft x 0.125 in per ft = 5.0 in. The method is identical and the drop halves. Which slope applies to a given pipe is the licensed plumber's and the code's call, and the drain reference below lists them.
• A maximum, not a minimum. Some specs cap slope (an accessible route is the familiar one, where the governing accessibility standard sets the limit). For a maximum, round toward less slope and check that no section exceeds it, which is the mirror of everything above.

Where it goes wrong in the field

Mixing a percent and an inch. Shown in step 1: 2 percent of a 40 ft run read as 0.8 in instead of 0.8 ft, or 9.6 in.

Measuring to two different surfaces. Top of pipe at one end and invert at the other carries the inside diameter plus one wall thickness of error into the fall.

A string that sags. Measuring down from a string that has a belly in it makes the middle stations read short and hides a sag in the pipe. Pull the string tight, support it on long runs, or use a laser.

Trusting the end elevations and skipping the middle. Ten inches of fall between the ends does not prove the line falls everywhere; station B above proves the point.

References

• See related: Drain Pipe Slope + Venting Quick Reference
• See related: Slope Four Ways: Percent, Ratio, Inches Per Foot and Degrees
• See related: Write the Calculation Down: The Field Math Habit
• International Plumbing Code, Table 704.1, and International Residential Code, Section R401.3, in the editions your jurisdiction has adopted