Octagon Calculator

A regular octagon with side length s has area A = 2 (1 + sqrt(2)) s^2, which equals about 4.828427 times s squared. For s = 10, the area is about 482.84 square units.

The long diagonal connects two opposite vertices and equals s sqrt(4 + 2 sqrt(2)), about 2.613126 s. The short diagonal connects two opposite flat sides and equals s (1 + sqrt(2)), about 2.414214 s, the same as twice the apothem.

Rearrange the area formula: s = sqrt(A / (2 (1 + sqrt(2)))) = sqrt(A / 4.828427). For example, an area of 100 square units gives a side of about 4.553 units.

The apothem is the perpendicular distance from the center to the midpoint of any side. For a regular octagon, apothem a = (s / 2) (1 + sqrt(2)), about 1.207107 s. It is also the inradius (radius of the inscribed circle).

Every interior angle measures 135 degrees, and every exterior angle measures 45 degrees. The eight interior angles add up to (8 - 2) x 180 = 1080 degrees.