Regular Polygon Area Calculator
The area and perimeter of a regular polygon from sides and side length.
Result
Area
64.95
Perimeter
30.00
How it works
A regular polygon has all sides equal and all angles equal. From the number of sides n and the side length c, the area is (n × c²) ÷ (4 × tan(π/n)) and the perimeter is simply n × c. The formula comes from slicing the shape into n identical triangles meeting at the centre. Each triangle has base c and a height (the apothem) that the tangent term encodes — which is why the same expression serves triangles, pentagons, hexagons and beyond. As n grows, the polygon closes in on a circle: with 100 sides the difference is already invisible to the eye, and the area formula converges on πr². Three sides is the minimum — a polygon cannot be closed with fewer. Hexagons are the practical favourite (tiles, honeycombs, bolts) because they tile a plane with no gaps.
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Frequently asked questions
What counts as regular?
All sides and all interior angles are equal — like a square, pentagon or hexagon.
What is the minimum number of sides?
Three — a triangle. This tool works for any polygon with three or more sides.
Why do hexagons appear so often in nature and engineering?
Because regular hexagons tile a plane with no gaps while enclosing the most area for the least perimeter of any such tiling — minimum material for maximum space. Hence honeycombs, tiles and bolt heads.
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