This segmented turning calculator works out the geometry for rings made of mitred segments — the segment angle, the length of each piece, and the ring diameter — so a stack of segmented rings glues up into a clean bowl or vessel. It takes the trigonometry out of a famously fussy technique.
Segments, angles and chords
A ring of N equal segments needs each segment mitred at 360 ÷ (2N) degrees on each end, so the joints close perfectly around the circle. The calculator gives that miter angle, and from your target ring diameter and segment count it computes the chord length and the board length each segment needs (including the overhang for the mitres). Get the angle even slightly wrong and the cumulative error opens gaps that no clamp can close.
Ring diameter, wall thickness, and the width of stock together decide how much usable bowl you get from each ring and how much you turn away. The tool lets you plan the segment count and stock width to leave enough wall after turning, which is where many first attempts go wrong.
Accuracy is everything
Because the errors multiply around the ring, segmented work rewards precise, repeatable cuts: a dead-accurate mitre, a sled or jig for consistency, and a sanding disc to sneak up on a perfect fit. Plan the rings with the calculator, dry-fit each one before glue-up, and the stack will align into a crisp pattern.
Designing a ring of 12 equal segments.
- Miter angle per end = 360 ÷ (2 × 12) = 15°.
- Each segment spans 30° of the circle (360 ÷ 12).
- Segment length comes from the ring diameter and that 30° chord, plus mitre overhang.
Each of the 12 segments is mitred at 15° per end; the calculator sizes the lengths from your diameter.
