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
- A full circle is 360°, so 12 segments each turn 360 ÷ 12 = 30.0°.
- Two cuts share that turn, so each is half of it: 15.0°.
- 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
| Segments | Miter per end | Cuts per course | Outer edge | Blank diameter |
|---|---|---|---|---|
| 6 | 30.0° | 12 | 6 15/16" | 13 7/8" |
| 8 | 22.5° | 16 | 5" | 13" |
| 10 | 18.0° | 20 | 3 7/8" | 12 5/8" |
| 12 | 15.0° | 24 | 3 3/16" | 12 7/16" |
| 16 | 11.3° | 32 | 2 3/8" | 12 1/4" |
| 18 | 10.0° | 36 | 2 1/8" | 12 3/16" |
| 24 | 7.5° | 48 | 1 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.
Work out your own numbers
- Segmented rings and columns
Miter and bevel for any number of sides, flat or flared, and how long each segment has to be.
- Miter angle calculator
The miter for baseboard, casing or chair rail at any corner angle — flat trim, so there's no bevel to set.
- Circle and arc layout
A trammel arm's length for a full circle, or the radius of a shallow arc from its chord and rise.
Related questions
- What angle for a 12 segment ring?
- 15° per end. Each segment turns 30° of the circle and the two cuts split it. Set the saw once, cut every segment without touching the setting, and any error in the setting partly cancels itself between the two ends.
- Why won't my segmented ring close?
- Because the error at every cut is multiplied by twice the number of segments, so an error too small to read on a protractor is not too small to see in the ring. Cut a full test ring in scrap and dry-fit it: the size of the gap tells you exactly how much to adjust, divided over all the cuts.
- How many segments should a ring have?
- More segments make a rounder ring with less waste when turning, but every one is two more cuts to get right and a shorter glue surface. Twelve is the usual starting point for a bowl-sized ring; sixteen or more suits a large diameter where twelve would leave the blank noticeably faceted.