How to lay out a miter cut on pipe
To lay out a miter cut on pipe, wrap a strip around the pipe to get its outside circumference, divide it into equal lines, and on each line mark the cutback from the long point: the pipe radius times the tangent of the cut angle times one minus the cosine of the line’s angle. Join the marks, wrap and scribe.
Drawn by Stretchout from the worked example below. Parallel line development.
What you need
- Paper or light sheet for the wrap template
- A tape and a straightedge
- Dividers or a scale for the spacing
- A flexible batten
- Soapstone or a scribe
Worked example
We’ll lay out a 45° miter on 10" pipe (10.750" OD), one end cut, 16 lines: half of a two-piece 90. The numbers:
- Pipe OD
- 10.75"
- Cut
- 45° from square
- Stretch-out (around the pipe)
- 33 3/4"
- Line spacing
- 2 1/8" × 16
- Long side
- 29 3/8"
- Short side
- 18 5/8"
Step by step
Step 1
Draw a baseline 33 3/4" long: the stretch-out. Square a line up at each end.
Step 2
Divide it into spaces 2 1/8" apart (16 around the whole pipe) and square a line up from each mark. Number them from the left.
Step 3
Mark each line up from the baseline for the cut. The top edge stays square:
Line Mark up 1 0" 2 7/16" 3 1 9/16" 4 3 5/16" 5 5 3/8" 6 7 7/16" 7 9 3/16" 8 10 5/16" 9 10 3/4" 10 10 5/16" 11 9 3/16" 12 7 7/16" 13 5 3/8" 14 3 5/16" 15 1 9/16" 16 7/16" Step 4
Join the marks with a smooth curve (a flexible batten helps) and cut on it.
Watch it laid out
Every step of the worked example. Play, or step through with Next and Back (or the arrow keys).
1.Draw a baseline 33 3/4" long: the stretch-out. Square a line up at each end.
The formula
With r the pipe’s outside radius and α the cut angle from square, the cutback on a line at angle θ around the pipe from the long point is r·tan α·(1 − cos θ). For a 45° cut, tan α = 1.
The deepest point is opposite the long point, θ = 180°, where the cutback is 2·r·tan α = OD·tan α. On 10" pipe at 45° that’s the full 10.750".
A two-piece 90 is two 45° cuts; a three-piece 90 is 22.5° on each joint. For both ends cut, or cuts rolled to each other, use the calculator.
Questions
How do I make a two-piece 90?
Cut each piece at 45° from square and turn one over so the cuts face each other. The worked example on this page is one of those pieces.
Can I use a saw instead?
On small pipe, yes. On bigger pipe, or with a torch, a wrap template marks the cut all the way around so it comes out true.
Why wrap the template on the OD?
The template sits on the outside of the pipe, so it’s laid out on the outside circumference. For a part rolled from plate, lay out on the mean line instead.
How many lines should I use?
16 lines is plenty for most pipe; use 24 or 32 on large diameters so the batten doesn’t have to guess between marks.
What if both ends are cut?
Lay out each end from its own long point. The calculator handles a second cut at any angle and any roll to the first.
Your sizes
Below is the miter calculator, opened on the worked example. Put in your own sizes and it redoes every number and every step for your fitting. It’s also at /stretchout/shapes/miter.