Enter a number of sides and a side length to calculate any regular polygon's perimeter, area, and angles.
How to Use the Polygon Calculator
Enter the number of sides (3 or more) and the side length. The calculator returns the perimeter, interior and exterior angles, apothem, area, and circumradius for that regular polygon.
Every regular polygon — no matter how many sides — reduces to the same handful of formulas once the side count n is known:
interior angle = (n − 2) × 180° ÷ n
exterior angle = 360° ÷ n
apothem = side ÷ (2 × tan(180° ÷ n))
area = (n × side²) ÷ (4 × tan(180° ÷ n))
circumradius = side ÷ (2 × sin(180° ÷ n))
Push n high enough — 50, 100, 1,000 sides — and a regular polygon starts behaving almost exactly like a circle: the apothem approaches the radius, and the area formula converges toward πr². That's not a coincidence; it's the same limiting argument Archimedes used more than two thousand years ago to estimate π by inscribing polygons inside a circle.