Octagon Area Calculator

Calculate the area of a regular octagon with eight sides of equal length. Includes the formula, a worked example, and stop-sign and tower references.

Calculate area of octagon

Regular octagon:

\\text{area} = 2 \\\\times (1 + \\\\sqrt{2}) \\\\times s^2

Where s is the side length.

Approximation:

\\text{area} \\\\approx 4.828 \\\\times s^2

Calculate the area of a regular octagon with side length 4 cm:

\\text{area} = 2 \\\\times (1 + 1.414) \\\\times 4^2 = 2 \\\\times 2.414 \\\\times 16

= 4.828 \\\\times 16 = 77.25 \\\\text{ cm}^2

Result: 77.25 cm²

Perimeter: $8 \\\\times \\\\text{side}$
Apothem: $a = \\\\frac{s}{2 \\\\tan(22.5°)}$
Area with apothem: $\\\\frac{1}{2} \\\\times \\\\text{perimeter} \\\\times \\\\text{apothem}$

What if the octagon is irregular? Divide it into triangles or use coordinate geometry.

What is the sum of interior angles? 1080° for any octagon.

Can I calculate from the radius? Yes, use $s = 2R \\\\sin(22.5°)$ to find the side first.

How many diagonals does an octagon have? 20 diagonals.