This **regular polygon calculator** can help you calculate the area, perimeter, interior angle, central/exterior angle, apothem and the radius of circumcircle if you provide the number of sides and the side length.

## What is a regular polygon?

A regular polygon is defined as a two-dimensional shape with **all sides** equal (equilateral) **and all angles equal** (equiangular). This is the list with most often referred to regular polygons:

Regular Polygon Name |
No. of sides (n) |
Interior angle (x) |
Exterior angle (y) |

equilateral triangle (trigon) | 3 | (π/3) = 60° | (2π/3) = 120° |

square (tetragon) | 4 | (2π/4) = 90° | (2π/4) = 90° |

pentagon | 5 | (3π/5) = 108° | (2π/5) = 72° |

hexagon | 6 | (4π /6) = 120° | (2π/6) = 60° |

heptagon | 7 | (5π/7) = 128.57° | (2π/7) = 51.43° |

octagon | 8 | (6π/8) = 135° | (2π/8) = 45° |

nonagon | 9 | (7π/9) = 140° | (2π/9) = 40° |

decagon | 10 | (8π/10) = 144° | (2/10)π = 36° |

undecagon | 11 | (9π/11) = 147.27° | (2π/11) = 32.73° |

dodecagon | 12 | (10π/12) = 150° | (2π/12) = 30° |

## How does this regular polygon calculator work?

The algorithm behind this *regular polygon calculator* requires the side length and the number of sides to be given, while it is based on the formulas provided below:

r = (s/2)*cotangent(180°/n)

R = (s/2)*cosecant(180°/n)

Area = (Perimeter*r)/2

Perimeter = n*s

Interior angle (x) = [(n-2)/n]*180**°**

Sum of interior angles = (n-2)*180**°**

Exterior angle (y) = 360°/n

Where:

n = number of sides

s = side length

r = apothem (radius of inscribed circle)

R = radius of circumcircle

Since in trigonometry there are used both degrees and radians this calculator will convert and display the equivalent in radians for the appropriate dimensions as well, by using this conversion rate:

**1 degree = 0.0174532925 radians**

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