FitUpGuide · The formula
Pipe offset formula: travel, run, and cut length
Travel = offset ÷ sin(angle). Run = offset ÷ tan(angle). Cut length = travel − 2 × take-out − 2 × gap. With 45 degree fittings the travel is the offset × 1.414 and the run equals the offset. For a rolling offset, put the true offset, √(rise² + roll²), in place of the offset.
Every pipe offset is a right triangle. The offset is one side, the run is the other, and the travel, the angled piece between the two fittings, is the long side. The fitting angle sets the shape of the triangle, so once you know the offset and the angle, the other two sides follow. The cut length is what is left of the travel after each fitting and each weld gap takes its share.
The terms, defined
- Offset (also called the set)
- The distance between the centerlines of the two parallel runs, measured square to them.
- Fitting angle
- The angle the travel makes with the run: 45, 22.5, 30, 60, 11.25, or whatever the fittings are cut to.
- Travel
- The centerline length of the angled piece, from the center of one fitting to the center of the other.
- Run (also advance or setback)
- How far the offset moves along the line while it moves over. It tells you where the second fitting sits.
- Take-out (take-off, center-to-end)
- The distance from a fitting's center to its end. The pipe stops there, so each fitting takes that much out of the travel.
- Gap (root gap)
- The space left between pipe and fitting at a butt weld, commonly 1/16 to 1/8 inch per joint. Each joint takes it out of the cut.
- Cut length
- The length of pipe you actually cut: the travel less both take-outs and both gaps.
- True offset
- In a rolling offset, the diagonal distance between the two centerlines, found from the rise and the roll.
Why the formulas work
In the offset triangle the offset is the side opposite the fitting angle, the run is the side next to it, and the travel is the hypotenuse. Sine is opposite over hypotenuse, so the travel is the offset divided by the sine. Tangent is opposite over adjacent, so the run is the offset divided by the tangent. Fitters write these as multipliers, 1 ÷ sin and 1 ÷ tan, so the job becomes one multiplication each.
| Angle | Travel × | Run × | Offset from travel × | Travel, 10" offset | Run, 10" offset |
|---|---|---|---|---|---|
| 11.25° | 5.126 | 5.027 | 0.195 | 51 1/4" | 50 1/4" |
| 22.5° | 2.613 | 2.414 | 0.383 | 26 1/8" | 24 1/8" |
| 30° | 2.000 | 1.732 | 0.500 | 20" | 17 5/16" |
| 45° | 1.414 | 1.000 | 0.707 | 14 1/8" | 10" |
| 60° | 1.155 | 0.577 | 0.866 | 11 9/16" | 5 3/4" |
Multipliers for every angle from 5 to 85 degrees are in the offset multiplier chart. The two angles fitters use most have their own guides: the 1.414 rule for 45s and the 60 degree offset formula.
Steps: from a measurement to a cut length
Measure the offset
Centerline to centerline, square to the runs. Measuring from the same side of both pipes gives the same number when the pipes are the same size.
Choose the fitting angle
45s are the usual choice. A smaller angle stretches the offset along the line; a bigger one makes it steeper.
Find the travel
Offset × the travel multiplier for the angle.
Find the run
Offset × the run multiplier. Use it to place the second fitting along the line.
Look up the take-out
Center-to-end for your pipe size and fitting, from the maker's chart or a take-out chart. For a 90 cut down to the angle, use R × tan(angle ÷ 2).
Subtract the allowances
Two take-outs, and two gaps if both joints are butt welds.
Round once
Convert the final decimal to the nearest 1/16 only at the end.
Worked examples
10 inch offset with 45s on 2 inch pipe
Two 45 LR butt-weld elbows, 1 3/8 inch take-out each, 1/8 inch root gap:
Travel = 10 × 1.4142 = 14.1421
Run = 10 × 1.0000 = 10
Cut = 14.1421 − 2.75 − 0.25 = 11.1421, marked 11 1/8
12 inch offset at 22.5 degrees on 2 inch pipe
Two 2 inch 90 LR elbows (3 inch center-to-end) cut down to 22.5 degrees, so each takes out 3 × tan 11.25° = 0.5967 inch:
Travel = 12 × 2.6131 = 31.3575
Run = 12 × 2.4142 = 28.9706
Cut = 31.3575 − 2 × 0.5967 − 2 × 0.125 = 29.9140, marked 29 15/16
Notice the run: a 22.5 degree offset needs almost 29 inches of line to move over 12.
Common mistakes
- Cutting the travel. The travel is center to center. The pipe is shorter by both take-outs and both gaps.
- Rounding the multiplier. 1.41 instead of 1.414 loses about 1/5 inch on a 48 inch offset. The 45 degree guide shows the numbers.
- Rounding every step. Rounding the travel, then each take-out, then subtracting can land a sixteenth off. Keep the decimals and round the cut once.
- Using a factory 45's take-out for a cut 90. A 90 cut down to 45 does not always match a factory 45 LR. On 1 inch pipe the difference is about 1/4 inch per fitting.
- Swapping run and offset. They are equal only at 45 degrees. At 30 degrees the run is 1.732 times the offset.
Related questions
- What is the 1.414 rule for 45 degree offsets?
- What is the formula for a 60 degree offset?
- What is the formula for a rolling offset?
- What are the offset multipliers for 22.5, 30, and 60 degrees?
- How do you figure cut length with take-outs and weld gaps?
- What is the take-out of a 2 inch 90 long radius elbow?
- How do you find the take-out of a 90 cut down to 45?
Doing this on the job
FitUp, an iPhone app, runs these seven steps with your pipe size and fittings and shows every line of the arithmetic, so the cut can be checked before it is made. The free pipe offset calculator on this site does the same math in a browser.
Verify measurements before cutting.