Segmented turning calculator
Enter the number of segments in a ring and its outside diameter to get the miter cut angle, the included angle, the outer length of each segment, and the total strip length you need with a waste allowance. Every figure updates as you type.
Cut / miter angle
15.00°
180 / n, each end
Included angle
30.00°
360 / n
Outer edge / segment
2.68 in
D x tan(180/n)
Strip for ring
36.98 in
32.15 in + 15% waste
The two angles in a segmented ring
A segmented ring is a regular polygon glued from wedge-shaped pieces. Two angles define it. The cut angle, the miter you set on the saw at each end of a segment, is 180 divided by the number of segments. The included angle, the wedge each segment occupies, is 360 divided by the number of segments, which is exactly twice the cut angle.
Cut angle = 180 ÷ n Included angle = 360 ÷ n
For 12 segments the cut angle is 180 ÷ 12 = 15 degrees, and the included angle is 360 ÷ 12 = 30 degrees. The full circle checks out: 12 segments times 30 degrees is 360 degrees. Common counts and their cut angles: 8 segments at 22.5 degrees, 12 at 15 degrees, 16 at 11.25 degrees, 24 at 7.5 degrees.
Segment length and strip length
The outer edge of each segment is the ring outside diameter times the tangent of the cut angle:
Outer edge = D × tan(180 ÷ n)
For a 10-inch outside diameter ring of 12 segments, the outer edge is 10 × tan(15°), which is about 2.68 inches. That figure runs a touch generous, which is what you want: it leaves stock to true the ring round after glue-up. Multiply by the segment count for the strip you need for one ring: 12 × 2.68 = 32.2 inches. Add a waste allowance for saw kerf and trimming, and about 37 inches of strip covers the ring at a 15 percent allowance.
A worked example
A 12-segment ring with a 10-inch outside diameter and 1 1/2-inch strips:
- Cut angle: 180 ÷ 12 = 15 degrees at each end
- Included angle: 360 ÷ 12 = 30 degrees per segment
- Outer edge per segment: 10 × tan(15°) ≈ 2.68 inches
- Strip for the ring: 12 × 2.68 ≈ 32.2 inches, or about 37 inches with 15 percent waste
The strip width, 1 1/2 inches here, sets the wall height of the ring and does not enter the angle math. Choose it for the profile you plan to turn, allowing extra for the inner and outer curves you will remove.
Choosing a segment count
More segments give a rounder ring and shorter, easier-to-handle pieces, at the cost of more joints to cut accurately. Twelve segments suit most bowls in the 6 to 10-inch range and keep the cut angle at a round 15 degrees. Larger rings usually move to 16 or 24 segments so no single piece spans too wide an arc, which would leave heavy flats to turn away. Feature rings, where a thin decorative band circles the bowl, often use higher counts so the pattern reads as a smooth curve rather than a set of facets.
The outer segment length also guides your stock. At 12 segments a 10-inch ring needs pieces about 2.68 inches long on the outer edge; the same ring at 24 segments needs pieces near 1.32 inches. Shorter segments waste less at the ends and fit a narrow strip, but they double the number of glue joints. Balance the look you want against the number of accurate cuts you are willing to make.
Why precision at the saw pays off
A ring closes only when its cut angles sum to a full 360 degrees. An error of even a quarter of a degree per cut repeats at every joint, so a 12-segment ring compounds a small drift 12 times and opens a gap you cannot sand away. Set the saw carefully, cut a test pair, and dry-fit a full ring before you reach for glue. Turning a segmented piece rewards the time spent squaring the saw far more than speed at the lathe.