Woodworking Angles: Calculate Miter and Bevel Cuts

Calculate a woodworking miter angle by entering the corner angle and the number of pieces that meet there; the calculator returns each piece’s miter setting. For a standard frame or box corner, it divides the corner angle equally between the two pieces.

Formula

For identical pieces arranged evenly around a corner or joint, calculate the miter setting with:

m = (180° − c) / n

• m is the miter angle cut from a square end, in degrees.
• c is the angle formed by the two outside faces of the completed joint, in degrees.
• n is the number of pieces sharing that joint.

The inside angle of each piece is i = 180° − m. This second result describes the angle across the cut face inside the piece; it is not the saw’s miter setting. The calculator assumes that all pieces are identical and share the joint equally. A two-piece joint with unequal angles, such as a sloped transition, needs a different calculation based on the actual geometry.

Worked Example

With the defaults, the corner angle is 90° and two pieces meet at the corner.

1. Subtract the corner angle from a straight angle: 180° − 90° = 90°.
2. Divide the remainder by the number of pieces: 90° ÷ 2 = 45°.
3. Calculate the inside angle of each piece: 180° − 45° = 135°.

The miter setting is 45.00°, and the inside angle of each piece is 135.00°. On a typical miter saw whose zero setting is a square crosscut, set the saw to 45° for this joint.

How Miter Angles Work

A miter is an angled cut across a board’s width that lets two pieces meet neatly at a corner. The angle of the completed corner and the saw setting are related, but they are not generally the same. For a 90° frame corner, each piece gets a 45° cut because the two cuts together fill the corner.

The formula also handles regular polygons. For a six-sided frame, the outside corner angle is 60°, so each piece’s miter setting is (180° − 60°) ÷ 2 = 60°. For a five-sided frame, it is (180° − 72°) ÷ 2 = 54°. These values assume equal sides and evenly divided joints; they do not account for variations in the actual parts or cutting setup.

In general, if k identical pieces form a regular polygon, each exterior turn is 360° ÷ k. That turn is the corner angle c used by this calculator. For example, a regular hexagon’s turn is 360° ÷ 6 = 60°.

Choosing the Right Angle and Tool Setting

First identify what your measurement describes. A drawing may show the inside angle of a frame, the outside corner angle, a saw setting, or the angle of the cut face. Those values can differ. The calculator’s input is the corner angle between the finished outside faces, and its first result is the miter cut measured away from a square end.

• Picture frame or rectangular box: Use a 90° corner and two pieces; the miter setting is 45°.
• Regular polygon: Work out the outside turn, 360° divided by the number of sides, then enter that turn as the corner angle.
• Three pieces meeting at one point: Enter the angle occupied by the joint and 3, provided the pieces divide it evenly.
• Unequal or compound joint: Do not assume each piece gets the same miter. The geometry may require separate angles, and a bevel may also be needed.

Saw scales do not all describe angles in the same way, so check the tool’s markings and instructions. A miter setting is commonly measured from a square crosscut; a bevel setting tilts the blade through the board’s thickness. A simple flat frame joint usually needs a miter only, while a joint on a sloping or angled surface may require both miter and bevel calculations.

Accuracy, Testing, and Common Mistakes

Even a correct calculation can leave a visible gap if the corner measurement, saw setup, or stock is inaccurate. Check the intended corner with a reliable square or angle-measuring tool, and confirm that the board sits flat and securely against the saw’s fence and table. Make a test cut on scrap of the same thickness before cutting finished pieces.

• Confusing the corner angle with the saw setting: A 90° frame corner uses a 45° miter on each piece, not a 90° saw setting.
• Using the inside angle as the input: The formula expects the corner angle between the finished outside faces. For a square frame, that is 90°.
• Rounding too early: Keep extra precision during calculations and round the saw setting only at the end. A small error can become more noticeable across multiple joints.
• Assuming the pieces share the joint equally: The formula gives an equal split, not the individual angle for an uneven or asymmetrical assembly.
• Mixing up miter and bevel: A miter turns the cut across the board’s face; a bevel tilts the cut through its thickness.

For safety, follow the saw manufacturer’s instructions, keep hands away from the blade path, and secure the workpiece before cutting. Disconnect power before changing a blade or making adjustments that require access to the cutting area. Do not force a cut or hold a short piece where it could move or become trapped.

Frequently Asked Questions

What angle do I cut for a 90-degree corner?
For two identical pieces sharing a 90° corner evenly, cut each miter at 45° from a square end.

How do I calculate a miter angle for a hexagon?
A regular hexagon has six equal exterior turns: 360° ÷ 6 = 60°. Each joint uses a 60° miter setting under the equal-piece assumption.

Is the miter angle the same as the inside angle of the cut?
No. The saw setting measured from a square cut is the miter angle. The inside angle across the cut face is 180° minus that setting.

Can I use this formula for crown molding?
Not by itself in every installation. Crown molding sits at an angle between the wall and ceiling, so the required cut can involve both miter and bevel settings. The wall corner and molding spring angle affect the calculation.

Why does my miter joint have a gap?
Possible causes include an inaccurate corner measurement, a saw that is not set precisely, a board that shifted or was not held flat, or stock that is not straight. Test the setup on scrap and adjust based on the actual joint.

Related

• River Rock Calculator: Estimate Cubic Yards and Bags
• Calculate Paint Coverage
• Board Feet Calculator

in c | Corner angle | deg | 90 | 0
in n | Number of pieces meeting | - | 2 | 2
out m | Miter angle per piece | deg | (180 - c) / n | 2
out i | Inside angle of each piece | deg | 180 - m | 2