Woodworking Miter Angle Calculator: Angles for Any Sided Shape
The miter angle for a regular flat-mitered shape equals 180 divided by the number of sides — a 4-sided square needs 45 degree miters, a 6-sided hexagon needs 30 degree miters, and an 8-sided octagon needs 22.5 degree miters — select or enter your number of sides below for the exact saw angle.
Quick Answer
The miter angle for a regular flat-mitered shape equals 180 divided by the number of sides — a 4-sided square needs 45 degree miters, a 6-sided hexagon needs 30 degree miters, and an 8-sided octagon needs 22.5 degree miters — select or enter your number of sides below for the exact saw angle.
Woodworking Miter Angle Calculator: Angles for Any Sided Shape
Enter your values below for an instant result, then see the formula, worked example, and common mistakes.
Select the number of sides, then click calculate.
How to Use This Calculator
This could be a 4-sided picture frame, a 6-sided planter box, an 8-sided window trim surround, or any other regular polygon.
Common shapes (triangle, square, pentagon, hexagon, octagon, dodecagon) are preset; use the custom field for anything else, like a 5-sided or 10-sided design.
This is the angle to set on your miter saw or miter gauge — each of the two pieces meeting at a corner is cut at this same angle so they join to form the full interior angle.
The interior angle plus twice the miter angle always equals 180 degrees, since the two mitered cut faces plus the interior angle form a straight line when the joint is laid flat.
Formula
Miter Angle = 180 / n, where n is the number of sides of the regular polygon. Equivalently, Miter Angle = (180 – Interior Angle) / 2, where Interior Angle = (n – 2) x 180 / n. Both formulas always agree for a regular (equal-sided) shape — this calculator uses 180/n directly since it is simpler and gives the same result.
Reference Table: Miter Angles by Number of Sides
| Sides | Shape | Interior angle | Miter angle (saw setting) |
|---|---|---|---|
| 3 | Triangle | 60 deg | 60 deg |
| 4 | Square/Rectangle | 90 deg | 45 deg |
| 5 | Pentagon | 108 deg | 36 deg |
| 6 | Hexagon | 120 deg | 30 deg |
| 8 | Octagon | 135 deg | 22.5 deg |
| 12 | Dodecagon | 150 deg | 15 deg |
Common Mistakes to Avoid
- Confusing the interior angle with the miter angle — the saw is set to the miter angle (half of what remains after the interior angle), not the interior angle itself.
- Assuming all miter joints use a 0-degree bevel — this calculator covers standard flat miters; compound miters (used for angled/canted shapes like tapered boxes or crown molding installed at a spring angle) require both a miter AND a bevel angle set together, a different calculation.
- Forgetting that most miter saws are marked with the angle from square (0 degrees = straight cut) rather than from the blade’s full range — double check your saw’s angle scale convention before cutting.
- Not test-cutting on scrap first — even a fraction of a degree of error per joint compounds across multiple corners on shapes with many sides, creating a visible gap on the final seam.
When the Estimate May Be Wrong
This calculator gives the miter angle for a REGULAR polygon (all sides and angles equal) cut as a flat (non-compound) miter. It does not cover compound miters for canted/angled assemblies, irregular polygons with unequal angles, or miters joining boards of different widths — those require additional trigonometry beyond a simple 180/n calculation.
FAQs
What is the formula for miter angle?
Miter angle equals 180 divided by the number of sides of the regular shape you are building — for example, 180/4 = 45 degrees for a square.
What angle do you cut a hexagon miter?
30 degrees per corner — calculated as 180 divided by 6 sides, or equivalently half of the 180-degree supplement of the 120-degree interior angle.
Is miter angle the same as bevel angle?
No — miter angle is the horizontal angle cut across the board’s width (seen from above), while bevel angle is a tilt of the blade through the board’s thickness, used for compound cuts on angled assemblies.
Why do miter joints need matching angles on both pieces?
Two mitered pieces must each be cut at the same miter angle so that when joined, their combined angle equals the shape’s interior angle exactly, leaving no gap at the seam.
Sources and Methodology
Miter angle formula (180/n for regular polygons) and interior angle formula ((n-2) x 180/n) are standard, universally used geometry confirmed against Omnicalculator’s Miter Angle Calculator, Skirting World’s Mitre Angle Calculator, and Calculator Academy’s Angle Cut Calculator — all citing the same n-sided polygon miter formula.
