What angle do you cut segments for a turned ring?

A twelve-segment ring is cut at 15° per end. The angle, the segment lengths, and why a ring that will not close is almost never the arithmetic's fault.

A 12-segment flat ring is cut at 15.0° on each end of every segment.

That is 12 segments and 24 cuts per course, every one of which has to be right — the error at each one is multiplied by 24 before the ring closes.

How that is worked out

  1. A full circle is 360°, so 12 segments each turn 360 ÷ 12 = 30.0°.
  2. Two cuts share that turn, so each is half of it: 15.0°.
  3. For a 12" ring 1 1/2" wide that gives an outer edge of 3 3/16" and an inner edge of 2 7/16" on every segment.

Flat rings, 12" across the flats, 1 1/2" wide

Flat rings, 12" across the flats, 1 1/2" wide
SegmentsMiter per endCuts per courseOuter edgeBlank diameter
630.0°126 15/16"13 7/8"
822.5°165"13"
1018.0°203 7/8"12 5/8"
1215.0°243 3/16"12 7/16"
1611.3°322 3/8"12 1/4"
1810.0°362 1/8"12 3/16"
247.5°481 9/16"12 1/8"

Worth knowing

  • This is the flat case, with the segments lying in one plane and the blade upright. A ring whose wall leans in or out is a compound miter and needs a bevel as well — the segmented ring calculator handles the slope.
  • Error is multiplied by twice the number of segments. Twelve segments each 0.1° over leaves 2.4° of the 360° unaccounted for, which shows as a gap you can see across a room.
  • The fix is a test ring in scrap, not a recalculation. Dry-fit it, measure the gap, and divide the correction over all the cuts.
  • Cut every segment the same way up, from one saw setting, so that whatever error the setting has cancels between the two ends rather than compounding.