FitUpGuide · Fittings
The take-out of a 90 cut down to any angle
Take-out = the 90's center-to-end × tan(angle ÷ 2). A 2 inch 90 LR has a 3 inch center-to-end, so cut down to 22.5 degrees it takes out 3 × tan 11.25° = 0.597 inch, about 5/8. Cut down to 45, it takes out 3 × tan 22.5° = 1.243 inch, about 1 1/4.
Factory fittings come in 90s and 45s. For a 22.5, a 30, a 60, or the odd angle a setback forces on you, the usual move is to cut a 90 down. The cut fitting is shorter, and its center moves, so it needs its own take-out.
Why it is the tangent of half the angle
A long radius 90's center-to-end equals its bend radius R, because tan 45° = 1. The fitting's center is the point where the tangents at its two ends cross. When you keep only θ degrees of the bend, the tangent at the new cut end crosses the tangent at the welding end at a distance R × tan(θ ÷ 2) from that end. That distance is the new take-out, the same at both ends of the cut fitting.
Factors for the common angles
Multiply the 90's center-to-end by the factor. For long radius 90s, that is 1.5 × the pipe size × the factor; for short radius, 1 × the size × the factor.
| Pipe size | 90 LR | 11.25° | 22.5° | 30° | 45° | 60° |
|---|---|---|---|---|---|---|
| Factor | 1.0000 | 0.0985 | 0.1989 | 0.2679 | 0.4142 | 0.5774 |
| 1/2 in | 1 1/2" | 1/8" | 5/16" | 3/8" | 5/8" | 7/8" |
| 3/4 in | 1 1/8" | 1/8" | 1/4" | 5/16" | 7/16" | 5/8" |
| 1 in | 1 1/2" | 1/8" | 5/16" | 3/8" | 5/8" | 7/8" |
| 1 1/4 in | 1 7/8" | 3/16" | 3/8" | 1/2" | 3/4" | 1 1/16" |
| 1 1/2 in | 2 1/4" | 1/4" | 7/16" | 5/8" | 15/16" | 1 5/16" |
| 2 in | 3" | 5/16" | 5/8" | 13/16" | 1 1/4" | 1 3/4" |
| 2 1/2 in | 3 3/4" | 3/8" | 3/4" | 1" | 1 9/16" | 2 3/16" |
| 3 in | 4 1/2" | 7/16" | 7/8" | 1 3/16" | 1 7/8" | 2 5/8" |
| 3 1/2 in | 5 1/4" | 1/2" | 1 1/16" | 1 7/16" | 2 3/16" | 3" |
| 4 in | 6" | 9/16" | 1 3/16" | 1 5/8" | 2 1/2" | 3 7/16" |
| 5 in | 7 1/2" | 3/4" | 1 1/2" | 2" | 3 1/8" | 4 5/16" |
| 6 in | 9" | 7/8" | 1 13/16" | 2 7/16" | 3 3/4" | 5 3/16" |
| 8 in | 12" | 1 3/16" | 2 3/8" | 3 3/16" | 5" | 6 15/16" |
| 10 in | 15" | 1 1/2" | 3" | 4" | 6 3/16" | 8 11/16" |
| 12 in | 18" | 1 3/4" | 3 9/16" | 4 13/16" | 7 7/16" | 10 3/8" |
Steps
Find the 90's center-to-end
From the take-out chart or by measuring the fitting.
Halve the angle you need
22.5 degrees becomes 11.25.
Multiply by the tangent of the half angle
That is the take-out of the cut fitting at each end.
Use it in the cut length
Travel − 2 × this take-out − 2 × gap, as in take-outs and cut length.
Worked examples
12 inch offset with 2 inch 90 LRs cut to 22.5
Take-out = 3 × tan 11.25° = 0.5967
Travel = 12 × 2.6131 = 31.3575
Cut = 31.3575 − 2 × 0.5967 − 2 × 0.125 = 29.9140, marked 29 15/16
4 inch 90 LR cut to 30
Take-out = 6 × tan 15° = 1.6077, marked 1 5/8
Where to mark the cut
The cut runs through the center of the bend, so it is longer on the outside (heel) than on the inside (throat). Measured along the fitting from the welding end, with θ in radians (degrees × 0.01745):
Heel = (R + OD ÷ 2) × θ
Throat = (R − OD ÷ 2) × θ
Centerline = R × θ
For a 2 inch 90 LR (R = 3, outside diameter 2.375) kept at 22.5 degrees, θ = 0.3927: the heel mark is 1.644 (1 5/8) from the end, the throat mark 0.712 (11/16), and the centerline marks on each side 1.178 (1 3/16). Join the four marks around the fitting for the cut line, and prepare the cut end for welding the way your procedure calls for.
Common mistakes
- Tangent of the full angle. tan 22.5° is 0.414; tan 11.25° is 0.199. Using the full angle doubles the take-out.
- Using the factory 45 value for a cut 90. On 1 inch pipe a factory 45 LR takes out 7/8 and a 90 cut to 45 takes out about 5/8.
- Measuring the heel and throat from the wrong end. Measure from the end you keep, the welding end.
- Forgetting the gap. A cut fitting still gets a root gap at each butt weld.
Related questions
- What are the travel and run multipliers for 22.5 degrees?
- How do you figure a 60 degree offset with 90s cut to 60?
- How do I find the angle for a rolling offset with a fixed setback?
- What is the center-to-end of a 90 LR for each pipe size?
Built into the app
At any angle other than 45, FitUp's offset tools use exactly this: a 90 LR or 90 SR cut to the angle, with the take-out worked out as center-to-end × tan(angle ÷ 2) and shown under the cut. Those angles are part of Pro. The free web calculator does it too.
Default values. Check your fittings. Verify measurements before cutting.