Segmented Turning Ring Calculator (Miter Angle & Segment Length)

How it works

miter angle = 180° ÷ N · outer edge = D × tan(180° ÷ N) (D across the flats) · inner edge = (D − 2w) × tan(180° ÷ N) · stock per ring = N × (outer edge + kerf) · accumulated error = 2N × angle error

A segmented ring is a regular polygon glued from trapezoidal pieces, so the angle on each end of a segment is half the polygon's exterior angle — 360° divided by the segment count, halved — and the outer edge follows from the diameter measured across the flats, which is what matters because the round vessel is turned from inside that polygon. Adding a turning allowance keeps the outside corners from disappearing when the ring is trued, and the inside edge is simply the same geometry at the smaller inner diameter. Because every joint must close at once, small angle errors do not average out but multiply by twice the segment count, which is why turners assemble half-rings, flatten them against a disc sander and then close the two halves.

Worked example

Twelve segments for a ring finishing at 200 mm, cut 6 mm oversize (206 mm across the flats) with 25 mm walls: the miter is 15°, each segment 55.2 mm on the outside edge and 41.8 mm inside, and one ring uses about 700 mm of 25 × 20 mm stock. A 0.1° error per cut would open a 2.4° gap; eight such rings stack to 160 mm.

Frequently asked questions