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Frames with more than four sides
A square frame is easy: four sides, each corner 90 degrees, each cut 45 degrees. But a hexagonal frame has six sides, an octagonal frame has eight, and the miter angle changes with every side you add. The more sides a frame has, the smaller each miter cut becomes, because the polygon gets closer to a circle and each corner turns less sharply.
This calculator finds the miter angle from the number of sides alone. The rule is simple: divide 180 by the number of sides. A hexagon gives 30 degrees, an octagon gives 22.5 degrees, and a twelve-sided frame gives 15 degrees. It also shows the inside angle at each corner, which is useful if you are drawing the frame or checking your work with a protractor.
Every piece in a regular polygon frame is identical: same length, same miter on both ends, with the cuts angled in opposite directions. That symmetry is what makes polygon frames satisfying to build, but it also means one wrong setting ruins every piece. Set the saw once, cut a test joint, and only then cut the full set.
A worked example
Take an octagonal picture frame. Eight sides give an inside angle of 135 degrees at each corner and a miter cut of 22.5 degrees on each end of each piece. Cut eight identical pieces at 22.5 degrees, with the miters facing opposite ways, and the pieces close into a regular octagon. The turning angle at each corner is 45 degrees, and eight turns of 45 degrees add up to the full 360 degree circle.
A hexagonal frame works the same way with different numbers. Six sides give an inside angle of 120 degrees and a miter of 30 degrees. The turning angle is 60 degrees per corner, and six turns of 60 degrees complete the circle. If your frame does not close, the total turning angle is the first thing to check: it must always add up to 360 degrees.
Measuring and cutting tips
Cut all pieces to exactly the same length, measuring from the long point of one miter to the long point of the other. A difference of even a sixteenth of an inch between pieces makes the frame close unevenly, with one corner tight and another gapped. Use a stop block on your saw so every piece is cut to the same length without remeasuring.
Glue polygon frames in stages rather than all at once. Glue two pieces into a pair, then join pairs, and check the shape as you go. A strap clamp or band clamp holds the whole frame evenly while the glue dries, which is much easier than juggling eight separate clamps around a polygon.
Sand the miters lightly before gluing, and keep glue off the outer faces, where it will show under a finish. If a small gap remains after gluing, a mixture of glue and fine sawdust from the same wood fills it nearly invisibly once sanded and finished.
Safety and building codes
This tool is an educational estimator only, never professional advice. Polygon frame results are estimates, so check your local building codes and consult a licensed builder or carpenter before building anything structural with polygon joints. Keep hands clear of the blade, clamp short pieces, and wear eye protection when cutting small frame parts.
Frequently asked questions
What is the difference between the miter angle and the inside angle? The inside angle is the angle inside the finished polygon at each corner. The miter angle is the cut on each piece, which is half of the angle the piece turns at the corner, and it equals 180 divided by the number of sides.
Can I use this for an irregular polygon? No. This calculator assumes a regular polygon, where all sides and all corners are equal. An irregular frame needs each corner measured separately, like a wall corner, and each joint cut at half its own angle.
Why does my octagon not close? The usual causes are pieces of unequal length, a saw setting slightly off, or a blade that is not square to the table. Check the saw setting with a test joint of two pieces first, and check that all pieces match in length before gluing.
Enter the number of sides, set the saw to the miter it gives, and cut a test pair before the full set. A polygon frame that closes cleanly on the first glue-up is one of the most satisfying small woodworking wins there is.
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