Octagon Calculator DE
Calculate the area, perimeter, diagonals and radii of a regular octagon from its side length.
How it works
Enter the side length of a regular (equal‑sided) octagon. The calculator returns the area, perimeter, the width across opposite flat sides, the longest diagonal, and the circumscribed and inscribed circle radii.
Frequently asked questions
How do I calculate the area of a regular octagon?
Use 2(1 + √2) × side², which is about 4.8284 × side². A side of 5 gives roughly 120.7 square units.
What is the perimeter of an octagon?
For a regular octagon it is 8 times the side length, since all eight sides are equal.
What is the interior angle of a regular octagon?
Each interior angle is 135°, and the eight angles sum to 1080°.
What is the width across the flats?
The distance between opposite sides is the side length times (1 + √2), about 2.414 times the side.
Does this work for irregular octagons?
No. These formulas assume a regular octagon with equal sides and angles. Irregular octagons must be divided into simpler shapes.
Where are octagons used?
In stop signs, gazebos, tiling and architecture — anywhere an eight-sided shape is needed.
Area and perimeter of a regular octagon
A regular octagon has eight equal sides and eight equal angles. From the side length a, the calculator finds the area, perimeter and other measures. The perimeter is simply 8a, and each interior angle is 135°.
The area formula
The area of a regular octagon is 2(1 + √2) × a², which is about 4.8284 × a². For a side of 5 units, the area is 4.8284 × 25 ≈ 120.7 square units. The constant comes from dividing the octagon into triangles.
Other measurements
The distance across the flats (the width between opposite sides) is a × (1 + √2) ≈ 2.414a, and the diagonal across the corners is a × √(4 + 2√2) ≈ 2.613a. These help when fitting an octagon into a square or a circle.
Octagons appear in stop signs, gazebos, paving and architecture, so the calculations are handy for building and design projects where you need material quantities or fitting dimensions.
Results are estimates for general guidance in Germany and may not reflect the latest local rates, fees or rules. Check official sources before making decisions.