How to Figure a Rolling Offset
Why this matters
A rolling offset moves a pipe sideways and up (or down) at the same time: the two parallel runs are separated both horizontally and vertically, and one diagonal piece has to cover both. It is common wherever a line has to clear something in two directions at once, under a beam and around a duct, from one side of a chase to the other at a different height. The mistake that ruins it is treating it as a simple offset in whichever direction looks bigger, which cuts the diagonal far too short. The fix is one extra line of arithmetic before the familiar one: find the true offset, the straight-line distance between the two run center lines, and then the job is an ordinary simple offset tipped over into a slanted plane.
The box, seen from the end
END VIEW, looking along the parallel runs
o upper run center
/|
/ |
true offset / |
20 in / | rise
(the plane / | 16 in
the travel / | (measured plumb)
lies in) / |
o-------+
lower run center
|<----->|
roll 12 in (measured level)
fittings rolled 36.9 deg off plumb, toward the roll
Seen from the end, the two runs are two points. The horizontal distance between them is the roll, the vertical distance is the rise, and the straight line between them is the true offset. The diagonal pipe lies in the slanted plane that contains that line and runs along the pipes. Turn your head to look square at that plane and you see an ordinary simple offset whose set is the true offset. Everything after step 2 is the simple offset method; see related: How to Cut a Simple Offset With Fitting Constants.
The steps, run on one offset
The job: a line has to roll 12 in sideways and rise 16 in to clear a beam and a duct, using two 45 degree socket fittings.
1. Measure the roll and the rise, center to center, in a plane square to the runs. Roll is measured level, rise is measured plumb, and both are taken at the same point along the line. Use a level across from the lower run's center and a plumb line or level dropped from the upper run's center, and measure where they meet. As with a simple offset, edge to same edge on equal pipe sizes gives center to center. Here: roll 12 in, rise 16 in.
Hazard at this step: rolling offsets are usually overhead. Work from a ladder or platform set for the height, maintain three points of contact while measuring, and do not stand on the top cap or the step below it. Hand a tape across rather than reaching past your balance.
Why this step is the one to be careful with: an error in either measurement carries into the true offset, though less than one for one. The true offset changes by (rise / true offset) times an error in the rise and (roll / true offset) times an error in the roll. Here that is 16 / 20 = 0.8 and 12 / 20 = 0.6, so a rise read 1/4 in long adds 0.2 in to the true offset and 0.28 in to the 45 travel (0.2 x 1.414). The larger of the two measurements carries more of the error, so it deserves the second look.
2. Find the true offset: the square root of roll squared plus rise squared. This is the Pythagorean relationship, and it holds because roll and rise were measured at right angles to each other.
Line Item Value Unit
1 Roll 12 in
2 Rise 16 in
3 Roll x roll 144 sq in
4 Rise x rise 256 sq in
5 L3 + L4 400 sq in
6 True offset = sq root of L5 20.00 in
Two checks on line 6. First, it must be longer than either input and shorter than their sum: 20 is more than 16 and less than 28. Second, 12-16-20 is the 3-4-5 triangle scaled by four, so the answer can be confirmed in your head (and if it is not a clean triple, a tape stretched straight between the two center lines confirms it on site, where they are reachable). Scaled triples are owned by How to Square a Layout With Diagonals and a Triple.
3. Multiply the true offset by the fitting's constants. For 45s, travel 1.414 and run 1.000, from Pipe Offset Constants for Every Fitting Angle.
Line Item Value Unit
7 Travel = 20.00 x 1.414 28.28 in
(unrounded 1.41421 x 20) 28.284 in
8 Advance along line = 20 x 1.000 20.00 in
The diagonal is 28.28 in center to center, and fitting B's center lands 20 in further along the line than fitting A's. Check the advance against the room you have along the pipe before going further: if the obstruction leaves less than 20 in for the offset to happen in, 45s will not fit.
4. Subtract the take-offs for the cut. The fittings for this job measure a 0.75 in take-off each (center-to-end less socket depth, measured as in the simple offset card).
Line Item Value Unit
9 Take-off, each fitting 0.75 in
10 Cut = 28.284 - 2 x 0.75 26.784 in
11 Nearest 1/16 in 26-13/16 in
0.784 in is 12.54 sixteenths, so the nearest sixteenth is 13/16. The cut is 26-13/16 in, 0.028 in long, which the sockets take up.
Hazard at this step: cutting into an existing line means isolating it, relieving pressure through a downstream fixture and draining below the cut first; an open drain or vent end gets capped as soon as it is cut. Ventilate for solvent cement and primer vapor, and keep ignition sources away from both.
5. Roll the fittings to the true-offset plane. This is the step that makes it a rolling offset in the metal as well as on paper. Both fittings have to turn out of plumb by the same angle so that the diagonal points from one run center to the other. Measured from plumb toward the roll side, that angle is the one whose tangent is roll / rise: 12 / 16 = 0.75, which is 36.9 degrees off plumb (or 53.1 degrees up from level; name the frame when you tell anyone the number). An angle finder on the fitting's outlet sets it. In practice, many fitters dry-fit the travel piece into fitting A, then turn the assembly until the far end lines up with the upper run's center line, and mark both fittings across the joint so the alignment survives being taken apart for gluing.
6. Dry-fit, check both distances, then join. With every piece pushed fully home, the upper fitting's outlet should sit on the upper run's center line: 12 in over and 16 in up from the lower run, and 20 in along the line from fitting A. Check all three. A dry fit that is right in rise and wrong in roll means the fittings are rolled to the wrong angle, not that the cut is wrong.
If you isolated an existing line, restore it only after the cement's labeled cure time: close the fixture you opened, open the supply slowly, and check every new joint for drips before anything is covered. A drain or vent gets its plug pulled and water run through it, with each joint checked dry.
The one-dimension mistake, in one number
Figuring this as a simple offset on the rise alone gives a travel of 16 x 1.414 = 22.63 in, 5.66 in short of the 28.28 it needs (28.28 minus 22.63). Figuring it on the roll alone gives 16.97 in, 11.31 short. Either piece is scrap, and the rise-only version is the more dangerous one because it is close enough to look plausible at a glance. A full case of that error, and how it was caught, is The Rolling Offset Cut Short Because the Roll Was Ignored.
The quick catch: the true offset is always longer than the larger of roll and rise. If the travel you are about to cut is only 1.41 times the larger measurement, the roll was never added.
When 45s do not fit: the same offset with 60s
If step 3 shows the 20 in advance is more room than the line has, a steeper fitting shortens it. With 60 degree fittings (travel constant 1.155, run constant 0.577):
- Travel = 20.00 x 1.155 = 23.10 in
- Advance = 20.00 x 0.577 = 11.54 in
The advance falls from 20 in to 11.54 in, at the cost of a sharper change of direction. Whether a steeper fitting is acceptable on a given line (flow, cleanout access, or a drain where the code as adopted limits fitting choice) is a separate decision; on drainage and venting it is the licensed plumber's.
What changes the method
- The runs are not parallel. Everything above assumes the two runs point the same way. If they converge or diverge, the roll and rise change along the line, and the offset is no longer a single plane problem. Make the runs parallel first, or lay the piece out full size.
- The two fittings differ. Each gets its own take-off in step 4, as with any simple offset.
- The offset turns downward. A rolling offset that drops rather than rises is the same box upside down: measure the drop plumb, it goes into the square root exactly as the rise did, and the fittings roll off plumb by the same angle toward the roll side, pointing down instead of up.
- The true offset can be measured directly. Where you can reach both center lines at the same point along the run, a tape stretched straight between them gives the true offset without the square root. Measure it and also compute it; two methods agreeing is worth more than either alone.
How to verify you got this right
- Roll was measured level and rise plumb, at the same point along the runs.
- The true offset is longer than the larger input and shorter than their sum, and a triple or a direct tape check confirms it.
- The travel is 1.414 times the true offset, not 1.414 times the rise.
- The fittings are rolled to the same angle and marked across the joint before it is made permanent.
- The dry fit lands on all three numbers: roll, rise and advance.
References
- See related: How to Cut a Simple Offset With Fitting Constants
- See related: Pipe Offset Constants for Every Fitting Angle
- See related: How to Square a Layout With Diagonals and a Triple
- See related: The Rolling Offset Cut Short Because the Roll Was Ignored
- Fitting manufacturers' dimensional data