Construction & DIY · Woodworking
Miter and bevel angle calculator.
Enter the number of sides and how far the walls lean from vertical to get the miter and bevel settings for the saw.
Inputs
Saw settings
Enter the number of sides and lean.
What are the miter and bevel angles for a box with N sides?
For a regular N-sided box with vertical walls, each joint is a bevel of 180 / N degrees with the miter set to zero: 45 degrees for four sides, 30 for six and 22.5 for eight. A flat frame with the same number of sides uses a miter of 180 / N degrees with the blade upright. When the walls lean (a planter, hopper or tapered box), the cut becomes compound: miter = atan(cos β × tan(180 / N)) and bevel = asin(sin β × sin(180 / N)), where β is the wall angle from horizontal, which is 90 degrees minus the lean from vertical.
Worked example. A four-sided planter with walls leaning 30 degrees from vertical needs a miter of 26.57 degrees and a bevel of 37.76 degrees, with each board lying flat on the saw table.
Method. The formulas come from the geometry of the plane that bisects two neighbouring walls. They are tested here against an independent vector calculation of the same joint and against the straight-wall and flat-frame limits. Saw scales vary, so test on scrap.
Frequently asked questions
What angle do I cut for a hexagon?
Six sides: each joint is 30 degrees (180 divided by 6). Cut a miter of 30 degrees with the blade upright for a flat frame, or tilt the blade 30 degrees with the miter at zero for a box with vertical walls.
What is the compound miter for a four-sided box with 30 degree sloped sides?
With walls leaning 30 degrees from vertical, the miter is 26.57 degrees and the bevel is 37.76 degrees, board flat on the table.
What does wall lean from vertical mean?
It is how far each wall tilts away from straight up. Zero is a straight-sided box; larger numbers give a more flared planter or hopper.
Do these settings work for every saw?
They are the angles between the blade and the board for the cut described. Saws read the angle scales differently, so check a test cut with a square or an angle gauge.
Sources
Checked
No published data table is used; this is geometry. The formulas are derived from the plane normals of two adjacent walls and verified in the test suite against an independent vector calculation, and against the known straight-wall results (bevel = 180/N, miter 0) and flat-frame result (miter = 180/N, bevel 0). Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Cutting guidance for woodworking. Test on scrap and use your saw guards and safety equipment.