# Polygon Calculator

A regular polygon is a convex polygon that has all sides equal and the angles between adjacent sides are also equal. To calculate the correct polygon, enter the edge length and the number of vertices. Then click calculate. The length of the diagonals along the edge length can also be calculated. The angles of p are displayed in degrees.

**Calculator of N-gons**

**Side length (a)**

**Number of vertices (n)**

**Perimeter (p)**

**Height (h)**

**Square (S)**

**The radius of the circumscribed circle (R)**

**Radius of the inscribed circle (r)**

**Inner corner**

**Number of diagonals**

**The diagonal between vertexes**

## Formulas:

n ∈ ℕ, N > 2>

p = a * n

h = 2 * r, If n is even, otherwise

h = a / (2 * tan (π / 2/n ) )

S = n * a2 / (4 * tan (π/n) )

R = a / (2 * sin (π/n) )

r = a / (2 * tan (π/n) )

Угол = 180° – 360° / n

d = n ( n-3 ) / 2

Diagonal through M edges, m ∈ ℕ, m ≤ n/2:

d_{m} = a * sin( π * m/n) / sin( π/n)

If you need to calculate the correct polygon with a cutout in the center.