Miter Angle Calculator

1. Enter the number of equal sides in your frame or polygon.
2. Read the miter angle to set on your mitre saw.
3. Cut each end of every piece at that angle.
4. Check the corner angle to confirm the shape you will get.

A miter angle is the angle you cut on the end of a piece so two pieces meet cleanly at a corner. For a frame with equal sides, each corner is shared by two mitred ends, so each end is cut at half the corner turn.

The classic case is a picture frame: four pieces, each cut at 45 degrees, meeting at 90 degree corners. The same idea scales to hexagons, octagons and any regular polygon, which is why the miter angle is a cornerstone of frame and trim work. Get it right and the joints close up with no gaps; get it wrong by even half a degree and the error multiplies around the frame until the last corner refuses to meet, which is why the exact number matters so much on a mitred job.

1. Divide 180 by the number of equal sides for the miter angle.
2. Each end of every piece is cut at that angle.
3. The corner angle is (sides minus 2) times 180, divided by the sides.
4. The exterior angle, or turn at each corner, is 360 divided by the sides.

Because two ends share each corner, the miter is half the exterior turn, which is exactly 180 over the number of sides.

A square picture frame has 4 sides. The miter angle is 180 divided by 4, which is 45 degrees, so you cut each end at 45. The corners meet at 90 degrees. For a hexagonal frame with 6 sides, the miter drops to 30 degrees and the corners open to 120 degrees. An octagon needs 22.5 degree miters for its eight 135 degree corners. The pattern is easy to remember once you see it: double the sides and the miter roughly halves, so the more sides a frame has, the gentler each cut becomes and the closer the whole shape creeps toward a circle.

Number of Sides

More sides means a shallower miter and a wider corner, since the turn at each corner shrinks.

Equal vs Unequal Sides

This formula is for regular, equal-sided frames; unequal corners each need their own angle.

Flat vs Sloped Work

A flat frame uses a simple miter; tilted or sloped joints need a compound miter with a bevel too.

Saw Reference

Some saws measure from square and some from straight, so check whether 45 or 45 off zero matches your machine.

Miter and corner angles for common regular frames.

Notice the miter angle always halves the exterior turn, so it falls steadily as you add sides.

Making Frames

Get the exact angle for a picture frame, mirror or panel of any number of sides.

Building Polygons

Work out miters for hexagon planters, octagon tables and multi-sided boxes.

Trim and Moulding

Set the saw for angled trim runs that turn corners of equal frames.

1. Confusing Miter and Corner Angle

The saw setting is the miter, not the wider corner angle; do not cut the corner angle by mistake.

2. Forgetting Both Ends

Each piece is mitred at both ends, so a small error doubles at every joint.

3. Assuming Equal Sides

This formula needs a regular frame; unequal corners need individual angles.

4. Ignoring Blade Reference

Check whether your saw reads from square or from straight so you dial in the right number.

The geometry is exact for a regular, equal-sided frame. It gives a flat miter, not a compound one for sloped work.

A four-sided picture frame uses 45 degree miters, since 180 divided by 4 is 45. Each of the four pieces is cut at 45 degrees on both ends.

Divide 180 by the number of equal sides. A hexagon frame with 6 sides needs 30 degree miters; an octagon needs 22.5 degrees.

A six-sided frame needs 30 degree miters, and its corners meet at 120 degrees.

The miter is the angle you cut on the saw; the corner angle is the wider interior angle where two pieces meet.

An eight-sided frame uses 22.5 degree miters for its 135 degree corners.

Because two mitred ends share each corner symmetrically, so each end takes half the corner turn, the miter angle.

No. This formula is for regular, equal-sided frames. Unequal corners each need their own miter based on the corner angle.

Those need a compound miter, adding a bevel to the miter. Use our compound miter calculator for that.

No. The calculator runs entirely in your browser and nothing you enter is stored or sent anywhere.

• Miter joint (Wikipedia).
• Regular polygon (Wikipedia).
• Internal and external angles (Wikipedia).