Regular Octagon Area Calculator

How it is calculated

For a regular octagon, with eight equal sides and equal angles, the area is A = 2 × (1 + √2) × s² and the perimeter is P = 8 × s, where s is the length of one side. The factor 2 × (1 + √2) is about 4.828. It comes from a square of side s(1 + √2) with four small right-angled corners cut off.

Use any length unit; the output says 'units' and 'units²', meaning the unit you entered and its square. Results are rounded to two decimals and the side must be greater than zero. If you know the distance across the flats rather than the side, divide it by 1 + √2, about 2.414, to get the side first.

Common mistakes

• Entering the width across the flats as the side. For a regular octagon that width is about 2.414 times the side, so the area would be far too large.
• Entering the corner-to-corner width. Divide it by about 2.613 first to get the side, otherwise the result is wrong.
• Using the formula for an irregular eight-sided shape. All eight sides and angles must be equal.
• Reading the output unit label literally. 'units' means whatever you typed, so centimetres give cm² for the area.
• Confusing area with perimeter when ordering material. Edging or trim uses the perimeter, while paint, tile or fabric uses the area.