Compound Miter Angle Calculator
Building a sloped-sided box, planter, or crown ring means every joint needs two angles set at once: the saw miter and the blade bevel. This calculator solves the standard compound-miter trigonometry for any regular polygon with sides that tilt out from vertical. Enter the number of sides and the slope (tilt from vertical) and it returns the saw setting and the bevel setting. The math is exact geometry, so the only real-world step left is to dry-fit a scrap ring to absorb blade kerf and scale error before cutting your finished stock.
Compound miter formula
Half-angle A = 180 / N degrees
Saw miter = atan( cos(slope) * tan(A) )
Blade bevel = asin( sin(slope) * cos(A) )
Flat miter (slope 0) = A
Angles are in degrees. With slope 0 the bevel is 0 and the miter equals 180/N, the ordinary flat miter for a regular polygon. As slope increases, the bevel grows and the miter shrinks slightly.
Tips for compound cuts
- A four-sided box at 0 slope gives a 45-degree miter, as expected.
- Crown molding uses the spring angle as the slope input.
- Cut and dry-fit scrap pieces before your finished stock.
- Label and keep all pieces oriented the same way around the ring.
- Small saw-scale errors accumulate; aim for a perfect dry fit first.
Compound miter: frequently asked questions
What is a compound miter?
A compound miter is a cut that combines a miter angle (the saw swung left or right) with a bevel angle (the blade tilted from vertical). It is used to build sloped-sided structures such as crown molding, planters, hoppers, and segmented frames where each joint meets at an angle in two planes at once.
How are compound miter angles calculated?
For a regular polygon with N sides whose walls tilt at slope angle S from vertical, the miter (saw) angle = atan(cos(S) x tan(180/N)) and the bevel (blade tilt) angle = atan(sin(S) x sin(180/N) ... ) derived from spherical trigonometry. This calculator uses the standard formulas: miter = atan(cos S x tan(180/N)) and bevel = asin(sin S x cos(180/N)).
What does the slope or tilt angle mean?
The slope angle is how far each side leans out from vertical. A slope of 0 degrees gives vertical walls (a normal frame), so the bevel becomes 0 and the miter becomes the flat 180/N angle. A larger slope tilts the sides outward like a flared planter, increasing the bevel.
Does this work for any number of sides?
Yes, for any regular polygon with three or more equal sides: triangles, squares, pentagons, hexagons, octagons, and beyond. Enter the number of sides and the wall slope, and the calculator returns the saw miter setting and blade bevel setting for each joint.
Why test cut scrap first?
Saw scales, blade kerf, and material thickness all introduce small errors, and compound cuts compound those errors around a closed shape. Cutting a set of short scrap pieces and dry-fitting the ring before committing to your finished stock is standard practice for compound work.
Official sources
- NIST Digital Library of Mathematical Functions: DLMF, trigonometric identities.
- National Institute of Standards and Technology: NIST, measurement references.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.