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 length of the outer and inner edges so you can rip stock to width and crosscut the segments efficiently.
Two practical notes matter. First, the saw scale and the angle from a square can differ: many miter saws read the angle off the fence, which is the complement of the geometric angle, so check which convention your saw uses. 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?
Many miter saws measure the angle from the fence, which is the complement of the geometric angle from a square. Check whether your saw reads the cut or its complement before trusting the dial.
How do I get the segment length for a ring?
Enter the ring outside diameter and the segment count. The tool spans each segment across its arc and returns the outer and inner edge lengths so you can rip stock to width and crosscut accurately.
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.