Calculations at a regular octagon, a polygon with eight vertices and edges and three different diagonals.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:
d = a * √ 4 + 2 * √2
e = a * ( 1 + √2 )
f = a * √ 2 + √2
Height = e = 2 * r_{i}
p = 8 * a
A = 2 * a² * ( 1 + √2 )
r_{c} = a / 2 * √ 4 + 2 * √2
r_{i} = a / 2 * ( 1 + √2 )
Angle: 135°
20 diagonals

Edge length, diagonals, height, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The regular octagon is point-symmetrical about the center and rotationally symmetrical at a rotation of 45° or multiples thereof. Furthermore, it is axially symmetrical to the long diagonals and the bisectors.
An octagon is created when you cut off the corners of a square, doubling their number. The middle diagonals of the regular octagon form a regular octagram. The short diagonals form the Star of Lakshmi, which in turn encloses a smaller, regular octagon. The regular octagon appears as a side surface in two Archimedean solids, the truncated cube and the truncated cuboctahedron. A tiling of regular octagons contains square gaps, where the side length of the squares corresponds to that of the octagons. This is called Archimedean tiling, which is formed from regular polygons analogous to Archimedean solids.
In ancient times, the octagon stood as a symbol of perfection. This form is known today, among other things, from the stop sign. Opened umbrellas often have an octagonal shape and octagonal table tops are also common. Some buildings have octagonal bases; they are particularly common in pavilions. They also form the floor plan for some religious buildings, such as the Dome of the Rock in Jerusalem. The Tower of the Winds in Athens, dating from the first century BC, is the oldest known building with an octagonal floor plan.