Pipe Offset Constants for Every Fitting Angle

Why this matters

An offset moves a pipe sideways to get around something, using two matching fittings and a diagonal piece between them. Everyone who has cut one knows the 45 degree constant, 1.414. The trouble starts when the job calls for a different fitting angle, the tech reaches for the number they know, and a pipe cut for a 45 gets installed between two 22-1/2 fittings. It comes up roughly 17 in short on a 14 in offset, because a shallower fitting needs a much longer diagonal to cover the same sideways distance.

The fix is a short table of constants, one pair per fitting angle, and an understanding of what each pair means. This card gives the constants for the common fitting angles, shows where they come from, works an offset with each, and shows how the run constant tells you which fitting angle fits the space you have. Cutting a simple offset step by step and figuring a rolling offset each have their own cards.

The three dimensions of an offset

SIMPLE OFFSET, TWO EQUAL FITTINGS

            fitting B
  line 2   --------o==========>
                  /
                 /  <- TRAVEL (center to center
                /      of fittings, diagonal)
               /
              /  a = fitting angle,
             / a   measured from the
  line 1 ===o     original line direction
        fitting A
           |<-- RUN -->|
  SET = sideways distance between line 1
        and line 2, center to center

• Set (also called offset): the distance the pipe moves sideways, measured center to center between the two parallel lines.
• Run (also called advance): the distance the offset takes up along the direction of the pipe, from the center of the first fitting to the center of the second.
• Travel: the center-to-center length of the diagonal piece, from one fitting's center to the other's.
• Fitting angle: how far the fitting turns the pipe away from its original direction. A 45 degree fitting turns it 45 degrees; a 22-1/2 turns it 22-1/2.

You measure the set, choose the fitting angle, and the constants give the travel and the run.

The constants and where they come from

The set, run and travel are the three sides of a right triangle, with the fitting angle at the corner where the diagonal leaves the original line. So:

• Travel = set / sine of the fitting angle. The travel constant is 1 / sin(angle).
• Run = set / tangent of the fitting angle. The run constant is 1 / tan(angle).

OFFSET CONSTANTS, PER INCH OF SET
------------------------------------------------
 fitting     travel = set x    run = set x
 angle       (1 / sin)         (1 / tan)
 --------    ------------      -----------
 11-1/4        5.126             5.027
 22-1/2        2.613             2.414
 30            2.000             1.732
 45            1.414             1.000
 60            1.155             0.577
------------------------------------------------
 check: set^2 + run^2 = travel^2

Reading the table. The shallower the fitting, the larger both constants, because a fitting that turns only a little has to travel a long way to move sideways at all. At 45 degrees the run equals the set (constant 1.000), which is why a 45 offset is easy to lay out: it takes up exactly as much room along the line as it moves sideways. At 60 degrees the run is a bit over half the set; at 11-1/4 it is more than five times the set.

Every constant can be rebuilt on site. Any calculator with sine and tangent gives them: 1 / sin(22.5) = 1 / 0.3827 = 2.613. You do not need to trust a table you half remember.

The worked example: a 14 inch set

A line has to move 14 in sideways, center to center, to clear a beam. The tech works the offset at each fitting angle to see what each one costs in length and in room.

Check one row by the triangle. For the 22-1/2: set squared plus run squared = 196 + 1,142.4 = 1,338.4, and the square root is 36.58 in, which matches the travel. Do this check on whichever row you are actually going to cut.

The 22-1/2 travel in tape terms. 36.58 in: 0.58 x 16 = 9.3 sixteenths, so 36-9/16 in center to center. See related: How to Convert Decimal Feet to Feet, Inches and Sixteenths.

The wrong-constant case. If the tech uses the 45 constant with 22-1/2 fittings, the travel comes out at 19.80 in instead of 36.58 in, 16.78 in short. Installed between 22-1/2 fittings, that piece does not reach: it gives only 19.80 x sin(22.5) = 7.58 in of set, about half of the 14 needed. The pipe is scrap.

The sanity check that catches it. For any fitting angle, the travel constant tells you how many times longer than the set the diagonal must be. For 22-1/2, that is about 2.6 times. A computed travel of 19.80 in on a 14 in set is only 1.4 times the set, which is the 45 ratio, and that mismatch is visible in a second without a calculator.

Choosing the fitting angle from the room you have

The run column is the one people skip, and it is the one that decides which fitting angle you can use. Say the beam leaves 30 in of straight space along the line in which the offset has to happen, fitting center to fitting center.

• 11-1/4 needs 70.38 in. Does not fit.
• 22-1/2 needs 33.80 in. Does not fit.
• 30 needs 24.25 in. Fits, with about 5-3/4 in to spare.
• 45 needs 14.00 in. Fits easily.
• 60 needs 8.08 in. Fits easily.

The shallower fittings make a gentler change of direction, which is often preferred for flow, for cleaning and for how the work looks, but they cost room along the line. When the run constant times the set is more than the space available, that angle is out regardless of preference. On drainage and venting, which fitting angles and offsets are permitted, and what an offset does to sizing, is set by the plumbing code your jurisdiction has adopted; that is a question for the licensed plumber on the job, not one this table answers.

From center-to-center to cut length

Every number above is center to center of the fittings. The pipe you cut is shorter, because part of each end sits inside a fitting and the fitting's own body takes up length.

Cut length = travel - (take-off of fitting A) - (take-off of fitting B).

The take-off (also called the fitting allowance) is the distance from a fitting's center to the point where the pipe stops inside it, and it depends on the fitting's type, size, angle and manufacturer. Read it from the manufacturer's dimension data, or measure it on the actual fitting: the distance from the fitting's center point to the bottom of the socket, or for threaded work, allowing for thread engagement. With two identical fittings, subtract the same take-off twice.

Where this goes wrong. Using the travel as the cut length makes the piece too long by two take-offs. Measuring the take-off on a 45 and using it for a 22-1/2 of the same size is a smaller error but a real one, because the fittings have different bodies. Write the take-off on the ticket next to the travel so the cut length can be checked.

Measuring the set correctly

The constants are exact; the set is the measurement, and it is where the real errors live.

• Center to center, not edge to edge across the gap. If both lines are the same pipe size, measuring from the same side of each pipe (top of one to top of the other) equals center to center. Measuring the clear gap between them does not; it is short by a full pipe diameter.
• Square to the lines. The set is measured perpendicular to the parallel lines. A tape held at an angle across them reads long, and the offset comes out too long to match.
• In one plane. A simple offset moves in one plane. If the line also has to rise or drop while it moves sideways, the offset is a rolling offset, and the true set is the diagonal of the two moves. See related: How to Figure a Rolling Offset.

A set error is multiplied by the same constant. Whatever you get wrong in the set, the travel gets wrong by the travel constant times as much. A set measured 1/4 in off becomes 0.25 x 1.414 = 0.35 in of travel error on a 45, 0.25 x 2.613 = 0.65 in on a 22-1/2, and 0.25 x 5.126 = 1.28 in on an 11-1/4. The shallower the fitting, the more carefully the set has to be measured, which is worth knowing before you pick the angle that looks nicest.

The same constants in other trades

The travel constants are the same numbers conduit benders use as bend multipliers, because a conduit offset is the same triangle made with two bends instead of two fittings. Conduit adds a correction for the length a bend consumes, called shrink, which pipe fittings do not have. See related: How to Figure Conduit Offset and Shrink. Duct offsets, rail and handrail transitions, and framing layouts for an angled member use the same sine and tangent relationships, and the table above applies to any of them where two equal angles make the offset.

References

• Pipe fitting manufacturers' dimension tables, for fitting take-off by type, size and angle
• The plumbing code as adopted by your jurisdiction, for permitted offsets and fittings on drainage and vent piping
• See related: Trade Math and Imperial Fractions Reference
• See related: How to Cut a Simple Offset With Fitting Constants
• See related: The Rolling Offset Cut Short Because the Roll Was Ignored