What is a regular polygon?
A shape where all sides and all angles are equal, like an equilateral triangle, a square, or a regular hexagon. This calculator handles any number of equal sides from three up.
// maths › 2D Shapes
Regular Polygon Calculator
Find the area, perimeter and interior angle of a regular polygon (all sides and angles equal) from the number of sides and the side length.
area = ¼·n·s²·cot(π/n) ; interior angle = (n−2)×180/n
Frequently asked questions
How is the interior angle found?
Each interior angle is (n - 2) times 180, divided by n, where n is the number of sides. A hexagon (n = 6) has 120-degree angles.
Why does the area formula use a cotangent?
Because a regular polygon splits into n identical triangles meeting at the centre, and the cotangent of pi over n captures each triangle's geometry. It looks fancy but is just that triangle area times n.
What happens as the number of sides grows?
The polygon gets closer and closer to a circle. With hundreds of sides, its area approaches pi r squared, which is one way mathematicians first estimated pi.
Where is this useful?
Designing nuts and bolts (hexagons), tiling floors, building gazebos, and any structure made from equal-sided shapes.