What mitre angle do I need for a hexagonal frame?

A hexagon (6 sides) has interior angles of 120 degrees. The mitre saw setting is 180 divided by the number of sides: 180 / 6 = 30 degrees. Set the saw to 30 degrees (measured from a square crosscut, which most saws read as 0 degrees). Each joint is made from two pieces, each cut at the 30 degree setting, and the two cuts together close the 120 degree corner.

How do I calculate the mitre angle for any polygon?

The interior angle is (n-2) x 180 / n, where n is the number of sides. The mitre saw setting is 180 / n (this equals 90 minus half the interior angle, measured from a square crosscut). For example: pentagon (5 sides) = 108 degrees interior, 36 degree saw setting; octagon (8 sides) = 135 degrees interior, 22.5 degree saw setting; square = 45 degrees; hexagon = 30 degrees.

What is the difference between mitre and bevel angles?

A mitre angle is a cut across the face of the board (the saw head rotates left or right). A bevel angle is a cut through the thickness of the board (the saw blade tilts). Compound angles require both mitre and bevel adjustments simultaneously.

How do I find angles when I know three side lengths?

Use the law of cosines: cos(A) = (b² + c² - a²) / (2bc). This calculator handles this automatically. Enter all three side lengths and it will compute all three angles. This is useful for fitting pieces into irregular spaces.

What are complementary and supplementary angles?

Complementary angles sum to 90 degrees (useful for right-angle joints). Supplementary angles sum to 180 degrees (useful for straight-line joints). If you know one angle of a right-angle joint, the complementary angle is what your mitre saw needs to be set to.

WoodCalcs

Angle Calculator — Mitres, Bevels & Polygon Joints

Calculate angles for mitres, bevels, and polygon joints in woodworking.

Calculation TypeChoose: polygon mitre (frame joints), triangle from 3 sides (SSS), complementary (sums to 90°), or supplementary (sums to 180°)

Number of Sides

3 = triangle, 4 = square, 5 = pentagon, 6 = hexagon, 8 = octagon

How We Calculate This

This calculator handles several common angle calculations for woodworking.

Polygon mitre angle

Interior angle = (n - 2) x 180 / n

Mitre saw setting = 180 / n (equivalently 90 − interior/2). This is the angle you dial into the saw, measured from a square crosscut — for example 30° for a hexagon, 22.5° for an octagon, 45° for a square.

The cut-face angle measured from the board’s long edge is interior/2 (60° for a hexagon). That describes the shape of the cut face, not a saw scale reading, so do not dial it into the saw.

Triangle angles (SSS)

cos(A) = (b² + c² - a²) / (2bc) (Law of cosines)

This finds all three angles from three known side lengths.

Frequently Asked Questions

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Last updated: February 2026

All calculations are estimates. Always verify measurements and material quantities before cutting or purchasing.