Miter Angle Calculator (any corner or polygon frame: saw setting & cut angle)

Understanding the miter angle calculator — concept and principle

This calculator gives the miter saw setting and cut angle for joining pieces at any corner, or for building a regular polygon frame such as a hexagon or octagon. Woodworkers use it for picture frames, trim, planters and boxes.

Half the turn at each corner: with the default inputs the result is 30° miter (12 cuts for 6 sides).

How it is calculated

Corner angle: for a regular polygon with N sides, (N − 2) × 180° ÷ N; otherwise the angle you enter.
Cut angle against the board edge = corner ÷ 2.
Miter saw setting (from square) = 90° − corner ÷ 2, which equals 180° ÷ N for a polygon.
Turning angle at each corner = 180° − corner angle.
Cuts = 2 × N for a polygon, or 2 for a single joint.

The principle

A miter joint splits the corner equally between the two pieces, so each piece is cut at half the corner angle measured from its edge. Miter saws are scaled from square, where 0° is a straight 90° cut, so the setting is 90° minus half the corner. For a regular polygon, the interior angles add up to (N − 2) × 180°, giving each corner (N − 2) × 180° ÷ N. The saw setting then simplifies to 180° ÷ N: 45° for a square frame, 30° for a hexagon, 22.5° for an octagon.

Worked example

Default inputs: regular polygon frame, 6 sides.

Corner angle = (6 − 2) × 180 ÷ 6 = 120°.
Cut angle against the edge = 120 ÷ 2 = 60°.
Saw setting = 90 − 60 = 30° (= 180 ÷ 6).
Turning angle = 180 − 120 = 60°.
Cuts = 2 × 6 = 12.

How to read the result

Set the saw to the shown setting and make a test joint with scrap before cutting good stock. Small errors multiply in a polygon: on a hexagon, being off by 0.5° on each cut adds up to a 6° gap at the last joint. All pieces of a regular frame must also be exactly the same length.

Common mistakes

Setting the saw to the cut angle (60°) instead of the setting from square (30°).
Assuming room corners are exactly 90°; measure them with an angle finder.
Cutting pieces of slightly different lengths.
Forgetting that crown moulding needs a compound miter with a bevel.

Keep in mind: Use saw guards and clamps, and keep hands clear of the blade. Follow the tool maker's safety instructions.

Frequently asked questions

What angle do I cut for a hexagon?

Set the miter saw to 30°; each corner is 120°.

What angle for an octagon frame?

22.5° on the saw (180 ÷ 8).

How do I cut trim for a 135° corner?

Set the saw to 90 − 135 ÷ 2 = 22.5°.

Sources: Euclidean geometry: interior angle of a regular polygon = (N − 2) × 180° ÷ N (any geometry textbook)

Checked 9 Nov 2026. Euclidean geometry: interior angle of a regular N-gon = (N − 2)·180°/N; a miter bisects the joint angle.

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