Sawdust Math

Segmented Turning Calculator

Segments, diameters in — miter angle, edge lengths, and strip length out, with a live ring diagram. The trig, done for you.

By bytesCaleb

15.00° miter (cut) angle

Outer edge length
2.679″
Inner edge length
1.876″
Segment (ring) width
1.50″
Strip length per ring
32.2″
…with 10% waste
35.4″

Set your miter gauge or saw to 15.00° — both ends of every segment, 12 segments per ring. Tiny angle errors stack: 12 segments × 2 cuts means a 0.1° error becomes 2.4° of gap.

Lengths are along the segment edges (circumscribed ring), so the glued ring finishes slightly proud of 10.0″ — you turn it down to final size. Cut a test ring from scrap first.

The geometry, shown honestly

A segment ring is a circumscribed polygon: N trapezoids glued edge to edge. Each joint must swallow 360° ÷ N of the circle, and since every joint is formed by two cut faces, each cut is half that:

cut angle = 180° ÷ N

The outer edge of each trapezoid is OD × tan(180°/N) and the inner edge ID × tan(180°/N). Multiply the outer edge by N and you know how long a strip to mill for the whole ring — we add 10% because kerf, snipe, and one sacrificial test segment are facts of life.

Working tips that save rings

  • Cut every segment from one strip with a stop block — identical lengths matter as much as identical angles.
  • Glue in half-rings. Two halves sanded flat and mated absorb tiny angle errors; a full-circle glue-up amplifies them.
  • True each ring flat before stacking — a drum sander or a sheet of sandpaper on the tablesaw wing both work.
  • Dry-fit with a hose clamp before glue touches anything.

Frequently asked questions

How do I calculate the segment cut angle?

Divide 180 by the number of segments: 12 segments → 15°, 8 segments → 22.5°, 16 segments → 11.25°. Each segment gets that angle cut on both ends, so the two ends together make up the segment’s share of the full 360° circle.

Why doesn’t my ring close without gaps?

Angle error accumulates. A ring of 12 segments has 24 cut faces — an error of just 0.1° per cut becomes a 2.4° gap at closing time. Fixes: sneak up on the angle with test cuts on scrap, and glue up in half-rings, then flatten the two halves against sandpaper on a flat surface before joining them. That trick absorbs the residual error invisibly.

How many segments should a ring have?

Beginners do well with 8–12: fewer, larger segments are more forgiving to cut and glue. More segments (16–24) give smoother curves and shorter grain runout but multiply the precision required. Very open patterns and feature rings often mix counts between rings — just keep each ring’s math independent.

How thick should segment stock be?

Ring thickness equals your stock thickness — typically 3/4″ to 1″ works for most bowls. What matters more is width: cut segments a bit wider than the finished wall needs (the calculator’s ring width), because rings get turned both inside and out and you need meat left after truing each glued ring.

Sources & further reading