Woodworking calculator
Miter Angle Calculator (Polygons and Segmented Rings)
Building a picture frame, a hexagon box, or a segmented bowl ring all come down to one number: the miter angle you set on the saw. This calculator takes the number of sides you want and returns the miter angle to cut, the interior angle of the shape, and, for segmented rings, the length of each segment from the ring diameter. Enter the side count and your dimensions to get cuts that close up tight with no gaps.
How it works
A regular polygon with N sides has equal corners, and the saw angle to form each corner follows a simple rule. The miter angle measured from a square cut is 180 divided by the number of sides, so the two mating pieces together turn through the full exterior angle of the polygon. A four-sided frame needs 45 degrees, a six-sided shape needs 30 degrees, and an eight-sided shape needs 22.5 degrees. The interior angle of the shape itself is N minus 2, times 180, divided by N.
For segmented rings, the kind used in turned bowls and round tabletops, the same miter angle cuts each segment, but you also need the segment length. Given the outside diameter of the ring and the number of segments, each piece spans an arc, and the calculator returns the outer edge length of each segment so you can crosscut it to length; rip your stock to the ring width and the inner edge comes out shorter automatically.
Two practical notes matter. First, check where your saw reads zero: a standard miter saw reads 0 degrees at a square crosscut, so you set it directly to the miter angle above (30 degrees for a hexagon). Some protractors and bevel gauges instead read zero parallel to the edge, giving the complement, so confirm the convention before trusting the dial. Second, a tiny error per joint multiplies around the ring, so cut test pieces and dry-fit a full ring before gluing.
Worked example
A six-sided frame or segmented ring: 180 / 6 = 30° miter cut on each end, meeting at a 120° interior corner.
Frequently asked questions
What miter angle do I cut for a six-sided frame?
Set the saw to 30 degrees from a square cut, because 180 divided by 6 sides equals 30. The two mating ends then meet to form each 120 degree interior corner of the hexagon cleanly.
How do I find the angle for any number of sides?
Divide 180 by the number of sides to get the miter angle measured from a square cut. So 4 sides gives 45 degrees, 8 sides gives 22.5 degrees, and 12 sides gives 15 degrees, and so on.
Why does my saw scale not match the calculated angle?
A standard miter saw reads 0 degrees at a square crosscut, so set it directly to the calculated angle, 30 degrees for a hexagon. If your scale or protractor instead reads 0 when parallel to the fence or workpiece edge, it shows the complement, so check where its zero sits before trusting the dial.
How do I get the segment length for a ring?
Enter the ring outside diameter and the segment count, and the tool returns the outer edge length of each segment, the long side of the trapezoid. Rip your stock to the ring width and the inner edge comes out shorter automatically once you cut the miters.
Why does my ring not close up perfectly?
Small angle errors add up around the ring. With many segments, a fraction of a degree per cut becomes a visible gap, so cut test pieces and dry-fit the whole ring before committing to glue.
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Sources
These calculators are for planning and estimation. Engineering results (shelf sag, wood movement) use published average material properties; real boards vary by grade, grain, moisture and defects. Verify load-bearing designs with a professional.