Segmented Turning Calculator

A segmented bowl or vase is built from rings, and each ring is a circle of mitered pieces. Get the angle or the length a hair off and the ring will not close, or it closes with gaps. This gives you the exact miter angle to cut, the length of each segment, and how much strip stock to prepare, from the segment count and the ring size.

The angle is a full turn, split

A ring is a circle, 360 degrees, shared equally among its segments, so each segment spans a full turn divided by the count. You cut that angle as two miters, one on each end, so each miter is half of it: 180 divided by the number of segments. Twelve segments means 15 degree miters; sixteen means 11.25. Set the saw there, cut both ends of every piece the same, and the ring closes on itself. The whole trick is that one angle, cut cleanly and identically every time.

Segment length from the diameter

Each segment is a little trapezoid: a long outer edge, a short inner edge, and the two mitered ends. The outer edge length comes from the outer radius and that same angle, and it is the dimension you cut your strip to. A bigger ring or fewer segments makes longer pieces; more segments makes shorter ones. The inner edge is shorter in the same proportion, set by the ring width. Cut the strip to the outer length between the miters and the ring comes out to size.

More segments, rounder ring, less waste

Few segments give a chunky, faceted ring with a lot wasted when you turn it round; many segments start closer to a circle, so you remove less and the wall can be thinner. The trade is more cuts and more glue joints to get perfect. Twelve is a common starting point, sixteen and twenty-four are popular for cleaner rings. Pick the count for the look you want and the patience you have, because every extra segment is two more cuts that all have to match.

Cut extra, true it round

Segmented work is unforgiving: one short or off-angle piece and the ring has a gap or will not close, so cut a spare segment or two, which is why the strip total here carries a margin. Prepare the strip slightly wider than the finished wall and a touch over on diameter, glue the ring with a band clamp to pull every joint tight, then true it flat and turn it round on the lathe. The math gets you a ring that closes; careful, identical cuts get you one with no gaps.

More MakerKiln tools

• miter angleMiter Angle CalculatorThe miter angle for a frame or box with any number of sides.→
• board feetBoard Foot CalculatorBoard feet and cost for a whole lumber list, with a waste allowance.→
• equal spacingEqual Spacing CalculatorSpace holes, pins or pickets evenly across a span, or divide into equal parts.→

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