Almighty Calculator

Segmented Bowl Ring Calculator

Each segment end is cut at 180° ÷ n, and the outside length of a segment is the ring diameter times tan(180° ÷ n) across the flats or sin(180° ÷ n) across the corners.

in
in
in
The width of your blade cut.
in
Miter angle for each segment end
15°
Segment length, outside edge2.144 in
Segment length, inside edge1.608 in
Ring inside diameter (across the flats)6 in
Board length needed for the ring (segments alternated)24.59 in

Cut a test ring first. Angle errors add up around the ring: 0.1° too much or too little on every cut of a 12-segment ring leaves a gap of roughly 0.17 inch at the outside of an 8 inch ring.

Show the math

Miter angle = 180° ÷ 12 = 15°
Outside length = 8 × tan(15°) = 2.144 in
Inside length = 2.144 − 2 × 1 × tan(15°) = 1.608 in
Stock = 12 × ((2.144 + 1.608) ÷ 2 + 0.09 kerf) + 1 = 24.59 in

Rounded the same way as the result above.

How it works

A segmented ring is a polygon made of identical wedge-shaped pieces. A ring with n segments has n joints, and each segment is cut with its ends angled at 180° ÷ n so the pieces close into a circle.

The outside length of a segment is one side of the outer polygon. The inside length is one side of the smaller inner polygon, shortened at each end by the ring width times tan(180° ÷ n). Cutting segments alternately, one flipped against the next, fits them from a single board with almost no waste other than the kerf.

Miter angle = 180° ÷ n Outside length = D × tan(180° ÷ n) (D across flats) or D × sin(180° ÷ n) (D across corners) Inside length = outside length − 2 × ring width × tan(180° ÷ n) Stock = n × (average length + kerf) + extra for squaring

Worked example

A flat 12-segment ring, 8 inches across the flats, 1 inch wide, with a 0.09 inch kerf:

  1. Miter angle = 180° ÷ 12 = 15°
  2. Outside length = 8 × tan(15°) = 2.144 in
  3. Inside length = 2.144 − 2 × 1 × tan(15°) = 1.608 in
  4. Stock = 12 × ((2.144 + 1.608) ÷ 2 + 0.09 kerf) + 1 = 24.59 in
InputValue
Segments in the ring12
Ring outside diameter8 in
Diameter is measuredAcross the flats (midpoint of one side to the opposite side)
Ring width (radial width of a segment)1 in
Saw kerf0.09 in
Extra stock for squaring the ends1 in
ResultValue
Miter angle for each segment end15 °
Segment length, outside edge2.144 in
Segment length, inside edge1.608 in
Ring inside diameter (across the flats)6 in
Board length needed for the ring (segments alternated)24.59 in

Assumptions and limits

  • A flat ring whose segments lie in one plane. Rings that tilt to form a bowl wall need compound angles, which the compound miter calculator gives.
  • Segments are identical and the ring is a regular polygon. Brick-lay staggers between rings are a design choice and do not change the ring geometry.
  • Outside diameter can be measured across the flats or across the corners. Pick the one your design software or drawing uses.
  • Stock length assumes segments are cut alternately end for end from a board at least as wide as the ring width.

Common questions

What angle do I cut for a 12-segment ring?

15 degrees on each end, which is 180 divided by 12. Set the miter gauge or saw to 15° and flip the board between cuts.

How long is each segment for a 12-segment ring?

Across the corners the outside edge is 0.2588 times the diameter, and across the flats it is 0.2679 times the diameter.

How many segments should a ring have?

Fewer segments mean fewer joints but a more visible polygon. More segments look rounder, but every joint adds any angle error, so accuracy matters more.

How wide can a ring be?

The inside length must stay positive. As the ring gets wider relative to the diameter, the inside edge shrinks toward a point, so wide rings need more segments.

Sources

  • Plane geometry of a regular n-gon: side = 2 × apothem × tan(180° ÷ n) = circumdiameter × sin(180° ÷ n). Verified in the tests by constructing the polygon vertices and measuring the sides.

Updated 2026-09-30