Angle Cut Calculator - Miter, Bevel & Compound Cuts

What is an angle cut calculator?

An angle cut calculator works out the angle to set on a saw for a cut in wood, metal, or another material. It covers three cut types: the miter cut, the bevel cut, and the compound cut, which combines the other two. Woodworkers, carpenters, and metalworkers use it to make two pieces meet at a corner without gaps.

Types of angle cuts

Miter cut

A miter cut runs across the width of a board at an angle other than 90 degrees, while the blade stays square to the board's face. Two matching miter cuts joined together form a corner, as in a picture frame or a length of trim.

Bevel cut

A bevel cut runs through the thickness of a board at an angle other than 90 degrees to its face. It tilts the edge of the cut rather than its direction. Bevel cuts are common on tabletops, countertops, and outdoor trim built to shed water.

Compound cut

A compound cut combines a miter and a bevel in one cut. Crown molding needs compound cuts because it sits at an angle against both the wall and the ceiling at once.

Miter angle formula

For a plain miter joint, the miter angle depends only on the corner angle: the angle at which the two pieces will meet.

$\text{Miter Angle} = \frac{180° - \text{Corner Angle}}{2}$

Example: Two boards meet at a standard 90° corner. Miter Angle = (180° − 90°) ÷ 2 = 45°. Each board is cut at 45°, and the two cuts together form the 90° corner.

For a frame with more than four sides, this simplifies to 180° divided by the number of sides. An eight-sided frame needs a miter angle of 180° ÷ 8 = 22.5° at each corner.

Bevel angle formula

For a plain bevel cut, the bevel angle equals the slope angle: the angle of tilt from horizontal, or from the face of the material.

$\text{Bevel Angle} = \text{Slope Angle}$

Compound angle formula

A compound cut needs both a corner angle and a slope angle. The corner angle first gets converted to a half-angle, the half-angle of the joint rather than of the corner itself:

$\text{Half Angle} = \frac{180° - \text{Corner Angle}}{2}$

$\text{Miter Angle} = \tan^{-1}\left(\cos(\text{Slope Angle}) \times \tan(\text{Half Angle})\right)$

$\text{Bevel Angle} = \sin^{-1}\left(\sin(\text{Slope Angle}) \times \sin(\text{Half Angle})\right)$

When the slope angle is 0°, these reduce to the plain miter formula above, since a flat cut has no bevel.

Example: A room corner measures 110°, and the crown molding sits at a 38° slope angle against the wall.

• Half Angle = (180° − 110°) ÷ 2 = 35°
• Miter Angle = tan⁻¹(cos 38° × tan 35°) ≈ 28.9°
• Bevel Angle = sin⁻¹(sin 38° × sin 35°) ≈ 20.7°

The saw is set to a 28.9° miter and a 20.7° bevel for each piece of molding.

How to use the calculator

1. Choose a cut type: miter, bevel, or compound.
2. For a miter cut, enter the corner angle.
3. For a bevel cut, enter the slope angle.
4. For a compound cut, enter both the corner angle and the slope angle.
5. Read the result, and copy it if needed.

The corner angle must fall between 1° and 179°. The slope angle must fall between 0° and 90°.

Where angle cuts are used

• Crown molding and other trim, at wall corners that are not exactly 90°
• Picture frames and mirror frames, including frames with more than four sides
• Furniture with tapered legs or angled joints
• Roof rafters and other framing that needs a compound angle
• Metal fabrication and pipe fitting, where two pieces meet at an angle

A short history

Craftsmen have cut mitered corners since at least ancient Egypt. Early builders relied on a square and careful measurement rather than a formula. The miter box, a guide that holds a hand saw at a fixed angle, appeared in the 19th century. Powered miter saws followed in the 20th century. Compound miter saws, which adjust both miter and bevel on one machine, became common in the 1970s. Digital angle finders and calculators later took most of the manual trigonometry out of the job.

Common problems and fixes

A gap in a miter joint usually means the corner was measured wrong, or the saw needs calibration. A digital angle finder gives a more accurate reading than assuming a corner is exactly 90°. A test cut in scrap material catches most remaining mistakes before they reach the final piece. This matters most on compound cuts, which are less forgiving than plain miters.

Frequently asked questions

What is the difference between a miter cut and a bevel cut?

A miter cut angles the end of a board across its width, while the blade stays square to the face. A bevel cut angles the cut through the board's thickness instead. Picture frames usually use miter cuts. Tabletop edges often use bevel cuts.

What angle do I cut for a 90° corner?

45°. Miter Angle = (180° − Corner Angle) ÷ 2, so a 90° corner gives (180° − 90°) ÷ 2 = 45°.

How do I find the miter angle for a frame with more than four sides?

Divide 180° by the number of sides. A six-sided frame needs 30° miter cuts (180° ÷ 6). An eight-sided frame needs 22.5° (180° ÷ 8).

Why doesn't a crown molding corner fit even with the right angles entered?

Walls are rarely perfectly square, and molding does not always sit at the same angle against the wall along its full length. A test cut helps. Coping the inside corners, instead of mitering both pieces, often fits better than a mitered inside corner.

Can this calculator be used for metal as well as wood?

Yes. The angles are geometric and do not depend on the material, though metal needs different blades and cutting tools than wood does.

What is spring angle, and how does it relate to the slope angle used here?

Spring angle is the angle crown molding tilts away from the wall, commonly 38° or 45°. That value is entered as the slope angle for a compound cut.