Miter and Bevel Cut Calculator
Computes the exact miter and bevel angles for picture frames, polygon frames, and crown molding joints. Use it before setting your miter saw to avoid costly cut errors on expensive molding stock.
About this calculator
For a simple corner joint (like a picture frame), the miter angle is simply (180° − wallAngle) / 2, because the two pieces must together fill the corner. For a regular polygon frame with N sides, the compound miter formula is: miterAngle = atan(sin(180°/N) / cos(180°/N)) × (180°/π), which reduces to 90°/N for a flat frame. Crown molding is more complex: the saw miter angle = atan(cos(springAngle) × tan(wallAngle / 2)), where the spring angle is the angle the molding makes against the wall (commonly 38° or 45°). All formulas rely on trigonometric identities to decompose a three-dimensional joint into two flat saw settings: the miter (horizontal rotation of the fence) and the bevel (tilt of the blade). Getting both right simultaneously is the key challenge of compound miter joinery.
How to use
Example: cutting a standard octagon (8-sided) frame. sides = 8, so each interior corner = 360°/8 = 45° miterAngle = (180 − 45) / 2 = 67.5° … wait, for a polygon frame the formula uses: miterAngle = atan(sin((360/8/2) × π/180) / cos((360/8/2) × π/180)) × 180/π = atan(sin(22.5°) / cos(22.5°)) × 180/π = atan(tan(22.5°)) × 180/π = 22.5° Set your miter saw to 22.5°. Each of the 8 pieces gets a 22.5° cut on both ends, and they will close into a perfect octagon.
Frequently asked questions
How do I find the miter angle for a picture frame with a 90-degree corner?
For a standard 90° corner, the formula simplifies to (180 − 90) / 2 = 45°, so each piece is cut at 45° on both ends. This is the most common miter cut in woodworking and is why a 45° stop is standard on every miter saw. Both pieces are identical, which makes setting up a stop block for repeatable cuts very easy. Always make a test cut in scrap first and check the joint closes tightly before cutting your finished material.
What is the spring angle for crown molding and how does it affect saw settings?
The spring angle is the angle at which crown molding rests against a flat wall — typically 38° or 45° for standard profiles. It matters because crown molding is a compound joint: the wall corner angle and the spring angle together determine both the miter and bevel settings on your saw. A 45° spring angle simplifies the math and is friendlier for cutting crown flat on the saw table. If your molding has an unusual spring angle, measure it by holding the molding against a flat surface and measuring the angle it makes with the surface.
Why do compound miter cuts require both a miter angle and a bevel angle simultaneously?
Crown molding and similar trim pieces sit at an angle relative to both the wall and the ceiling, meaning the joint exists in three-dimensional space rather than a flat plane. A single flat miter cut would leave a gap because it doesn't account for the tilt of the molding. By tilting the blade (bevel) and rotating the fence (miter) at the same time, you effectively project the true joint angle onto both the face and edge of the board. Getting either setting wrong, even by a degree, results in a visible gap that is difficult to fill cleanly.