Woodworking & Construction Calculators

Fine woodworking & cabinetry

Polygon Miter and Segment Length Calculator

For n sides, each miter from square is 180°/n. The outside face of a ring segment is D × tan(π/n). The straight chord is D × sin(π/n).

Inputs

Units
in

Results

Miter from square
22.500°
Outside face
4.971in
Chord
4.592in

Recommended gear

Calculation method

A regular n-gon is n identical isosceles triangles. Half-angle π/n gives both the miter (90° − π/n from the long grain, which is 180/n from square) and the two lengths.

Exact formula

Hexagon: miter 30°, face = D / √3, chord = D / 2. Diameter is the outside diameter of the finished ring.

Bowls and gazebos

The same n and D describe a turning ring and an octagonal picnic table. Only the diameter unit changes with the toggle.

Frequently asked questions

Miter 22.5° on an octagon?

Yes. 180/8 = 22.5°. That is the saw setting from a square cut.

Face vs chord?

Use outside face for staved rings. Chord is the straight line between vertices — handy for gazebo plates.

Does wall thickness matter?

This diameter is outside. For thick staves, some turners size the face at the mid-wall. This tool stays on the outside.

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