123 123Calculator

Bowl Segment Calculator

Use this bowl segment calculator to confidently measure and cut your precious wood pieces to their correct sizes to create perfectly fitting segments.

Clear
Miter angle15°cut both ends of every segment at this — 180° ÷ 12
Segment outer face length2 5/32 in2.14359 in
Segment inner face length1 3/4 in1.74167 in
Board width needed25/32 inthe wall thickness divided by cos 15°, so the ring cleans up to full thickness
Segments per ring12
Segments in total726 rings
Board length per ring25.723 inbefore allowing for saw kerf
Board length for all rings12 ft 10.34 in154.34 in — add a kerf per cut
Outside diameter8 in
Inside diameter6.5 in
Ring height1 instack height 6 in for 6 rings
Glue surface per joint0.7765 sq inend grain to end grain, so keep the joints tight

The formula

miter = 180° ÷ n; segment length = 2 × radius × tan(180° ÷ n)

Miter is half the exterior angle

A ring of n segments is a regular polygon, so each joint closes an exterior angle of 360°/n shared between two cuts — 180°/n each. Twelve segments means 15°, sixteen means 11.25°.

The board has to be wider than the finished wall, because the segment is cut at an angle: divide the wall thickness by the cosine of the miter. Skip that and the ring will not clean up to full thickness when you turn it.

Accuracy compounds around the ring. A quarter-degree error in the miter multiplies by twenty-four cuts on a twelve-segment ring, which is enough to leave a visible gap — so cut a test ring and adjust before committing the good timber.