Calculations in a regular n-gon. Enter edge length and number of vertices and choose the number of decimal places. Then click Calculate. The length of a diagonal across a number of edges can also be calculated. Angles are calculated and displayed in degrees, here you can convert angle units.
N-gon shape (up to 100 vertices):
n ∈ ℕ
p = a * n
h = 2 * ri if n is even, else
h = a / ( 2 * tan( π/2/n ) )
A = n * a² / ( 4 * tan(π/n) )
rc = a / ( 2 * sin(π/n) )
ri = a / ( 2 * tan(π/n) )
Angle = 180° - ( 360° / n )
d = n ( n - 3 ) / 2
Diagonal across m edges, m∈ℕ, m≤n/2:
dm = a * sin( π * m/n ) / sin( π/n )
π = 180° = 3.141592653589793...
Edge length, diagonal, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).