The square footage of a regular octagon is 2(1+√2) × side² ≈ 4.828 × side². For example, 6-foot sides cover 4.828 × 6² ≈ 173.8 square feet.
Building an octagon deck or gazebo? Our octagon deck square feet guide turns this area into deck boards, and the square footage calculator covers unit conversions.
How to Calculate the Square Footage of a Regular Octagon
A regular octagon has eight equal sides, so the calculator needs just one side length. Octagons are common for gazebos, hot-tub decks and bay-window floors, and they are often laid out by cutting the corners off a square.
The formula
Area = 2(1 + √2) × side² ≈ 4.828 × side²
If you know the width across the flat sides (W) instead, the area is about 0.8284 × W².
How to measure
Measure one side from corner to corner. To turn a square into an octagon, each side of the octagon is the square's width ÷ 2.414: a 12-ft square gives sides of about 4.97 ft and an octagon of about 119.29 square feet.
Worked example
An octagonal gazebo has 8-ft sides.
Area = 4.828 × 8² = 4.828 × 64 ≈ 309.02 square feet. For decking, add 10–15% for the angled cuts.
Where this shape is used
- Gazebos and pergolas: Floor decking, roofing and concrete footprints.
- Hot-tub and corner decks: Octagonal decks fit round tubs with straight boards.
- Bay windows and rooms: Flooring for octagonal bays and feature rooms.
Related shape calculators
Working with a different shape? Try the hexagon calculator, heptagon calculator, decagon calculator, or the pentagon calculator. Each one shows the formula, a worked example and unit conversions.