Segmented bowls are built from rings of trapezoid-shaped segments glued edge to edge. Each segment’s ends are cut at 180°/n so that n segments close into a ring, and allowances on the outside and inside leave wood to turn the final shape.
How to use the Bowl Segment Calculator
- Segments per ring
- Outer radius
- Inner radius
- Outer allowance
- Inner allowance
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the number of segments in the ring, the finished outer and inner radii and the turning allowances.
Tips for an accurate estimate
- Measure angles with a digital angle finder or sliding bevel, not by eye.
- Make a test cut in scrap before cutting expensive stock.
- Small angle errors add up over many joints – check the first assembly before cutting the rest.
- Keep a written list of the dimensions and angles you set on the saw or machine.
Common mistakes to avoid
- Reading the saw scale as the angle from the edge rather than from square.
- Rounding intermediate results too early.
- Mixing degrees and percent grade.
Inputs explained
| Field | What to enter |
|---|---|
| Segments per ring | A number |
| Outer radius | Units: in, cm, mm, ft, m |
| Inner radius | Units: in, cm, mm, ft, m |
| Outer allowance | Units: in, cm, mm, ft, m |
| Inner allowance | Units: in, cm, mm, ft, m |
What each result means
- Miter angle (each end) = 180÷[Segments per ring]
- Outer segment length = 2×tan(rad(180÷[Segments per ring]))×([Outer radius] + [Outer allowance])
- Inner segment length = 2×sin(rad(180÷[Segments per ring]))×([Inner radius] – [Inner allowance])
- Strip width = ([Outer radius] + [Outer allowance]) – cos(rad(180÷[Segments per ring]))×([Inner radius] – [Inner allowance])
- Strip length for one ring (approx.) = [Segments per ring]×([Outer segment length] + [Inner segment length])÷2
Example values
How the main result changes when Segments per ring changes and everything else stays at the example values above:
| Segments per ring | Outer segment length (in) |
|---|---|
| 6 | 4.763 |
| 9 | 3.003 |
| 12 | 2.211 |
| 15 | 1.754 |
| 18 | 1.455 |
| 24 | 1.086 |
Formula
Miter angle α = 180° ÷ nOuter length Lo = 2 tan(180°/n) × (Ro + ao)Inner length Li = 2 sin(180°/n) × (Ri − ai)Strip width Ts = (Ro + ao) − cos(180°/n) × (Ri − ai)Worked example
Inputs — Segments per ring: 12; Outer radius: 4 in; Inner radius: 3 in; Outer allowance: 0.125 in; Inner allowance: 0.125 in.
Results — Miter angle (each end) = 15 °; Outer segment length = 2.211 in; Inner segment length = 1.488 in; Strip width = 1.348 in; Strip length for one ring (approx.) = 22.19 in.
Frequently asked questions
What angle do I cut for 12 segments?
15° at each end (180 ÷ 12), so two segments form a 30° joint.
Why add allowances?
They leave extra wood outside and inside the finished profile so you can turn the bowl true.
How do I fix gaps in a ring?
Sand the halves flat on a disc sander and correct the angle slightly; small errors add up over many joints.
What formula does the Bowl Segment Calculator use?
Miter angle α = 180° ÷ n.