Segmented Woodturning Calculator

How It Works

Segmented woodturning builds rings from multiple flat board segments glued together, then turns the assembly round on a lathe. The key geometry problem is calculating the miter angle and segment length so that N pieces form a perfect closed polygon.

The math:

• Miter angle = 180° ÷ N (half the included angle of each segment)
• Saw tilt = 90° − miter angle (the angle you set on your miter saw or table saw sled)
• Segment outer length = outer diameter × sin(π ÷ N) — the outer edge of each piece
• Inner diameter = outer diameter − (2 × board thickness)
• Board min width = thickness ÷ cos(π ÷ N) — ensures the board covers the segment geometry

The calculator includes a 10% waste factor for total stock length to account for saw kerf, setup cuts, and defects.

How to Use

1. Set number of segments — 12 is the most common (15° miter), 8 for bold patterns, 24+ for smooth curves
2. Enter target outer diameter — the finished outside diameter of the ring before turning
3. Enter board thickness — the radial depth of each segment (how thick the ring wall will be)
4. Read cutting angles — set your saw to the miter angle displayed
5. Cut segments to the outer length — measure along the outer (longer) edge of each piece
6. Check warnings — the calculator alerts you to impractical configurations

Tips

• Always make a test cut first. Cut two scrap pieces at the calculated miter angle and check that they form the correct included angle when mated.
• Grain direction matters — orient grain along the segment length for maximum strength at the glue joints.
• Sanding to final diameter removes 1-2mm per side. Size your ring 2-4mm oversize in both diameter and height.
• Glue in halves, then join halves. Gluing all segments at once makes alignment nearly impossible. Glue pairs, then join pairs into quarters, then halves, then the full ring.
• Precision compounds — a 0.5° error at the saw multiplies by N segments. For 12 segments, that's 6° of cumulative error. Use a digital angle gauge.
• More segments = smoother ring but harder to cut. 12-16 segments offers the best balance of smoothness and practicality for most turners.

FAQ

Why 12 segments? Can I use a different number?

12 is popular because 15° is easy to set on most miter saws and produces a ring that looks nearly circular even before turning. You can use any number from 6 (hexagonal) to 36+. Fewer segments create a more polygonal look and bold pattern; more segments produce smoother rings but require tighter precision.

How do I calculate the miter angle formula?

The miter angle is simply 180° divided by the number of segments. For 12 segments: 180/12 = 15°. For 8 segments: 180/8 = 22.5°. This is the angle each cut makes relative to the segment's centerline — the two cuts on adjacent segments meet to form the full polygon vertex angle.

What does "minimum board width" mean?

The board width must be at least as wide as the segment's radial projection — that is, the board must fully contain the trapezoidal cross-section of the segment. If your board is narrower than the minimum, the segment edges will extend beyond the board face, leaving gaps in the ring.

Why does the waste factor matter?

The 10% waste factor accounts for: saw kerf (1-3mm per cut), setup/test cuts, defects in the wood, and slight variations in segment length. For exotic or expensive woods, you might reduce this to 5%, but always have at least one extra segment's worth of material.

How thick should my segments be?

It depends on the finished wall thickness you want after turning. If your final bowl wall is 6mm, you need at least 10-12mm segment thickness (6mm final + 2mm turning allowance per side). For vessels with thick walls (decorative pieces), 20-25mm is common.

Related Tools

• Wood Shrinkage Calculator — Predict dimensional changes as your wood acclimates
• Sheet Metal Bend Calculator — Calculate flat patterns for metal ring segments

Last reviewed: June 2026