Regular Polygon Calculator
Calculate area, perimeter, interior angle, and apothem of any regular polygon.
How it works
- 1Enter the number of sides (n ≥ 3) and the side length. The perimeter is simply n × side.
- 2The interior angle at each vertex equals (n − 2) · 180 ÷ n degrees.
- 3The apothem (inradius) is side ÷ (2 · tan(π ÷ n)), and area = ½ · perimeter · apothem.
Use cases
- Architects and designers calculating floor-tile or paving layouts in polygonal shapes.
- Students verifying geometry homework on regular polygons and their angle properties.
- Makers and laser-cutters computing dimensions for custom polygon panels or frames.
Frequently asked questions
What makes a polygon regular?
A regular polygon has all sides equal in length and all interior angles equal. Examples include the equilateral triangle (n = 3), the square (n = 4), and the regular hexagon (n = 6).
What is the apothem?
The apothem is the perpendicular distance from the centre of the polygon to the midpoint of any side. It equals side ÷ (2 · tan(π ÷ n)) and is the inradius of the inscribed circle.
Why does the interior angle approach 180° as n grows?
As the number of sides increases, each interior angle (n − 2) · 180 ÷ n approaches 180°, because the polygon increasingly resembles a circle.
Related tools
See all →Calculate the area and perimeter of a rectangle from its width and height, with a labeled diagram.
Calculate the area and circumference of a circle from its radius, with a labeled diagram.
Calculate the area (Heron’s formula) and perimeter of a triangle from its three sides.
Calculate the area and perimeter of a trapezoid from its two parallel sides, height, and legs.