Regular Polygon Angle Calculator

Calculate and visualize the interior angles of any regular polygon.

Number of Sides:

Calculating...

Calculated Interior Angle :

How the Angle is Calculated:

Step 1: Sum of Interior Angles
The sum of the interior angles of any polygon (regular or irregular) with 'n' sides is given by the formula: Sum = (n - 2) × 180°. This formula comes from the fact that any polygon can be divided into (n-2) triangles.

Step 2: For Regular Polygons
In a regular polygon, all interior angles are equal. Therefore, to find the measure of a single interior angle, we divide the sum of interior angles by the number of sides.

Step 3: Final Formula
Thus, the formula for each interior angle (x) of a regular polygon with 'n' sides is: x = [(n - 2) × 180°] / n.

How to Use This Tool

1. Enter the number of sides of your regular polygon (e.g., 3 for a triangle, 4 for a square, 5 for a pentagon) into the input field.

2. Click the "Calculate Angle" button.

3. The calculated interior angle will be displayed, along with a visual representation of the polygon and a step-by-step explanation of the calculation.

4. If you enter an invalid number (less than 3 sides), an error message will appear.