Segmented Bowl Calculator - Free Woodturning Tool

What is a segmented bowl calculator?

A segmented bowl calculator works out the size and angle of each wooden piece needed to build a segmented bowl. A segmented bowl is a woodturning project made from many small wood pieces, called segments, glued into a ring and then stacked and turned on a lathe. The calculator takes a bowl's diameter, height, and number of segments per ring, and returns the length, width, and cutting angle of each segment.

What is a segmented bowl?

A segmented bowl is built from short lengths of wood glued edge to edge into a ring, rather than turned from one solid block. Woodturners stack several rings and glue them together before shaping the whole piece on a lathe.

Building a bowl this way has a few practical benefits:

• It uses smaller, cheaper pieces of wood instead of one large blank.
• It lets the maker mix wood colors and species in a pattern.
• Smaller, well-dried pieces are less likely to crack or warp than one solid block.
• The joints between segments create geometric patterns that solid wood cannot produce.

Each ring in a segmented bowl is shaped like a regular polygon, a flat shape with equal sides and equal angles, such as a hexagon or a 12-sided shape. The bowl's outer wall follows the flat sides of that polygon rather than a perfectly round curve, though with enough segments the ring looks close to round.

Segment length formula

Each segment is one side of a regular polygon. The polygon's apothem, the distance from its center to the middle of a side, equals the bowl's outer radius. That geometry gives this formula for the outer length of one segment:

$\text{Segment Length} = 2 \times R \times \tan\left(\frac{\pi}{N}\right)$

Here, R is the bowl's radius (diameter divided by 2) and N is the number of segments in the ring. The angle inside the tangent function is in radians; in degrees it is 180°/N.

This formula gives the length of the polygon's side, so the finished ring matches the target diameter exactly. A related formula, using sine instead of tangent, gives the length of the chord connecting two corner points of the polygon. A chord is always shorter than the matching polygon side, so using it would produce a ring that turns out smaller than the diameter entered.

Segment width

Segment width is the height of each piece before assembly. For a bowl made of a single ring, the segment width simply equals the bowl height entered into the calculator:

$\text{Segment Width} = \text{Bowl Height}$

A bowl built from several stacked rings divides its total height across those rings, so each ring's segments would use a smaller width. This calculator assumes one ring and uses the full height as the segment width.

Segment angle (miter angle) formula

Each segment sits between two straight cuts, one at each end. Those two cuts meet the two cuts on the neighboring segments to close the ring. The full angle at the center of the ring taken up by one segment is 360°/N, but that angle is split between the segment's two ends. The angle to set on a miter saw or table saw sled is therefore half of the central angle:

$\text{Segment Angle} = \frac{180°}{N}$

Setting the saw to the full central angle (360°/N) instead of half of it will double every miter cut, and the ring will not close.

Example calculation

Take a bowl with a diameter of 300 mm, a height of 45 mm, and 12 segments per ring.

1. Radius: R = 300 ÷ 2 = 150 mm
2. Segment length: 2 × 150 × tan(180° ÷ 12) = 2 × 150 × tan(15°) ≈ 300 × 0.2679 ≈ 80.4 mm
3. Segment width: equals the bowl height, 45 mm
4. Segment angle: 180° ÷ 12 = 15°

Each of the 12 segments in this ring should be cut 80.4 mm long, 45 mm wide, with both ends mitered at 15°.

How to use the calculator

1. Enter the bowl's diameter in millimeters.
2. Enter the bowl's height in millimeters.
3. Enter the number of segments per ring (at least 3).
4. Read the segment length, width, and angle from the results.
5. Use the "Copy Results" button to copy the numbers for use at the saw.

The calculator also draws a top view of the ring and a diagram of one segment with its dimensions labeled.

Tips for accurate segments

• Kerf: A saw blade removes a thin strip of wood with each cut, called the kerf. This calculator does not add kerf to the segment length, so account for it separately, typically by adding a small amount per cut or by cutting oversized and trimming to fit.
• Test fit: Cut a small batch first and dry-fit them into a ring before cutting all the pieces for a project.
• Saw setup: Check the miter angle with an accurate gauge, since even a small error compounds across many segments in a ring.
• Wood movement: Use wood dried to a stable, low moisture content, and keep grain direction consistent between segments to reduce the risk of joints opening up later.

Frequently asked questions

What is the minimum number of segments per ring? The calculator requires at least 3, since 3 sides are the fewest that can form a closed polygon. Most segmented bowls use 8 or more segments per ring for a smoother, rounder appearance.

Why does the calculator use tangent instead of sine for segment length? The tangent formula gives the length of the polygon's side, matching the bowl's outer diameter exactly. The sine formula gives a shorter chord length, which would leave the finished ring smaller than the diameter entered.

Should I set my miter saw to 360°/N or 180°/N? Set it to 180°/N. Each segment has two mitered ends that together account for the full central angle of 360°/N, so each individual cut uses half that value.

Does the calculator account for saw blade kerf? No. The segment length is the finished, glued length. Add extra length to compensate for material removed by the blade during cutting.

Can I use this calculator for a bowl with several stacked rings of different heights? The calculator produces dimensions for one ring based on the height entered. For a bowl with multiple rings, calculate each ring separately using that ring's own height.

What wood works best for segmented bowls? Stable, well-dried hardwoods such as maple, walnut, and cherry are common choices, often combined with contrasting species like padauk or purpleheart for pattern.

See also

• Woodturning
• Lathe (woodworking)
• Miter joint
• Regular polygon