Regular Octagon Area Calculator

About this calculator

This calculator finds the area, A = 2(1+√2)·s², and perimeter, P = 8·s, of a regular octagon — an eight-sided polygon with equal sides and equal interior angles of 135° — from its side length s alone. The area formula comes from splitting the octagon into eight congruent isosceles triangles meeting at the center, or equivalently from cutting the corners off a square.

Architects and builders use this when designing octagonal rooms, gazebos, or turrets, since the shape is popular for its wide field of view and structural stability; sign manufacturers use the same geometry for stop signs (arguably the most recognizable regular octagon in daily life). Woodworkers and DIY builders constructing octagonal tables or planters, and geometry students verifying textbook problems, use this calculator to get exact area and perimeter figures from a single side measurement.