# Bowl Segment Calculator

URL: https://speedycalculator.com/calculators/construction/bowl-segment/
Last updated: 2026-10-25

> The bowl segment calculator works out the miter angle, outer and inner segment lengths and strip width for a segmented woodturning ring from the number of segments and the ring radii, with allowances for turning.

## Inputs

- Segments per ring
- Outer radius (in, cm, mm, ft, m)
- Inner radius (in, cm, mm, ft, m)
- Outer allowance (in, cm, mm, ft, m)
- Inner allowance (in, cm, mm, ft, m)

## Results

- Miter angle (each end)
- Outer segment length
- Inner segment length
- Strip width
- Strip length for one ring (approx.)

## Formula

```
Miter angle α = 180° ÷ n
Outer 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)
```

## Explanation

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

FieldWhat to enterSegments per ringA numberOuter radiusUnits: in, cm, mm, ft, mInner radiusUnits: in, cm, mm, ft, mOuter allowanceUnits: in, cm, mm, ft, mInner allowanceUnits: 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 ringOuter segment length (in)64.76393.003122.211151.754181.455241.086

## 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.

## FAQ

**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.