Segmented Turning Calculator

Q: What angle do I cut segments for a segmented ring?

Miter each end at 180 ÷ number of segments. A 12-segment ring is 15° per end; a 16-segment ring is 11.25°.

Building a segmented bowl or vessel? Get the exact miter angle and outer/inner segment lengths for each ring — so the ring closes tight with no gaps. Sign in to save your rings.

Segments per ring

Outer diameter (in, to the corners)

Ring width (in, radial)

Miter angle (each end)

15.00°

Outer face

3.106"

Inner face

2.588"

Cut 12 segments, mitering both ends at 15.00°. Stock at least 1.00" wide.

Diameter is measured to the outer corners before turning round — leave a little extra and dry-fit the ring before glue-up.

For planning purposes only. Woodworking involves variation in materials, moisture, and technique, so results are estimates — always double-check the numbers against your own measurements and judgment, and test on scrap before committing to a real workpiece. Sawdust Journey is not liable for material loss, injury, financial damages, or errors resulting from use of this tool.

Segmented turning, calculated segment by segment

Segmented turning builds a bowl or vessel from rings of mitered segments glued edge to edge, then turned round. The whole thing lives or dies on the segment angles and lengths: if every joint is even and tight, the rings close with no gaps and glue up clean; if the angle is off by a fraction of a degree, that error multiplies around the ring and you chase gaps forever. This calculator gives you the exact miter angle and the outer and inner face lengths for any ring, so each segment comes off the saw ready to close.

The ring segment math

Each ring is a set of trapezoid segments whose outer and inner faces are the edges of two concentric regular polygons. For a ring of N segments:

Miter each end at 180 / N degrees — a 12-segment ring is 15° per end, a 16-segment ring 11.25°. The two ends of each segment add to 360 / N, and the N segments close the full 360°.
Outer face length = 2 × R_o × sin(180 / N), where R_o is the outer radius (half the outer diameter).
Inner face length = 2 × R_i × sin(180 / N), where R_i = outer radius − ring width.

The outer diameter is measured to the corners of the ring before you turn it round, so always leave a little extra to true up.

How to use the calculator

Enter the number of segments per ring — more segments make a smoother curve but more joints.
Enter the outer diameter (to the corners) and the ring width (how deep the ring is, radially).
Cut every segment with both ends mitered at the given angle, to the outer and inner face lengths shown.

Tips for tight segmented rings

Nail the angle first. Cut a full test ring in scrap and check it closes with no gap before touching good stock — a tiny per-joint error becomes a big gap over a whole ring.
Use a sled and stop block so every segment is exactly the same length; consistency is what makes the ring close.
Dry-fit each ring with a hose clamp or tape, and sand the glue faces flat on a disc sander for gap-free joints.
Offset the joints ring to ring (rotate each ring half a segment) for strength and a cleaner pattern.
Leave extra diameter — you turn the faceted ring down to a true circle, so the flats need somewhere to go.

Frequently asked questions

What angle do I cut segments for a segmented ring?

Miter each end at 180 ÷ the number of segments. A 12-segment ring is 15° per end; a 16-segment ring is 11.25°; a 24-segment ring is 7.5°.

How long should each segment be?

The outer face = 2 × outer radius × sin(180/N) and the inner face = 2 × inner radius × sin(180/N), where inner radius = outer radius − ring width. This tool computes both for you.

How many segments should a ring have?

More segments give a rounder ring with less wood to turn away, but more joints to cut perfectly. Twelve is a common, forgiving starting point; larger vessels often use 16, 24, or more.