Segmented Bowl Ring Calculator (Miter Angle and Segment Length)

A segmented ring is a regular polygon of wedge-shaped pieces glued end to end, then turned round. Enter the finished outside and inside diameters of the ring and the number of segments, and this calculator gives the miter angle to set on the saw, the long and short sides of each segment, the width of strip to rip, and the strip length to cut the whole ring, allowing for the saw kerf and for wood to turn away inside and out.

Segmented ring calculator

How it works

Miter angle = 180° ÷ segments (each end of each segment, measured from square)
Outer flat R = outside diameter ÷ 2 + turning allowance
Inner flat r = (inside diameter ÷ 2 − allowance) x cos(180° ÷ n), so that the inside corners still clear the finished inside diameter
Long side = 2 x R x tan(180° ÷ n); short side = 2 x r x tan(180° ÷ n)
Strip width = R − r; strip length = n x (average of the two sides + kerf ÷ cos(180° ÷ n)), flipping the strip between cuts

The side and corner formulas are the standard regular-polygon relations: side = 2 x apothem x tan(180° ÷ n) and corner radius = apothem ÷ cos(180° ÷ n).

Worked example

A ring 8 in across the outside and 7 in across the inside (a 1/2 in wall), 12 segments, 1/8 in to turn away on each face and a 1/8 in kerf:

Units: Inches
Finished outside diameter of the ring: 8 in
Finished inside diameter of the ring: 7 in
Segments in the ring: 12
Turning allowance on each face: 0.125 in
Saw kerf: 0.125 in
Number of rings this size: 1

The calculator gives:

Miter angle (each end, from square): 15 degrees
Segment long side (outside): 2.211 in (2-7/32")
Segment short side (inside): 1.747 in (1-3/4")
Segment width (strip width): 0.865 in (7/8")
Strip length per ring, flipping alternate cuts: 25.299 in (25-5/16")
Total strip length: 25.299 in (25-5/16") (2.11 ft)
Included angle at each glue joint: 30 degrees

Set the miter gauge or sled to 15°. Each segment is 2-7/32 in on its long side and 1-3/4 in on its short side, cut from a strip 7/8 in wide. Flipping the strip after every cut, the ring takes about 25-5/16 in of strip. The 1/2 in wall becomes a 7/8 in strip because the allowance is added inside and out and the inside corners of the polygon have to clear the 7 in circle.

Segment miter angles and lengths

Segments	Miter angle	Long side, 8 in ring	Long side, 12 in ring
6	30°	4.763 in	7.073 in
8	22.5°	3.417 in	5.074 in
9	20°	3.003 in	4.459 in
10	18°	2.681 in	3.98 in
12	15°	2.211 in	3.282 in
16	11.25°	1.641 in	2.437 in
18	10°	1.455 in	2.16 in
20	9°	1.307 in	1.94 in
24	7.5°	1.086 in	1.613 in

Long side includes a 1/8 in turning allowance on the outside.

Notes and limits

Small angle errors add up: with 12 segments, a saw 0.1° off leaves a 2.4° gap at the last joint. Cut test segments and dry-fit a half ring before cutting the rest.
Glue up two half rings first, sand the joining faces flat, then glue the halves. That takes out any remaining error.
Flipping the strip between cuts (top face up, then down) cuts both ends of each segment without changing the saw setting and saves wood.
Turning allowance depends on how true your glue-up is: 1/8 in (3 mm) each side is common for small work; use more for large rings.
Wood movement still applies: segments with the grain running around the ring move far less than a solid bowl.

Frequently asked questions

What angle do I cut for a 12 segment bowl?

15° on each end of every segment (180 ÷ 12). Two segments meet at 30°.

What is the miter angle for 8 segments?

22.5° on each end (180 ÷ 8).

How long should each segment be?

Long side = 2 x outer radius x tan(180° ÷ segments). For an 8 in ring with 12 segments and 1/8 in allowance, that is about 2.21 in.

How wide a strip do I need?

The outer radius minus the inner flat distance, which is more than the finished wall thickness because of the turning allowance and the polygon corners. Enter your numbers to get it exactly.

How many segments should a ring have?

12 is the most common. More segments give a rounder ring and narrower strips; fewer means bigger angles to cut and more waste to turn off.

Sources

Wikipedia, "Regular polygon": side length = 2 x apothem x tan(180 degrees / n) and circumradius = apothem / cos(180 degrees / n)

Last reviewed: 16 October 2026. The calculation is covered by automated tests with known answers taken from the sources above. Found an error? Please let us know.