How to Cut a Simple Offset With Fitting Constants
Why this matters
A simple offset moves a run of pipe sideways to clear a joist, a duct or a wall jog, using two matching fittings and one diagonal piece between them. The constant that turns the sideways distance into the diagonal is the easy part, and most techs know 1.414 for a 45. The piece still gets cut wrong, because the constant gives a distance between fitting centers and the saw needs a distance between pipe ends, and two different corrections have to be made to get from one to the other. Miss one and the piece is either too long to seat or too short to engage at all, and on a glued or soldered joint you find out after it is permanent. This card runs one offset from tape to saw, with each step's number carried into the next.
The geometry, labeled
B (center of upper 45)
+======================== upper run
/:
/ :
travel / :
14.14 / : set
in / : 10 in
/ :
/ :
====+.......:
A (center of lower 45)
lower run
|<----->|
run 10 in
cut = travel - (C to E at A) - (C to E at B)
+ (socket at A) + (socket at B)
take-off per fitting = C to E - socket depth
Four terms, and they are worth having straight before any numbers:
- Set: the sideways distance between the two run center lines, measured square to the runs.
- Travel: the length of the diagonal along its center line, from the center of fitting A to the center of fitting B.
- Run: how far along the pipe line the offset advances while it moves sideways.
- Take-off (also called the fitting allowance): for each fitting, the distance from its center to the point where the pipe stops inside it. It is the fitting's center-to-end dimension less the depth the pipe goes into it.
The constants themselves, for every common fitting angle, and why each one is what it is, are owned by Pipe Offset Constants for Every Fitting Angle. This card uses the 45 degree pair: travel constant 1.414, run constant 1.000.
The procedure, run on one offset
The job: a 1-1/2 in line has to jog sideways to clear a framing member, using two 45 degree socket elbows. The fitting dimensions below are the ones measured on the fittings in hand for this example; yours come from your fittings.
1. Measure the set center to center, square to the runs. The set is not the gap between the pipes and it is not measured on a slant. When both runs are the same size, measure from the top of one pipe to the top of the other, or the bottom of one to the bottom of the other: the same edge on both pipes puts the half diameters on both sides of the measurement and they cancel, so edge to same edge equals center to center. If the two runs are different sizes, correct for half the difference in outside diameters. Here the reading is 10 in, top to top, with a square against the runs.
Why it matters: every error in the set comes through multiplied by the travel constant. A set read 1/4 in long on a 45 puts 0.25 x 1.414 = 0.35 in into the travel.
2. Pick the fitting angle and look up its pair of constants. 45s: travel 1.414, run 1.000. Before going on, check the run: 10 in x 1.000 = 10 in along the line. If the obstruction leaves less than 10 in of room along the pipe for the offset, 45s do not fit and a steeper fitting is needed. Better to know now than after the first fitting is glued.
3. Multiply the set by the travel constant. 10 in x 1.414 = 14.14 in, center to center. Carry the unrounded figure: with the full constant, 1.41421 x 10 = 14.142 in. Do not round to a fraction yet. See related: Write the Calculation Down: The Field Math Habit.
4. Measure the fitting, and find its take-off. On the elbow in hand, find the fitting's center: the point where the center lines of its two openings cross. Measure from there to the face of the socket (the center-to-end dimension), and measure the socket depth from its face to the shoulder where the pipe bottoms out. For this fitting:
Line Item Value Unit
1 Center to end (to socket face) 1.25 in
2 Socket depth (face to shoulder) 0.75 in
3 Take-off = L1 - L2 0.50 in
Both elbows are the same make and size, so both have a 0.50 in take-off. On a different make, even of the same size and angle, the take-off can differ; read the maker's dimension data or measure the actual fitting rather than reusing a figure from another box.
5. Figure the cut length from the travel. Subtract each fitting's center-to-end, then add back each fitting's socket depth, which is the same as subtracting the two take-offs:
Line Item Value Unit
4 Travel (center to center) 14.142 in
5 Less C to E, A and B: 2 x 1.25 2.50 in
6 Plus socket A and B: 2 x 0.75 1.50 in
7 Cut length = L4 - L5 + L6 13.142 in
8 Check: L4 - 2 x take-off
14.142 - 2 x 0.50 13.142 in
9 Nearest 1/16 in 13-1/8 in
0.142 in is 2.27 sixteenths, so the nearest sixteenth is 2/16, which is 1/8. The cut is 13-1/8 in, 0.017 in short of exact, which a socket absorbs without notice. Converting decimals to tape fractions is owned by How to Convert Decimal Feet to Feet, Inches and Sixteenths.
Hazard at this step: if the offset goes into an existing line, isolate the supply, open a fixture downstream to relieve pressure and drain the line below the cut before the saw touches it. On a drain or vent line, cap or plug the open end as soon as it is cut so sewer gas does not come into the room. Cut with the pipe supported on both sides of the blade so the off-cut does not pinch it.
6. Mark the layout so fitting A lands where it must. The run tells you where fitting B's center will fall: 10 in along the line from A's center. Mark A's center on the lower run, mark B's center 10 in further on the upper run, and confirm the obstruction sits between them with room for the fitting bodies.
7. Dry-fit every piece before any joint is made permanent. Push the cut piece fully home in both sockets, hold the assembly in place, and check that the upper fitting's outlet lines up with the upper run at the 10 in set without being forced. A dry fit that needs a shove to line up means one of the numbers above is wrong, and it costs a minute to find now and a fitting and a length of pipe to find after the joint is glued.
Hazard when joining: solvent cement and primer give off flammable vapor that is also an inhalation hazard. Ventilate the space, keep ignition sources away, cap the cans between uses and follow the product's safety data sheet. On copper, soldering is hot work: a fire extinguisher at hand, a heat shield against framing, and a check of the area for smoldering after the joint cools. Cut pipe edges are sharp; deburr them, which is also part of making the joint seat.
8. Restore and test. If you isolated a supply line, wait the cure time on the cement label (or let solder joints cool), close the fixture you opened, then open the supply slowly and check every new joint for drips before anything is covered. On a drain or vent, pull the plug and run water through the new section, checking each joint dry. A joint that weeps comes apart and gets redone; it does not get closed in.
What each wrong cut looks like
The two corrections in step 5 pull in opposite directions, and each one dropped produces a different, recognizable failure.
Both center-to-end figures subtracted, socket depth forgotten. Cut = 14.142 minus 2.50 = 11.64 in. That length runs exactly from the face of one socket to the face of the other, so the pipe enters neither socket. There is no joint at all, which you will see at the dry fit if you do one. Glued, it does not hold, and if someone forces the run over to make it reach, the offset's set changes.
No allowance at all, travel cut as center to center. Cut = 14.14 in, 1.00 in longer than it should be (14.142 minus 13.142). The pipe bottoms out in both sockets with the fitting centers still 1.00 in too far apart along the diagonal. That pushes the upper fitting 1.00 x sin 45 = 0.71 in further sideways and 0.71 in further along the line. On a rigid run, 0.71 in of extra set either will not go together or goes together under stress that the joint carries for its whole life.
Right allowance, wrong constant. A 22-1/2 offset figured with the 45 constant comes up far short. The constants card works that case through, and the sanity check it gives is the quickest catch: the travel for a 45 is about 1.4 times the set, so a 10 in set that produced a 14 in travel is right for 45s and wrong for anything else.
What changes the method
- Threaded fittings. The pipe does not enter a smooth socket to a shoulder; it threads in to a thread engagement that depends on the size and how tight the joint is made. Take-off = center-to-end minus the thread engagement, and the engagement comes from the fitting maker's data or a standard thread engagement table for that size. Make up a test joint if the work is unfamiliar.
- Unequal fittings. If the two fittings differ (a street elbow at one end, a different make at the other), each gets its own take-off, and the cut subtracts the two different values rather than twice one.
- Drain and vent piping. Whether an offset is allowed where you want it, which fitting angles may be used, and what it does to pipe sizing on a drain or vent are set by the plumbing code as adopted by your jurisdiction. The math on this card is the same; the decision to make that offset belongs to the plumber on the job, licensed where your state or locality requires it.
How to verify you got this right
- The set was measured edge to same edge and square to the runs.
- Lines 7 and 8 agree: center-to-end and socket depth give the same cut as twice the take-off.
- The travel is about 1.41 times the set for 45s (14.14 / 10 = 1.41).
- The dry fit lines up without force, and the pipe seats fully in both sockets with its insertion depth marked before any joint is made.
- The record shows the take-off for that make of fitting, so the next offset with the same fittings starts from a measured figure.
References
- See related: Pipe Offset Constants for Every Fitting Angle
- See related: How to Convert Decimal Feet to Feet, Inches and Sixteenths
- See related: Write the Calculation Down: The Field Math Habit
- Fitting manufacturers' dimensional data (center-to-end and socket depth)
- Solvent cement and primer safety data sheets