How to Use the Regular Polygon Angle Calculator
A regular polygon has all sides and all angles equal. Its interior angle (one angle) is found with (n-2) × 180 / n, and its exterior angle with 360 / n, where n is the number of sides. Just enter the number of sides to instantly see both angle sizes plus the sum of all interior angles and the sum of all exterior angles.
For example, a regular hexagon (n=6) has an interior angle of (6-2)×180/6 = 120 degrees and an exterior angle of 360/6 = 60 degrees. Its interior angles sum to (6-2)×180 = 720 degrees, while its exterior angles always sum to 360 degrees regardless of the number of sides — because walking once around the outside of any polygon means turning a full 360-degree circle.
These angle calculations show up in architecture and design when planning tiles or structures shaped like regular polygons, and they're a staple of school geometry. The number of sides must be a whole number of 3 or more; as it increases, the interior angle grows and the exterior angle shrinks, and the polygon looks increasingly like a circle.
Frequently Asked Questions
Interior angle = (n-2) × 180 / n, where n is the number of sides. A regular hexagon (n=6) has an interior angle of (6-2)×180/6 = 120 degrees.
Yes, every regular polygon's exterior angles sum to exactly 360 degrees, no matter how many sides it has.
No, a polygon needs at least 3 sides, so entering a number below 3 shows an error message.