Calculate precise miter angles for polygon corners in carpentry projects. Enter the number of sides to determine the exact angle for your miter saw cuts.
Formula
180° ÷ 4 = 45.00°Miter Angle
45.00°
The miter angle is the angle you need to set your miter saw to when cutting corners for a regular polygon. For example, when making a picture frame (4 sides), you would set your miter saw to 45°.
The miter angle is a critical measurement in carpentry, woodworking, and construction projects. It determines the precise angle at which materials need to be cut to create tight-fitting joints in polygonal shapes. Our Miter Angle Calculator simplifies this process by automatically computing the exact miter angle needed for any regular polygon. Whether you're building a picture frame, a hexagonal table, or a complex multi-sided structure, this tool ensures your miter cuts will fit together perfectly every time.
A miter angle is the angle at which you need to set your miter saw or cutting tool to create angled cuts that form perfect corners when joined together. In woodworking, these precise angles are essential for creating strong, seamless joints in projects with multiple sides.
The miter angle depends on the number of sides in your polygon. For example:
The formula for calculating the miter angle for a regular polygon is remarkably simple:
Where:
This formula works because in a regular polygon, the sum of all interior angles equals . Each interior angle equals . The miter angle is half of the supplementary angle to the interior angle, which simplifies to .
The calculator automatically validates your input to ensure it's a valid number of sides for a polygon (3 or more).
| Number of Sides | Polygon Name | Miter Angle | Interior Angle |
|---|---|---|---|
| 3 | Triangle | 60° | 60° |
| 4 | Square | 45° | 90° |
| 5 | Pentagon | 36° | 108° |
| 6 | Hexagon | 30° | 120° |
| 8 | Octagon | 22.5° | 135° |
| 10 | Decagon | 18° | 144° |
| 12 | Dodecagon | 15° | 150° |
While our calculator provides the standard miter angle for regular polygons, there are alternative approaches for certain projects:
It's important to distinguish between miter and bevel cuts:
For most regular polygon construction, simple miter cuts are sufficient. However, more complex projects may require compound cuts.
The use of miter joints dates back thousands of years. Ancient Egyptian furniture and sarcophagi show evidence of precisely mitered corners. The technique was highly developed by Roman and Greek craftsmen who created sophisticated joinery for furniture and architectural elements.
During the Renaissance, as furniture became more ornate, mitered joints gained popularity for their clean appearance and ability to hide end grain. The development of the miter box in the 18th century made it easier for craftsmen to cut consistent angles.
The invention of the dedicated miter saw in the 20th century revolutionized woodworking, making precise angle cuts accessible to both professionals and hobbyists. Modern compound miter saws, introduced in the 1970s, further expanded capabilities by allowing both miter and bevel cuts simultaneously.
Today, digital angle finders and calculators like this one have made the process even more precise, ensuring perfect fits for complex polygonal projects.
Here are examples of how to calculate miter angles in various programming languages:
1' Excel formula for miter angle
2=180/A2
3' Where A2 contains the number of sides
41def calculate_miter_angle(sides):
2 """Calculate the miter angle for a regular polygon."""
3 if sides < 3:
4 raise ValueError("A polygon must have at least 3 sides")
5 return 180 / sides
6
7# Example usage
8sides = 6 # hexagon
9miter_angle = calculate_miter_angle(sides)
10print(f"For a {sides}-sided polygon, the miter angle is {miter_angle}°")
111function calculateMiterAngle(sides) {
2 if (sides < 3) {
3 throw new Error("A polygon must have at least 3 sides");
4 }
5 return 180 / sides;
6}
7
8// Example usage
9const sides = 8; // octagon
10const miterAngle = calculateMiterAngle(sides);
11console.log(`For an ${sides}-sided polygon, the miter angle is ${miterAngle}°`);
121public class MiterAngleCalculator {
2 public static double calculateMiterAngle(int sides) {
3 if (sides < 3) {
4 throw new IllegalArgumentException("A polygon must have at least 3 sides");
5 }
6 return 180.0 / sides;
7 }
8
9 public static void main(String[] args) {
10 int sides = 5; // pentagon
11 double miterAngle = calculateMiterAngle(sides);
12 System.out.printf("For a %d-sided polygon, the miter angle is %.2f°%n", sides, miterAngle);
13 }
14}
151public class MiterAngleCalculator
2{
3 public static double CalculateMiterAngle(int sides)
4 {
5 if (sides < 3)
6 {
7 throw new ArgumentException("A polygon must have at least 3 sides");
8 }
9 return 180.0 / sides;
10 }
11
12 static void Main()
13 {
14 int sides = 12; // dodecagon
15 double miterAngle = CalculateMiterAngle(sides);
16 Console.WriteLine($"For a {sides}-sided polygon, the miter angle is {miterAngle:F2}°");
17 }
18}
19A miter angle is the angle at which you need to set your cutting tool (typically a miter saw) to create angled cuts that form perfect corners when joined together in a polygon. The formula is 180° divided by the number of sides in your polygon.
The most common reasons for gaps in 45° miter joints include: saw blade not perfectly calibrated, material not held firmly during cutting, or wood movement after cutting due to moisture changes. Try making a fresh cut with a newly calibrated saw and assemble the joint immediately.
No, this calculator is designed for regular polygons where all sides are equal in length and all interior angles are equal. Irregular polygons require individual angle calculations for each corner.
A miter cut is made across the width of the material (changing the horizontal angle), while a bevel cut is made through the thickness of the material (changing the vertical angle). Many projects require both types of cuts.
You can use a miter box with a hand saw, a table saw with a miter gauge, a circular saw with an angle guide, or even a hand plane for small miters. For precise angles, a protractor and careful marking are essential.
A polygon must have at least 3 sides (a triangle). Our calculator accepts any number of sides from 3 upward, though woodworking projects rarely exceed 12 sides due to practical limitations.
Compound miter cuts involve both a miter angle and a bevel angle. These calculations are more complex and depend on the specific geometry of your project. Specialized compound miter calculators are available for these situations.
Yes, the geometric principles are the same regardless of material. However, different materials may require different cutting tools and techniques.
Wood movement due to changes in humidity is the most common cause of miter joints separating over time. Using proper wood conditioning, appropriate glue, and reinforcement techniques (splines, biscuits, etc.) can help prevent this issue.
For visible joints in fine woodworking, aim for precision within 0.1 degrees. Even small errors can result in visible gaps, especially in polygons with many sides where errors compound.
Meta Description: Calculate precise miter angles for woodworking projects with our free Miter Angle Calculator. Perfect for picture frames, furniture, and multi-sided projects.
Ready to create perfect miter joints for your next woodworking project? Try our Miter Angle Calculator now and achieve professional results with every cut!
Discover more tools that might be useful for your workflow