Polygon Calculator
With this polygon calculator, you can find the essential properties of any nsided 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 is a polygon 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 how does it look like? Many shapes you learned about are polygons  triangle, square, parallelogram, rhombus, kite, pentagon, hexagon, octagon... 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 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  tetragon, quadrilateral (square)  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  (n2) * 180°/n  360°/n 
If your polygon has 13 or more sides, it's easier to write 13gon, 14gon, 20gon ... "100gon", etc.
Other polygons
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  Pentadecagon  15  156°

24° 
16  sided polygon  Hexakaidecagon  16  157.5°

22.5° 
17  sided polygon  Heptadecagon  17  158.824°

21.18° 
18  sided polygon  Octakaidecagon  18  160°

20° 
19  sided polygon  Enneadecagon  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°

9° 
50  sided polygon  Pentacontagon  50  172.8°

7.2° 
60  sided polygon  Hexacontagon  60  174°

6° 
70  sided polygon  Heptacontagon  70  174.857°

5.14° 
80  sided polygon  Octacontagon  80  175.5°

4.5° 
90  sided polygon  Enneacontagon  90  176°

4° 
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° 
10^{100}  sided polygon  Googolgon  10^{100}  ~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:
 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.
 Perimeter
perimeter = n * a
Read more about polygon perimeter in the perimeter of a polygon calculator.
 Angles :
α = (n  2) * π / n
, whereα
is an interior angle;β = 2 * π / n
, whereβ
is an exterior angle.
 Incircle radius (apothem)
ri = a / (2 * tan(π/n))
 Circumcircle radius
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:
 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.
 Enter one parameter. One given value is enough. Assume that we know the perimeter of our shape, let's say it's 18 in.
 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