Miter Angle Calculator
Find the miter angle for any regular polygon frame, and the number to actually set on your saw — which is usually not the same figure. Works for picture frames, hexagonal planters, octagonal tabletops and any equal-sided shape.
Calculator
3 or more. A picture frame is 4.
Result
Set your miter saw to
30°
Assumes 0° on your saw is a square crosscut, which is the usual convention.
This covers flat frames only: pieces lying in one plane with equal corners. Compound miters — crown moulding, sprung angles, canted sides — need a spring angle and a bevel setting as well, and are deliberately not calculated here.
Three different angles, and why people cut the wrong one
The interior angle is the angle inside the finished corner. On a square frame it is 90°; on a hexagon, 120°.
The miter angle is half of that — the angle each of the two mating pieces is cut at, so the two halves add up to the corner. Square: 45°. Hexagon: 60°.
The saw setting is what you dial into a miter saw, and most saws are marked with 0° as a square crosscut rather than as a straight-through cut. That makes the setting 90° minus the miter angle. Square: 45°. Hexagon: 30°.
The square frame is the trap. Its interior, miter and saw setting are 90, 45 and 45 — so whichever rule you half-remember appears to work. Then you cut a hexagon at 60° on the saw instead of 30° and six pieces are scrap. All three numbers are shown separately above for exactly this reason.
The formula
For a regular polygon with n sides, the interior angle is ((n − 2) × 180) ÷ n. The miter angle is half of that, and the saw setting is 90° minus the miter angle.
There is a shortcut worth knowing because it is easier to do in your head at the saw: the saw setting is simply 180 ÷ n. A hexagon is 180 ÷ 6 = 30°. An octagon is 180 ÷ 8 = 22.5°. A square is 180 ÷ 4 = 45°. The two derivations agree exactly.
For a corner that is not part of a regular polygon, switch to custom mode and enter the included angle you measured. Each piece gets exactly half of it.
Worked example
You are building an octagonal mirror frame from eight equal pieces.
Interior angle: ((8 − 2) × 180) ÷ 8 = 135°. Miter angle: 67.5°. Saw setting: 90 − 67.5 = 22.5°.
So you set the saw to 22.5° and cut both ends of every piece, flipping the stock or swinging the saw to the opposite side between cuts so the two ends mirror rather than parallel each other. Eight pieces, sixteen cuts, and the exterior angles sum to 360° as they must for the shape to close.
Cutting an accurate miter
Small angular errors multiply around a closed frame. A quarter of a degree of error at each corner of an octagon accumulates to two degrees by the time you return to the start, which shows up as a visible gap in the last joint.
Cut a test frame from scrap at the same setting before committing. Four short offcuts dry-assembled will show a cumulative error immediately, and a saw whose scale reads a fraction off its true angle is common enough to be worth checking every time.
Length matters as much as angle. Mitered pieces must be identical in length for the shape to close square; a difference of half a millimetre between opposite sides skews the whole frame regardless of how good the angles are.
Common mistakes
Setting the interior angle on the saw is the classic one, and it is why this page separates the three numbers rather than reporting a single "angle".
Assuming a miter saw reads from the same zero as a protractor is the second. Confirm which convention your saw uses before trusting either number: if 0° on your scale gives a square crosscut, use the saw setting shown above.
Trying to use this for crown moulding is the third. Crown sits at a spring angle against the wall, which makes it a compound cut needing both a miter and a bevel. Flat-frame numbers will not work and are not offered here.
From one angle to the whole piece
Angles are one part of a build. Describe the piece you are making and Plank CAD works out the dimensions, the joinery and the cut list together — currently for bookcases and open storage cabinets.
Common questions
45° on each of the two pieces meeting at a corner. A picture frame is a four-sided regular polygon, its interior angle is 90°, and half of that is 45°. On a standard miter saw you also set 45°, because the saw measures from a square crosscut.
The interior angle of a regular hexagon is 120°, so each piece is mitered at 60°. On a miter saw you set 30°, not 60° — this is the case where confusing the two numbers is most likely to waste stock.
Usually cumulative angular error rather than one bad cut: each corner being a fraction of a degree off adds up around the frame. It can also be uneven piece lengths, or stock that is not perfectly straight. Cutting a test frame in scrap first will show which of the two you are dealing with.
No. Crown moulding is installed at a spring angle to the wall, which makes every corner a compound cut requiring both a miter and a bevel setting. The flat-frame numbers here do not apply, and using them will produce joints that do not close.