Calculate Mitre Angles

Easily calculate mitre angles for woodworking projects, whether you’re joining two pieces at a specific corner angle or constructing a regular polygon frame.

Calculate Mitre Angles

Common Mitre Angles Table

Mitre saw settings for regular polygons (angle from 90° cut).

Sides (Polygon)	Internal Angle (°)	Mitre Saw Setting (°)
3 (Triangle)	60	30.00
4 (Square)	90	45.00
5 (Pentagon)	108	36.00
6 (Hexagon)	120	30.00
7 (Heptagon)	128.57	25.71
8 (Octagon)	135	22.50
10 (Decagon)	144	18.00
12 (Dodecagon)	150	15.00

What is a Mitre Angle?

A mitre angle is the angle at which a piece of material, typically wood, is cut to join with another piece to form a corner or a polygon. When two pieces are joined at a mitre joint, each is usually cut at half the total angle of the corner they form. For instance, to create a 90-degree corner with two pieces, each piece is cut at a 45-degree mitre angle. This calculator helps you determine the precise angle needed for your mitre saw setting.

Anyone involved in woodworking, picture framing, trim carpentry, or building polygonal structures should use a mitre angle calculator or understand how to calculate mitre angles. Common misconceptions include thinking the mitre angle is always 45 degrees (only true for 90-degree corners) or that the saw setting directly matches the internal angle of a polygon.

Mitre Angle Formula and Mathematical Explanation

There are two main scenarios for calculating mitre angles:

1. Joining two pieces to form a specific corner angle (C): The mitre angle (M) for each piece is half the corner angle.
   
   M = C / 2
2. Creating a regular polygon with N sides: The internal angle of a regular polygon is (N-2) * 180 / N degrees. To join two sides, each is cut at half this angle: (N-2) * 90 / N degrees relative to the edge. However, mitre saws are typically set to the angle away from a 90-degree cut (or relative to the fence). This saw setting (S) is:
   
   S = 180 / N degrees.
   
   The actual angle cut into the wood is 90 - S or (N-2) * 90 / N when measured from the face. We display the saw setting ‘S’.

The mitre angle calculator uses these formulas based on your selected mode.

Variable	Meaning	Unit	Typical Range
C	Total Corner Angle	degrees	1 – 359
N	Number of Sides of Polygon	integer	3 – 20+
M	Mitre Angle per piece (from corner)	degrees	0.5 – 179.5
S	Mitre Saw Setting (for polygon)	degrees	9 – 60

Practical Examples

Example 1: Picture Frame (Square Corner)

You are building a square picture frame, which has 90-degree corners.

• Input Mode: Known Corner Angle
• Corner Angle (C): 90 degrees
• Number of Pieces: 2
• Mitre Angle per piece (M) = 90 / 2 = 45 degrees.

You would set your mitre saw to 45 degrees to cut each piece of the frame.

Example 2: Building a Hexagonal Table Top

You want to build a table with a hexagonal top, made of 6 equal pieces of wood forming a regular hexagon.

• Input Mode: Regular Polygon
• Number of Sides (N): 6
• Mitre Saw Setting (S) = 180 / 6 = 30 degrees.
• Internal Angle = (6-2) * 180 / 6 = 4 * 180 / 6 = 120 degrees.

You set your mitre saw to 30 degrees for each of the 6 pieces to form the 120-degree internal corners of the hexagon.

How to Use This Mitre Angle Calculator

1. Select Mode: Choose “Known Corner Angle” if you know the angle of the corner you are forming, or “Regular Polygon” if you are making a frame with equal sides.
2. Enter Values: If “Known Corner Angle”, enter the angle in degrees. If “Regular Polygon”, enter the number of sides.
3. Calculate: The calculator automatically updates, or click “Calculate”.
4. Read Results: The “Mitre Saw Angle Setting” is the main result to set on your saw. Intermediate results provide context like the internal angle for polygons.
5. Decision-Making: Always make test cuts on scrap wood to verify the angle and fit, especially for non-90-degree corners or complex polygons. Small adjustments might be needed due to blade kerf or material variations. Using our tool to calculate mitre angles is the first step.

Key Factors That Affect Mitre Angle Results

• Accuracy of Corner Angle Measurement: If using the “Known Corner Angle” mode, the accuracy of your measured angle directly impacts the mitre angle.
• Saw Accuracy and Calibration: Your mitre saw’s angle guide must be accurately calibrated. Even a small error can lead to gaps in the joint.
• Blade Kerf: The thickness of the saw blade (kerf) removes material. For precise joints, especially in small projects, you might need to account for which side of the line to cut on.
• Wood Movement: Wood expands and contracts with changes in humidity and temperature. This can affect how well mitred joints stay closed over time.
• Material Flatness and Straightness: Warped or bowed wood will not form a clean mitre joint even if the angle is perfectly cut.
• Clamping and Joining Method: How the pieces are clamped and joined (glue, fasteners) can influence the final angle and joint tightness.

Frequently Asked Questions (FAQ)

Q: What is the most common mitre angle?
A: The most common is 45 degrees, used to create 90-degree corners in square or rectangular frames and structures.

Q: How do I calculate the mitre angle for crown molding?
A: Crown molding requires compound mitre cuts (both mitre and bevel angles) because it sits at an angle to both the wall and ceiling. You’ll need the spring angle of the molding and the corner angle of the wall. Our basic calculator here is for simple mitre angles on a flat plane. You’d need a compound mitre calculator for that.

Q: My mitre joints have gaps. What am I doing wrong?
A: Gaps can be due to inaccurate saw settings, blade kerf not accounted for, wood movement, or non-flat material. Double-check your measurements and saw calibration. Try test cuts.

Q: Can I use this calculator for angles other than 90 degrees?
A: Yes, using the “Known Corner Angle” mode, you can input any corner angle you need to form.

Q: How do I calculate mitre angles for an octagon?
A: Use the “Regular Polygon” mode and enter 8 for the number of sides. The calculator will give you the mitre saw setting.

Q: What’s the difference between a mitre cut and a bevel cut?
A: A mitre cut is an angle cut across the width/face of the board. A bevel cut is an angle cut through the thickness of the board. Compound cuts involve both. This calculator is for simple mitre angles.

Q: Why is my mitre angle not exactly half the corner angle for polygons?
A: For polygons, we provide the mitre saw setting (180/N), which is the angle relative to a 90-degree crosscut. The angle *on the piece* that forms the internal corner is indeed half the internal angle ((N-2)*90/N). The saw setting is just a different reference.

Q: How accurate is this mitre angle calculator?
A: The calculations are mathematically precise. However, real-world accuracy depends on your measurements, saw calibration, and material. It’s a great tool to calculate mitre angles accurately before cutting.