Regular Polygon Calculator
Find a regular polygon's interior angle, perimeter, and area from its number of sides and side length.
Area
64.9519
Area = (n × s²) / (4 × tan(π/n)). A regular hexagon with side 5 covers about 64.95 square units.
Interior angle
120°
Exterior angle
60°
Perimeter
30
Apothem
4.3301
How it works
A regular polygon has every side the same length and every angle the same size. Once you know how many sides it has and how long each one is, everything else follows from a handful of clean formulas.
Each interior angle equals (n − 2) × 180 / n, so a pentagon's corners are 108° and a hexagon's are 120°. The perimeter is simply n × s. The area comes from (n × s²) / (4 × tan(π/n)), which packs the apothem and the number of triangles the shape splits into.
Enter the number of sides — a whole number, three or more — and the side length. A hexagon with side 5, for example, has 120° corners, a perimeter of 30, and an area of about 64.95 square units.
Frequently asked questions
How do I find the area of a regular polygon?
Use area = (n × s²) / (4 × tan(π/n)), where n is the number of sides and s is the side length. The formula works for any regular polygon, from a triangle upward.
What is the interior angle of a regular polygon?
Every interior angle equals (n − 2) × 180 / n degrees. For a square that's 90°, for a hexagon 120°, and the angle grows toward 180° as the number of sides climbs.
Why does this need at least three sides?
A polygon is a closed shape made of straight sides, and you can't enclose a region with fewer than three. So the tool expects a whole number of sides that's three or more.