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 half the interior angle: 60 degrees. On most mitre saws, set the angle to 30 degrees from the fence (since saws measure from 90 degrees). Each joint has two mitre cuts at 60 degrees.

How do I calculate the mitre angle for any polygon?

The formula is: Interior angle = (n-2) x 180 / n, where n is the number of sides. The mitre angle (saw setting) is half the interior angle. For example: pentagon (5 sides) = 108 degrees interior, 54 degree mitre; octagon (8 sides) = 135 degrees interior, 67.5 degree mitre.

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 Type

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 angle = Interior angle / 2

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.