How do I calculate the miter angle for a corner?

For a simple flat join (such as skirting board or picture frame), the miter angle you set on the saw for each piece is 90 degrees minus half the corner angle. A standard 90-degree corner requires each piece to be cut at 45 degrees. A 135-degree bay-window corner requires each piece to be cut at 22.5 degrees, and a 120-degree corner requires 30 degrees. The formula is: miter angle = 90 - (corner angle / 2). For a compound cut on a sloped or angled surface, both a miter angle (horizontal blade rotation) and a bevel angle (blade tilt) are needed, and the formulas involve trigonometry.

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

A miter cut is a cut made at an angle across the face (width) of a piece of timber, with the saw blade kept vertical. You set the miter angle by rotating the saw table or fence left or right. A bevel cut is a cut made at an angle through the thickness of the piece, with the saw blade tilted away from vertical. A compound cut uses both: the table is rotated (miter angle) and the blade is tilted (bevel angle). Compound cuts are needed when joining pieces that meet at a corner where one or both surfaces are not flat or vertical, such as crown moulding or sloped roof trim.

What miter angle do I use for a six-sided hexagonal frame?

A regular hexagon has interior corner angles of 120 degrees. To join six pieces into a hexagonal frame, each end of each piece must be cut at half the exterior supplement angle. The interior angle is 120 degrees, so the miter cut on each end is 30 degrees (because 180 degrees minus 120 degrees equals 60 degrees, and half of that is 30 degrees). You can also calculate this as 90 degrees minus (interior angle / 2), which gives 90 minus 60 equals 30 degrees. For a square (4 sides, 90-degree corners), this gives 90 minus 45 equals 45 degrees.

Angle Cut Calculator

This calculator works out the exact miter and bevel angles to set on your saw when two pieces of timber meet at a corner, covering skirting boards, picture frames, crown moulding and polygon-shaped frames. Start by choosing whether you need a simple miter cut, where the blade stays vertical, or a compound cut, where both the saw table and the blade tilt, then enter your corner angle in degrees, or pick a common preset such as a square corner, bay window, hexagon or pentagon. For compound cuts you also enter the spring (slope) angle the trim sits at against the wall, and if you are building a regular polygon frame you can select the number of sides instead, which sets the corner angle automatically. Piece length and width can be entered for reference alongside the results. The calculator returns the miter angle for each end, the bevel angle, the combined cut angle per piece, and the corner angle entered, plus a full cut breakdown and a reference table of common corner angles with their matching cuts. Use the results to set your saw before cutting, and always cut a test piece first. These are ideal geometric angles: allow for blade kerf and material thickness, and remember real-world corners are rarely exactly square, so measure your actual corner before committing to a final cut.

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Standard formula Trigonometric relationships for compound miter geometry. No material-specific variability.

1. Corner Details

Cut type

Corner angle (the angle between the two walls or surfaces)

degrees

Enter a corner angle between 1 and 179 degrees.

Spring (slope) angle (angle the piece sits against the wall)

degrees

Enter a slope angle between 1 and 89 degrees.

Common preset

2. About Your Join

Number of sides in shape (for regular polygon frames)

Piece length (for reference)

Piece width (for reference)

Saw Settings

Miter Angle (each end)
45.0°
Blade rotation (horizontal)

Bevel Angle

0.0°

Blade tilt from vertical

Cut Angle per Piece

90.0°

Combined end-to-end

Corner Angle

90.0°

Entered corner

Common Corner Angles Reference

Corner Angle	Miter Cut (each end)	Typical Use	Sides in Shape

Cut Breakdown

Corner angle90.0°

Cut typeSimple miter (flat)

Miter angle (each piece)45.0°

Bevel angle0.0°

Piece length1200 mm

Total cut angle (both ends)90.0° (both ends)

Polygon Frame Reference

Shape selectedSquare / Rectangle

Number of sides4

Interior angle90.0°

Miter cut per end45.0° per end

Piece width90 mm

Pieces needed4 pieces

Summary: Enter your corner angle above to see the saw settings.

How Angle Cuts Work

When two pieces of timber meet at a corner, each piece must be cut so that the faces meet flush and the joint closes tightly. The angle you cut depends on the corner angle between the two surfaces.

For a simple flat miter join, both pieces are cut on the same plane (no blade tilt). The miter angle you set on the saw for each piece is 90 degrees minus half the corner angle. A standard room corner at 90 degrees requires each piece to be cut at 45 degrees. A bay window corner at 135 degrees requires a 22.5-degree cut on each piece (90 - 135/2).

For a compound miter join (used for crown moulding or any trim that sits at an angle to both the wall and ceiling), both a horizontal rotation (miter angle) and a blade tilt (bevel angle) are required. The formulas involve the arctangent and arcsine of the corner and spring angles.

The Formulas

Simple miter (flat trim):

Miter angle = 90 - (corner angle / 2)
Bevel angle = 0 degrees (blade stays vertical)

Compound miter (sloped surface, spring angle S, corner angle C):

Half corner = C / 2 (in radians for calculation)
Miter angle = arctan(sin(S) x tan(C / 2))
Bevel angle = arcsin(cos(S) x cos(C / 2))

Where S is the spring (slope) angle -- the angle the piece makes with the wall -- and C is the full corner angle. These formulas apply to crown moulding set at a fixed spring angle against the wall and ceiling.

Regular Polygon Frames

When building a picture frame, box, or decorative border in the shape of a regular polygon, all corners have the same interior angle. The miter cut for each end of each piece is:

Interior angle of a regular n-sided polygon = (n - 2) x 180 / n
Miter angle per end = 90 - (interior angle / 2)

For a square frame (4 sides): interior angle = 90 degrees, miter cut = 90 - 45 = 45 degrees. For a hexagonal frame (6 sides): interior angle = 120 degrees, miter cut = 90 - 60 = 30 degrees.

Worked Example

For the default settings (simple miter, 90-degree square corner):

Corner angle = 90 degrees
Miter angle each end = 90 - 90/2 = 45 degrees
Bevel angle = 0 degrees (flat cut, blade vertical)
Set your miter saw to 45 degrees, bevel at 0 degrees
Cut both ends of both pieces at 45 degrees, mirrored (one left, one right on each piece)

This matches the calculator output for the default 90-degree corner with simple miter selected.

Tips for Accurate Angle Cuts

Always check your actual corner angle before cutting -- walls and corners are rarely exactly 90 degrees. Use a digital angle finder or protractor.
For out-of-square rooms, bisect the actual measured angle rather than assuming 90 degrees.
When fitting skirting boards, cut a test piece first and hold it in place to check the fit before cutting all pieces.
Mark which end of each piece gets which cut (left or right miter) to avoid cutting the wrong end.
For crown moulding, the spring angle is usually printed on the back of the moulding or available from the manufacturer. Common spring angles are 38 degrees and 45 degrees.

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Method: Simple miter formula: miter = 90 - corner/2. Compound miter formulas: miter angle = arctan(sin(S) x tan(C/2)), bevel angle = arcsin(cos(S) x cos(C/2)), where S is the spring angle and C is the corner angle. Regular polygon interior angle = (n - 2) x 180 / n. Standard geometric relationships for joinery and carpentry.

This calculator provides ideal geometric angles. In practice, allow for blade kerf width, material thickness, and the fact that room corners are rarely exactly the stated angle. Always measure your actual corner before cutting.