Segmented Turning Ring Calculator
Segmented woodturning glues up rings of trapezoidal segments, then turns them on the lathe. Getting the segment angle and length right is what makes a ring close cleanly with no gaps. This calculator works from the number of segments and your target outer and inner flat radii to give the exact miter angle for each cut, the outer and inner segment lengths, and the total board length one ring consumes including saw kerf. The geometry is exact regular-polygon trigonometry, so the only judgment left is how much waste margin to add for truing on the lathe.
Segmented ring formula
Miter angle = 180 / segments degrees
Outer length = 2 * outer radius * tan(180 / segments)
Inner length = 2 * inner radius * tan(180 / segments)
Board length = segments * (outer length + kerf)
Radii are measured to the polygon flats, not corner to corner. The miter angle is cut on both ends of each segment. Add your own waste margin to outer and inner dimensions for truing on the lathe.
Segmented turning tips
- A 12-segment ring uses a 15-degree miter on each end.
- Cut a test ring and check it closes flat with no light gaps.
- Stagger segment joints between stacked rings for strength.
- Size the flats slightly oversize so the lathe can true the ring.
- Account for kerf so a single board yields the segments you expect.
Segmented turning: frequently asked questions
How do I calculate the miter angle for a segmented ring?
Each segment is a trapezoid, and the miter angle cut on each end is 180 divided by the number of segments. For a 12-segment ring that is 15 degrees per cut, so the two ends total 30 degrees and the joint between segments forms the interior polygon angle.
How long should each segment be?
The segment outer length = 2 x outer radius x tan(180 / segments) and inner length = 2 x inner radius x tan(180 / segments), where the radii are measured to the polygon flats. Cutting to these flat-to-flat dimensions ensures the ring closes to the intended outer diameter.
What is the difference between ring diameter and segment radius?
The finished blank diameter is the diameter of the circle that circumscribes the polygon (corner to corner). The flat-to-flat measurement is smaller. Most turners size segments so the polygon flats sit just outside the final turned diameter, leaving material to turn away. This calculator works from the flat radius you supply.
How much extra width should segments have?
Add waste to both the outer diameter and ring width so the lathe tool has material to true up. A common allowance is a quarter inch or more on the radius. Enter your target flat dimensions; the calculator reports the cut lengths so you can add your own waste margin.
Why does board length per ring matter?
Knowing the total length of stock a ring consumes (segment count times the longer cut length plus saw kerf per cut) lets you buy the right amount of wood and plan grain orientation across the whole vessel before cutting.
Official sources
- NIST Digital Library of Mathematical Functions: DLMF, polygon trigonometry.
- USDA Forest Products Laboratory: Wood Handbook, gluing and wood properties.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.