Miter Angle Calculator
Calculate precise miter cutting angles for perfect woodworking joints and carpentry projects
Calculate Miter Angles
The total angle of the corner (e.g., 90° for a right angle, 120° for hexagon)
Width of the first board to be joined
Width of the second board to be joined
ℹ️ Equal Width Boards: When boards have the same width, each miter angle is simply half the joint angle.
Miter Angle Results
Miter Angles (α and β)
Angles to cut on each board
Miter Saw Angles
Angles to set on your miter saw
Formula used: Miter angle = θ / 2 (equal widths)
Miter saw angle: |90° - miter angle| (complementary angle)
How to Use These Angles
1. Set your miter saw: Use the miter saw angles (complementary angles) to set your saw's protractor.
2. Cut board A: Set saw to 45.00° and cut the first board.
3. Cut board B: Use the same setting (45.00°) for the second board.
4. Test fit: Join the boards to verify a perfect 90° corner angle.
Example Calculation
Picture Frame Corner (Equal Widths)
Joint angle: 90°
Board widths: Both 5 cm
Calculation: Miter angle = 90° / 2 = 45°
Miter saw setting: |90° - 45°| = 45°
Result: Cut both boards at 45° on your miter saw
Different Width Boards (120° Joint)
Joint angle: 120°
Board A (narrower): 10 cm
Board B (wider): 15 cm
Calculation:
α = arctan(10 × sin(120°) / (15 + 10 × cos(120°)))
α = arctan(8.660 / 10) ≈ 40.89°
β = 120° - 40.89° ≈ 79.11°
Miter saw settings: Board A = 49.11°, Board B = 10.89°
Common Miter Angles
90° corners, equal widths
120° corners, equal widths
135° corners, equal widths
108° corners, equal widths
Miter Cutting Tips
Always test your cuts on scrap wood first
Use a sharp blade for clean, accurate cuts
Measure carefully - accuracy is crucial for tight joints
Mark your boards clearly to avoid cutting errors
For complex angles, make a template first
Secure your workpiece firmly before cutting
Understanding Miter Angles in Woodworking
What is a Miter Cut?
A miter cut is an angled crosscut made across the width of a board. When two pieces with miter cuts are joined together, they form a corner at a specific joint angle. Miter cuts are commonly used in picture frames, crown molding, door and window trim, and furniture construction.
What is a Miter Angle?
The miter angle is the angle at which each board needs to be cut so that when joined to another board, they form the desired corner angle. For boards of equal width, this is simply half the joint angle. For example, to create a 90° corner with equal-width boards, each board is cut at 45°.
Why Different Widths Matter
When joining boards of different widths, the miter angles are not equal. The geometry requires different angles on each board to achieve a perfect joint. This calculator uses trigonometric functions to determine the exact angles needed for any combination of board widths and joint angles.
Formula Explanations
Equal Width Boards
Miter angle = θ / 2
Where θ is the joint angle. This simple formula works when both boards have the same width.
Different Widths at 90°
α = arctan(a / b)
β = arctan(b / a)
Where a and b are the board widths. The angles are complementary (sum to 90°).
Different Widths at Any Angle
α = arctan(n × sin(θ) / (m + n × cos(θ)))
β = θ - α
Where n is the narrower width, m is the wider width, and θ is the joint angle.
Understanding Miter Saw Angles
Most miter saws have a protractor that measures the angle from a 90° (perpendicular) cut. This means the saw angle is the complementary angle to the miter angle you need to cut.
Miter Saw Angle = |90° - Miter Angle|
For example, to cut a 45° miter angle, set your saw to 45°. To cut a 60° miter angle, set your saw to 30°. To cut a 79° miter angle, set your saw to 11°.
Common Applications of Miter Cuts
Picture Frames
Standard rectangular frames use 45° miter angles at each corner to create clean, professional-looking joints.
90° corners, equal widths
Crown Molding
Interior and exterior corners require precise miter cuts for seamless transitions in decorative molding installations.
Various angles, often equal widths
Door & Window Trim
Mitered corners provide a finished look for door casings and window trim in both residential and commercial settings.
Typically 90° corners
Furniture Construction
Tables, cabinets, and boxes often use mitered corners for strength and aesthetics in fine woodworking.
Various angles and widths
Baseboard & Wainscoting
Wall base moldings and wainscoting panels require accurate miter cuts for professional installations at corners.
Inside and outside corners
Deck Railings
Outdoor deck railings and handrails use mitered corners for both functionality and visual appeal.
Various angles for stairs and turns
Frequently Asked Questions
What is a miter angle?
A miter angle is the angle at which two pieces of material are cut to fit together at a corner, commonly used in carpentry and construction. It's essential for creating aesthetic and structural joints in frames, trim, moldings, and other carpentry projects. The miter angle ensures that when two pieces are joined, they form a neat, angled joint at the desired corner angle.
How do I calculate the miter angle for a joint?
To calculate the miter angle for a joint using materials of the same width:
- Determine the total angle of the corner or joint. For example, a standard corner is 90 degrees.
- Divide this angle by the number of pieces meeting at the joint. For two pieces, divide by 2.
- For a 90-degree corner, each miter angle is 45 degrees (90° ÷ 2 = 45°).
This method ensures a perfect fit for pieces of equal width. For different widths, use the advanced formulas provided in this calculator.
What tool do I use to cut a miter angle?
To cut a miter angle, you typically use a miter saw, a specialized power tool designed for making precise angled cuts. It allows for adjustments to cut various angles, making it ideal for creating corners in frames, trim, or other carpentry projects. Other tools like a table saw with a miter gauge or a hand miter box can also be used, but a powered miter saw offers the most accuracy and efficiency for repetitive cuts.
How many degrees do I set for a hexagonal frame miter cut?
If you want to set the miter saw for a hexagonal frame, you should set it to 30 degrees. Here's the calculation:
- Determine the total internal angle of a regular hexagon, which is 120 degrees per corner.
- Divide this angle by 2 to get 60 degrees for the miter angle on each board (120° ÷ 2 = 60°).
- Subtract this miter angle from 90 degrees to find the saw setting: 90° - 60° = 30 degrees.
- Set your miter saw to 30 degrees.
This angle ensures each side fits perfectly to form a hexagon.
What's the difference between a miter angle and a miter saw angle?
The miter angle is the actual angle of the cut on the board (measured from perpendicular), while the miter saw angle is the setting you use on your miter saw's protractor. Since most miter saws measure from the 90° (perpendicular) position, the saw angle is the complementary angle to the miter angle. For example, to cut a 45° miter angle, you set your saw to 45°, but to cut a 60° miter angle, you set your saw to 30° (90° - 60° = 30°).
Why do different width boards need different miter angles?
When joining boards of different widths, the geometry of the joint changes. The wider board needs a larger miter angle and the narrower board needs a smaller angle to properly meet at the desired corner angle. This is due to the trigonometric relationships in the triangle formed by the joint. Using equal angles on different width boards would result in gaps or overlaps at the corner.
How accurate do my miter cuts need to be?
Miter cuts should be extremely accurate for professional results. Even a difference of 1-2 degrees can create noticeable gaps in your joints, especially on longer pieces. Always use a sharp blade, secure your workpiece properly, and double-check your saw settings before cutting. Testing on scrap wood first is highly recommended. For critical projects like fine furniture or visible trim work, aim for accuracy within 0.5 degrees.
Can I use this calculator for crown molding?
Yes, this calculator works for crown molding when you're joining two pieces at a corner on the same plane (such as where two walls meet). However, crown molding also involves compound angles (both miter and bevel cuts) when cutting individual pieces because they're installed at an angle to both the wall and ceiling. For standard crown molding installation, you'll need to consider both the horizontal angle (miter) and the vertical angle (bevel). This calculator focuses on the miter angle component.