By Zencalcy Editorial TeamLast reviewed About us
A segmented ring is a polygon, so each joint is half the exterior angle and each segment's length is the chord of the ring's circle divided by the number of segments. A 12-segment ring therefore uses a 15° miter and segments cut to the chord length.
Miter angle and segment length for a segmented bowl.
miter = 180° ÷ segments ÷ 2 ... (half of exterior angle) segment length = π × D ÷ segments (approximate chord)
The exact chord is D × sin(180° ÷ n); the πD/n approximation runs about 1% long and is fine for cutting stock. The miter saw setting is 180° ÷ n for a two-sided cut.
| Symbol | Meaning |
|---|---|
| D | Ring diameter. |
| n | Number of segments. |
| θ | Miter angle at each joint. |
Each segment is about 3.11 inches long and the miter is 15°, giving 24 cuts for the ring.
Continue with the Angle Cut Calculator, Angle of Depression Calculator, Bolt Circle Calculator, or the Countersink Depth Calculator — or browse more layout & geometry and all construction calculators.
15°. The formula is 180 ÷ segments for the saw setting, since each joint takes half the 30° exterior angle from each side.
Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.
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Content updated: September 2026