The area of a regular octagon is the space inside its eight equal sides. Octagons show up on stop signs, in Islamic architecture, on tiled floors, and in many patterns — because the shape is close to a circle while still being a polygon.

The Formula

A = (8 × t²) / (4 × tan(π/8))

• A — area of the octagon (cm², m², etc.)
• 8 — number of sides
• t — side length
• tan(π/8) — tangent of 22.5°, which equals tan(22.5°) ≈ 0.41421

The formula comes from splitting the octagon into 8 equal isosceles triangles from the center and adding up all their areas.

Step-by-Step Example