Regular Polygon Calculator
Area, angles, apothem and diagonals for any side count.
Work out Regular Polygon. Area, angles, apothem and diagonals for any side count. Names the mistake everyone makes here.
Area of a regular hexagon
10.3923
perimeter 12 · interior angle 120°
Area is half the perimeter times the apothem — the perpendicular distance from the centre to a side. That is the same structure as a triangle's ½ base × height, because a regular polygon is n identical triangles meeting at the centre. Interior angles sum to (n − 2) × 180° for any polygon, regular or not. Exterior angles always sum to exactly 360° however many sides there are, which is why each one is simply 360/n. As n rises the polygon approaches a circle: the apothem and circumradius converge, and the area tends to πr².
How the Regular Polygon Calculator works
Enter the number of sides and a side length for the area, perimeter, interior and exterior angles, apothem, circumradius and diagonal count. Works for anything from a triangle to a thousand-sided figure, which is close enough to a circle to demonstrate the point.
Also known as: polygon area calculator · interior angle calculator · apothem calculator · hexagon area calculator
Frequently asked questions
How do I find the area of a regular polygon?
Half the perimeter times the apothem. That mirrors a triangle's ½ base × height, because a regular polygon is n identical triangles meeting at the centre.
What is the apothem?
The perpendicular distance from the centre to the middle of a side — the inradius. The circumradius, from the centre to a corner, is always larger, and the two converge as the side count rises.
What is the interior angle of a polygon?
(n − 2) × 180° ÷ n for a regular one. A hexagon gives 120°, an octagon 135°. The sum of (n − 2) × 180° holds for any polygon, regular or not.
Why do exterior angles always sum to 360°?
Because walking the perimeter turns you through one full rotation whatever the shape. That is why each exterior angle of a regular polygon is simply 360/n.
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