Bowl Segment Calculator
Enter the number of segments in your ring, the outer radius, and the ring thickness to get the miter cutting angle, outer and inner segment lengths, and segment thickness. Toggle fudge factors for safe-to-trim extra stock, and switch between metric (mm) and imperial (inches). Results update instantly as you type.
What is a segmented bowl, and why do the cuts need to be so precise?
A segmented bowl is built up from rings, and each ring is assembled from identical wedge-shaped pieces of wood glued end-to-end. Because every joint must close perfectly, the miter angle on each segment must be exact. Even a single degree of error, multiplied across all segments in a ring, can produce gaps that ruin the joint and weaken the bowl. This calculator gives you the cut angle and every dimension you need before you make your first cut.
How to read the outputs
The cutting angle (also called the miter angle) is what you set on your miter saw, table saw sled, or disc sander: tilt each end of every segment to this angle. The outer segment length is measured along the outside face of the wood; the inner segment length is the shorter inside face. The segment thickness tells you how deep (radially) each blank needs to be, which determines the board width to cut from. The outer and inner diameters and circumferences are reference values that help you plan how many rings fit inside a given board or plank.
Fudge (safety) factors explained
Toggle "Add fudge factors" to pad the segment dimensions by a small allowance. The outer fudge factor widens the outer measurement so you have material to turn back to the finished radius on the lathe. The inner fudge factor shrinks the inner opening slightly so you are not in danger of cutting the hollow too large before turning. Typical values are 1/8 in (3 mm) on the outside and 1/16 in (1.5 mm) on the inside, but experienced turners often work to zero allowance and rely on precise setup instead.
Designing a multi-ring bowl
Most segmented bowls use several rings stacked vertically, each potentially at a different diameter as the bowl widens then narrows. Run this calculator once for each ring, entering its own outer radius and thickness. Use the comparison table at the bottom to compare how the cut angles and segment lengths change across rings. Plan your board usage by dividing the outer circumference by the outer segment length (plus kerf width) to see how many segments fit from one plank cut.
Common segment counts and their cutting angles
| Segments | Cut angle (deg) | Interior angle (deg) | Typical use |
|---|---|---|---|
| 6 | 30.00 | 60.00 | Bold, faceted look |
| 8 | 22.50 | 45.00 | Classic octagonal bowl |
| 10 | 18.00 | 36.00 | Decagonal ring, minimal faceting |
| 12 | 15.00 | 30.00 | Most popular - good balance of ease and roundness |
| 16 | 11.25 | 22.50 | Near-round, fine segments |
| 20 | 9.00 | 18.00 | Very smooth ring, precise cuts essential |
| 24 | 7.50 | 15.00 | Ultra-smooth, small segments |
The cutting angle is set on each side of the segment - both cuts together form the interior angle.
Frequently asked questions
What cutting angle do I set on my miter saw for a 12-segment ring?
180 divided by 12 gives 15 degrees. Set both ends of every segment to 15 degrees (a symmetric miter). When two adjacent segments are placed together, their two 15-degree cuts meet to form the 30-degree interior angle of each of the twelve equal wedges.
What is the difference between the cutting angle and the interior angle?
The interior angle is the full wedge angle of one segment, which is 360 degrees divided by the segment count. The cutting angle is half of that - each saw cut takes away half the interior angle from the end of the segment. For a 12-segment ring the interior angle is 30 degrees and the cut angle is 15 degrees.
How do I convert outer diameter to outer radius?
Divide the diameter by two to get the radius. If you want your finished bowl to have a 10-inch outer diameter, enter 5 inches as the outer radius. The calculator also displays the outer and inner diameters as outputs if you prefer to work in diameter.
How many segments should I use for my first bowl?
Twelve segments is the most popular starting point. The 15-degree miter angle is easy to set accurately, the segment dimensions are manageable, and the ring looks nearly round after turning. Six or eight segments create a more deliberately faceted look and are faster to cut, but any misalignment in the glue-up is more visible.
Why does my ring gap when I dry-fit the segments?
Small gaps usually mean the miter angle was slightly off. Even 0.1 degree of error per cut - compounded over all segments - can open a visible gap. Sand each segment face lightly on a flat reference plate and re-check your saw angle with a reliable digital protractor. Gaps can also result from segments that are not all the same length: make a stop block to ensure identical length on every piece.
Can I use this calculator for non-bowl projects, like stave construction?
Yes. The formulas are purely geometric and apply to any polygon ring - frames, vases, hollow forms, and even architectural columns use the same miter-angle math. For stave (barrel) construction where the staves taper in height as well as width, you also need a compound angle, but the basic miter angle from this calculator is still the starting point.