Enter a side length or perimeter to calculate a regular octagon's area and apothem.

How to Use the Octagon Calculator

Choose Side or Perimeter, enter the value, and the octagon's area, apothem, and circumradius fill in below.

perimeter = 8 × side
apothem = side ÷ (2 × tan(22.5°))
area = 2 × (1 + √2) × side²

Stop signs are the everyday reference point for a regular octagon — eight equal sides, eight 135° interior angles — which is also why octagon-shaped paving stones and gazebo floor plans show up more often than any other polygon past a square: the shape reads as "rounded" from a distance while still being buildable out of straight cuts.

Where the Area Formula Comes From

Every regular polygon's area reduces to half the perimeter times the apothem — an octagon is no exception, it just has a messier apothem than a square or hexagon does, which is why 2(1+√2) shows up instead of a cleaner-looking coefficient.