Practical tools for measured work
Segmented Bowl & Ring Calculator
Calculate miter angle, trapezoid edge lengths and kerf-aware stock length for a segmented turning ring.
Calculate the layout, check the diagram, then print the result for the shop or jobsite.
Whole number from 4 to 48.
Measured at each long-edge midpoint; blank corners project beyond it.
Measured at each short-edge midpoint.
Added once per blank in the total stock-length estimate.
The diagram uses real millimetre coordinates for calibrated SVG/PDF output. Print at 100% and verify the calibration mark before using it as a shop reference.
How it works
Direct answer. Enter the tangent/finished ring diameters and segment count to get the miter setting, trapezoid edge lengths, radial width and a kerf-aware stock estimate.
Geometry. Bisecting one regular-polygon segment produces a right triangle, so half-edge = r tan(pi/N). The outside and inside straight edges are therefore D tan(pi/N) and d tan(pi/N), and each end cut is 180/N degrees.
Diameter datum. Diameters are measured at the midpoint of each straight edge - the tangent circles shown. Blank corners project outside the finished diameter and are normally turned away; no extra machining allowance is added beyond that geometry.
Checks. Common miter settings are 15 degrees for 12 segments, 22.5 degrees for 8, 7.5 degrees for 24, and 20 degrees for 9.
Current-input example
The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.
- Units
- Millimetres
- Segments per ring
- 12
- Outside tangent / finished diameter
- 300
- Inside tangent / finished diameter
- 220
- Saw kerf
- 3
Primary result: Miter saw setting per end: 15.000 deg.
Before using the result
- Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
- Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
- When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.
Limitations
This is ideal regular-ring geometry. Saw calibration, fence setup, blade runout, wood movement, sanding, glue-line compression and cumulative angle error affect the real closure. Make a test ring, keep segment orientation consistent, and use appropriate guarding and clamping. The stock estimate adds one entered kerf per blank and does not include end trim or defect allowance.
Frequently asked questions
Why do tiny angle errors matter?
The error repeats at every joint. A small error multiplied across all segments can leave a visible opening at closure.
Are the edge lengths arc lengths?
No. They are straight tangent-side lengths for trapezoidal blanks, derived from the regular polygon geometry.
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