Interior Angle Calculator

The Interior Angle Calculator helps users quickly find the angle measurements inside polygons. It supports students, teachers, architects, engineers, designers, and anyone working with shapes. Because interior angles are important in geometry and design, this calculator makes the process fast and accurate. It removes calculation errors and gives reliable results within seconds. This tool belongs to the Academic Calculators and Geometry Calculator category.

Formula

Sum of All Interior Angles

This formula gives the total of all interior angles in any polygon:

n is the number of sides in the polygon.

Single Interior Angle of a Regular Polygon

For regular polygons, all interior angles are equal. Use this formula:

Single Interior Angle = ((n – 2) * 180°) / n

n is the number of sides.

Finding a Missing Interior Angle

When some angles are known and one is missing, use:

Missing Angle = Sum of Interior Angles – Sum of all Known Angles

Sum of Interior Angles is (n – 2) * 180°.
Sum of all Known Angles is the total of the measured angles.

General Terms and Quick Reference Table

This table helps users find common polygon interior angle values without doing calculations:

Example

Imagine you want to find the missing interior angle of a pentagon.
A pentagon has 5 sides.

Step 1: Calculate the sum of all interior angles
Sum = (5 – 2) * 180°
Sum = 3 * 180°
Sum = 540°

Step 2: Add the known angles
Known angles: 120°, 100°, 90°, 80°
Total known = 390°

Step 3: Find the missing angle
Missing Angle = 540° – 390°
Missing Angle = 150°

So, the missing interior angle is 150°.

Most Common FAQs