Boneyard Tools

Regular Polygon Calculator

Enter the number of sides and the side length of a regular polygon to find its perimeter, area, interior and exterior angles, apothem and circumradius.

How to find the area of a regular polygon

  1. Enter the number of sides, three or more.
  2. Enter the length of one side.
  3. Read the perimeter, area, angles, apothem and circumradius instantly.

Examples

Hexagon, 6 sides of length 10

sides = 6, side length = 10
perimeter = 60, area = 259.8076, apothem = 8.6603, circumradius = 10

Pentagon, 5 sides of length 6

sides = 5, side length = 6
interior angle = 108, area = 61.9372, circumradius = 5.1039

Frequently asked questions

What is the formula for the area of a regular polygon?

The area equals one half times the perimeter times the apothem. The apothem is the distance from the centre to the middle of a side.

How do I find the interior angle?

The interior angle equals the number of sides minus two, times 180, divided by the number of sides. Every interior angle of a regular polygon is equal.

What is the exterior angle?

The exterior angle equals 360 divided by the number of sides. The interior and exterior angles always add up to 180 degrees.

What is the difference between apothem and circumradius?

The apothem reaches the midpoint of a side while the circumradius reaches a vertex. The circumradius is always the larger of the two.

Why must the polygon have at least three sides?

A closed polygon needs at least three sides. Values below three, or a side count that is not a whole number, are rejected.

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