Regular Polygon Calculator
Area, angles, apothem and diagonals for any side count.
Area, angles, apothem and diagonals for any side count.
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
Where to go next
The Regular Polygon question rarely arrives on its own. These are the ones that usually come with it:
- Circle Calculator — Area, circumference, radius and diameter from any one of them.
- Rhombus Area Calculator — Half the product of the diagonals — the half matters.
- Triangle Area Calculator — Area from three sides, using Heron's formula.
- Percentage Calculator — Every common percentage question in one place.
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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