# Polygon Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jun 05, 2023

With this polygon calculator, you can find the essential properties of any n-sided regular polygon. Whether you are looking for the area of a heptagon or the angles in a decagon, you're at the right place. Below you'll find the polygon definition and a table with the names of polygons along with their shapes. After reading this short article, you'll know what a polygon is and how many sides a particular polygon has - keep reading, or simply give this calculator a go!

## What is a polygon? Polygon definition

A polygon is a 2D closed figure made up of straight line segments. That's the polygon definition. But what does it look like? Many shapes you learned about are polygons - triangles, squares, parallelograms, rhombus, kites, pentagons, hexagons, octagons... A lot of them. But popular shapes that are not polygons also exist - take a circle and an ellipsis as an example.

Polygons are classified based on their sides and angles, as well as their convexity, symmetry, and other properties.

In this polygon calculator, we solve the properties of regular polygons - the special polygon types which are:

• equiangular - all angles are equal in measure
• equilateral - all sides have the same length

Every regular polygon with n sides is formed by n isosceles triangles.

## How many sides does a polygon have? Names of polygon shapes The answer to the question depends on which polygon you have on your mind. "Usually, you can use the polygon name as a hint to deduce how many sides it has - the prefixes come from Greek numbers.

Polygon

Name

n (sides)

Regular polygon shape

α

β

3 - sided polygon

trigon (equilateral triangle)

3 π/3 = 60°

2π/3 = 120°

4 - sided polygon

4 π/2 = 90°

π/2 = 90°

5 - sided polygon

pentagon

5 3π/5 = 108°

2π/5 = 72°

6 - sided polygon

hexagon

6 2π/3 = 120°

π/3 = 60°

7 - sided polygon

heptagon (septagon)

7 5π/7 = 128.57°

2π/7 = 51.43°

8 - sided polygon

octagon

8 3π/4 = 135°

π/4 = 45°

9 - sided polygon

nonagon

9 7π/9 = 140°

2π/9 = 40°

10 - sided polygon

decagon

10 8π/10 = 144°

π/5 = 36°

n - sided polygon

n - gon

n (n-2) × 180°/n

360°/n

If your polygon has 11 or more sides, it's easier to write 11-gon, 14-gon, 20-gon ... "100-gon", etc. But if you're really curious...

Polygon

Name

n (sides)

α

β

11 - sided polygon

Hendecagon (undecagon)

11

147.273°

32.73°

12 - sided polygon

Dodecagon

12

150°

30°

13 - sided polygon

Triskaidecagon

13

152.308°

27.69°

14 - sided polygon

Tetrakaidecagon

14

154.286°

25.71°

15 - sided polygon

15

156°

24°

16 - sided polygon

Hexakaidecagon

16

157.5°

22.5°

17 - sided polygon

17

158.824°

21.18°

18 - sided polygon

Octakaidecagon

18

160°

20°

19 - sided polygon

19

161.053°

18.98°

20 - sided polygon

Icosagon

20

162°

18°

30 - sided polygon

Triacontagon

30

168°

12°

40 - sided polygon

Tetracontagon

40

171°

50 - sided polygon

Pentacontagon

50

172.8°

7.2°

60 - sided polygon

Hexacontagon

60

174°

70 - sided polygon

Heptacontagon

70

174.857°

5.14°

80 - sided polygon

Octacontagon

80

175.5°

4.5°

90 - sided polygon

Enneacontagon

90

176°

100 - sided polygon

Hectagon

100

176.4°

3.6°

1,000 - sided polygon

Chiliagon

1,000

179.64°

0.36°

10,000 - sided polygon

Myriagon

10,000

179.964°

0.036°

1,000,000 - sided polygon

Megagon

1,000,000

~180°

~0°

10100 - sided polygon

Googolgon

10100

~180°

~0°

## Regular polygon formulas: sides, area, perimeter, angles

If you want to calculate the regular polygon parameters directly from equations, all you need to know is the polygon shape and its side length:

1. Area
• area = n × a² × cot(π/n)/ 4

Where n- number of sides, a - side length

Other equations, which use parameters such as the circumradius or perimeter, can also be used to determine the area. You can find them in a dedicated calculator of polygon area.

1. Perimeter
• perimeter = n × a

Read more about polygon perimeter in the perimeter of a polygon calculator. 1. Angles :
• α = (n - 2) × π / n, where α is an interior angle;
• β = 2 × π / n, where β is an exterior angle.

If you're particularly interested in angles, you may want to take a look at our polygon angle calculator.

• ri = a / (2 × tan(π/n))
• rc = a / (2 × sin(π/n))

All these equations are implemented in our polygon calculator.

## How to use this polygon calculator - an example

If you're still wondering how to use our tool, have a look at the following example:

1. Choose the polygon shape and type its number of sides. To calculate the properties of, e.g., a nonagon, type 9 into the number of sides box.
2. Enter one parameter. One given value is enough. Assume that we know the perimeter of our shape; let's say it's 18 in.
3. Great! Our polygon calculator finds all the remaining values! We determined that:
• side = 2 in
• area = 24.727 in²
• α = 140°
• β = 40°
• rc = 2.924 in
• ri = 2.7475 in
Hanna Pamuła, PhD
Number of sides
Name
Parameters
Side (a)
in
Perimeter
in
Area
in²
α
deg
β
deg
in
in
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