FabLayout

Pipe miter cut calculator

For a pipe end cut at an angle, such as one piece of a two-piece elbow or a pipe against a sloped face: enter the diameter, the shortest side and the cut angle. You get the longest side and a scale drawing.

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Pipe miter cut

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634.6 mm166.1 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

98.8mm

Exact geometry

Shortest side
49.4 mm
Longest side
166.0 mm
Sheet size
634.6 × 166.0 mm

How to lay it out

  1. Draw the stretchout

    Draw a straight base line as long as the circumference of the sheet middle and divide it into equal parts.

  2. Raise the measuring lines

    Square a line up from every division point. The first and last lines are the seam, on the shortest side of the pipe.

  3. Mark the heights

    On each line, mark its height from the base line. The heights rise from the shortest side at the seam to the longest side on the middle line.

  4. Draw the cut curve and cut

    Join the marks with a smooth curve, add your seam allowance outside both seam lines and cut.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 31, Fig. 310, p. 125

Method and formula

A round pipe cut by a flat plane at an angle unrolls into a strip with a straight bottom edge and a wave-shaped top edge. The seam sits on the shortest side.

  • Height of the line at angle θ around the pipe h = H + (r − rn × cos θ) × tan α, where H is the shortest side, r is half the diameter, rn is the radius of the sheet middle and α is the cut angle.
  • Longest side (θ = 180°) = H + (r + rn) × tan α.
  • Strip length = 2π × rn.

The cut angle is measured from a square cut, so 0° gives a plain rectangle. With sheet thickness the strip is developed on the middle of the sheet, while the cut plane stays where you measured it. The pattern is exact.

Worked example

D = 200 mm, shortest side 50 mm, cut angle 30°, thin sheet: r = 100, tan 30° = 0.57735. The lines at 0°, 90°, 180° and 270° are 50, 107.74, 165.47 and 107.74 mm high, and the seam line at 360° is 50 mm again. They stand 157.08 mm apart on a strip 628.32 mm long.

Questions

What is the cut angle measured from?

From a square cut. 0° is a plain square end. The angle is the tilt of the cut plane away from the pipe section, up to 89°. For each piece of a two-piece 90° elbow it is 45°.

How is this different from the pipe roof penetration page?

This page gives only the pipe, cut by one flat plane. The roof penetration page also gives the roof plate with its elliptical hole, and handles a pipe that sits over a ridge.

Which measurement is the shortest side?

The length of the pipe on its short side, from the square end to the cut. The seam is placed on that line, so it is the shortest weld or lap.

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