What angle do I cut for a hexagon or octagon?

Divide 180 by the number of sides and set the miter saw to that. A hexagon is 180 ÷ 6 = 30°, an octagon 180 ÷ 8 = 22.5°, a square frame 180 ÷ 4 = 45°. Every piece gets the same cut at both ends, and the joints close up to a full 360°.

How do I cut trim for a corner that is not 90 degrees?

Measure the corner with an angle finder, then the saw setting for each piece is (180 − corner angle) ÷ 2. A 135° bay-window corner is (180 − 135) ÷ 2 = 22.5° a side; a 100° corner is 40°. Use the same setting on both pieces, one left and one right.

Is the miter setting the same for inside and outside corners?

Yes — if you measure the angle between the two wall faces on the side that reads less than 180°, the saw setting is identical. What changes is which way the cut faces: on an inside corner the long point is on the back (the wall side); on an outside corner it is on the face.

How long do I cut each side of a picture frame?

For a frame with square corners, the outside length of each piece (long point to long point) equals the outside size of the frame, and the inside (short point) is that less two moulding widths. A 20 in frame in 2 in moulding is 20 in long point, 16 in short point (508 mm and 406 mm).

Miter angle calculator

Odd corner — measured wall angle

The angles are plain geometry for flat stock cut on a miter saw. They do not cover crown moulding sprung against the wall (that is a compound miter and bevel), saw scales that are out of calibration, or walls that are out of plumb — cut a test pair first.

Two calculators. The first takes the number of sides of a closed frame — box, planter, picture frame, gazebo rim — and gives the saw setting and the long- and short-point length of each piece. The second takes a measured corner angle and gives the setting for the two pieces of trim that meet there.

Worked example

Imperial. A hexagon planter 24 in across the flats in 2 in stock. Saw setting 180 ÷ 6 = 30°. Each outside face is 24 × tan 30° = 13.86 in, about 13 7/8 in long point to long point; the inside face is 13.86 − 2 × 2 × tan 30° = 11.55 in, about 11 9/16 in short point to short point. A trim corner measuring 135° needs (180 − 135) ÷ 2 = 22.5° on each piece.

Metric. The same hexagon at 600 mm across the flats in 50 mm stock: 600 × tan 30° = 346 mm long point, 346.4 − 2 × 50 × tan 30° = 289 mm short point, saw at 30°. A square frame 500 × 400 mm outside in 40 mm moulding is two pieces of 500 mm and two of 400 mm long point, 420 and 320 mm short point, all at 45°.

On the job

Split the error. Eight joints at 22.5° means any error in the saw is counted sixteen times. Half a degree off leaves an 8° gap at the last joint. Cut a test ring from scrap, or cut every piece at the same setting without moving the saw.

Odd corners: measure, don't assume. A “45° bay” is a 135° corner on paper and 133° or 137° in drywall. Measure with an angle finder, type the reading, and cope or back-bevel the joint if it still opens.

Length is long point to long point. Hook the tape on the long point of the first cut and mark the long point of the second. The short point is where the stock width eats back into each end.

What went wrong?

Quick referencesaw settings, 0° = square

Closed frame, n sides: 180 ÷ n — 3 sides 60° · 4 sides 45° · 5 sides 36° · 6 sides 30° · 8 sides 22.5° · 12 sides 15°
Measured corner A: (180 − A) ÷ 2 — 90° → 45° · 135° → 22.5° · 120° → 30° · 100° → 40°
Face length, n sides: outside flat-to-flat × tan(180 ÷ n) — 6 sides: × 0.577 · 8 sides: × 0.414
Short point: long point − 2 × stock width × tan(saw setting)
Inch ↔ mm: 1 in = 25.4 mm · 2 in = 50.8 mm · 24 in = 609.6 mm

The formula

frame: saw = 180° ÷ n · corner: saw = (180° − A) ÷ 2 · face = D × tan(180° ÷ n)

A closed frame turns 360° in n joints, and each joint's turn is shared by two pieces, so each end is cut 360 ÷ n ÷ 2 = 180 ÷ n from square. A corner of angle A turns 180 − A, again shared by two pieces. D is the outside size across the flats.

Questions

What angle do I cut for a hexagon or octagon?: Divide 180 by the number of sides and set the miter saw to that. A hexagon is 180 ÷ 6 = 30°, an octagon 180 ÷ 8 = 22.5°, a square frame 180 ÷ 4 = 45°. Every piece gets the same cut at both ends, and the joints close up to a full 360°.
How do I cut trim for a corner that is not 90 degrees?: Measure the corner with an angle finder, then the saw setting for each piece is (180 − corner angle) ÷ 2. A 135° bay-window corner is (180 − 135) ÷ 2 = 22.5° a side; a 100° corner is 40°. Use the same setting on both pieces, one left and one right.
Is the miter setting the same for inside and outside corners?: Yes — if you measure the angle between the two wall faces on the side that reads less than 180°, the saw setting is identical. What changes is which way the cut faces: on an inside corner the long point is on the back (the wall side); on an outside corner it is on the face.
How long do I cut each side of a picture frame?: For a frame with square corners, the outside length of each piece (long point to long point) equals the outside size of the frame, and the inside (short point) is that less two moulding widths. A 20 in frame in 2 in moulding is 20 in long point, 16 in short point (508 mm and 406 mm).

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