Calculator Soup^{®}
r = inradius (apothem)
R = circumradius
a = side length
n =
number of sides
x = interior angle
y = exterior angle
A = area
P = perimeter
π = pi = 3.14159 ...
√ = square root
Use this calculator to calculate properties of a regular polygon. Enter any 1 variable plus the number of sides or the polygon name. Calculates side length, inradius (apothem), circumradius, area and perimeter. Calculate from an regular 3gon up to a regular 1000gon.
* Units: Note that units of length are shown for convenience. They do not affect the calculations. The units are in place to give an indication of the order of the calculated results such as ft, ft^{2} or ft^{3}. Any other base unit can be substituted.
A regular polygon is a polygon that is both equiangular and equilateral. All sides are equal length placed around a common center so that all angles between sides are also equal. When the number of sides, n, is equal to 3 it is an equilateral triangle and when n = 4 is is a square.
The following formulas were used to develop calculations for this calculator where a = side length, r = inradius (apothem), R = circumradius, A = area, P = perimeter, x = interior angle, y = exterior angle and n = number of sides.
Polygon Name  n  Polygon Shape  x  y 
trigon (equilateral triangle) 
3  (1/3)π = 60° 
(2/3)π = 120° 

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

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

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

heptagon  7  (5/7)π = 900°/7 = 128.57° 
(2/7)π = 360°/7 = 51.43° 

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

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

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

undecagon  11  (9/11)π = 1620°/11 = 147.27° 
(2/11)π = 360°/11 = 32.73° 

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

tridecagon  13  (11/13)π = 1980°/13 = 152.31° 
(2/13)π = 360°/13 = 27.69° 

tetradecagon  14  (12/14)π = 2160°/14 = 154.29° 
(2/14)π = 360°/14 = 25.71° 
Zwillinger, Daniel (EditorinChief). CRC Standard Mathematical Tables and Formulae, 31st Edition New York, NY: CRC Press, p. 323, 2003.
Weisstein, Eric W. "Regular Polygon." From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/RegularPolygon.htm
Cite this content, page or calculator as:
Furey, Edward "Regular Polygon Calculator" From http://www.CalculatorSoup.com  Online Calculator Resource.