# Calculator of a regular polygonal ring

A regular polygon ring is the same regular polygon from which a smaller polygon was removed (cut out) strictly in the center. Enter the length of the edges of the outer and inner polygon and the number of vertices of the polygon. Then click calculate.

**Calculator of regular Polygonal Rings**

**Outside length (a)**

**Length of the inner side (b)**

**Number of vertices (n)**

**Thickness at the top (c)**

**Side thickness (d)**

**Perimeter (p)**

**Square (S)**

**Formulas:**

Example of an octagonal ring

n ∈ ℕ, N > 2>

c = ( a-b ) / (2 * sin (π/n) )

d = ( a-b ) / (2 * tan (π/n) )

p = ( a + b ) * n

S = n * ( a2 – b2 ) / (4 * tan (π/n) )