Octagon Calculator CA
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
What is the area of a regular octagon?
Area = 2(1 + √2) × side², which is about 4.828 × side². For a side of 5 that is roughly 120.71 square units.
How do I find the perimeter of an octagon?
Multiply the side length by 8, since a regular octagon has eight equal sides.
What is the width of an octagon across the flats?
The distance across opposite flat sides is (1 + √2) × side, about 2.414 times the side length.
Does this work for irregular octagons?
No. These formulas assume a regular octagon with equal sides and angles. Irregular octagons must be split into triangles to find their area.
Octagon Calculator
A regular octagon is an eight‑sided shape with equal sides and angles — think stop signs and gazebo floors. This calculator computes every key measurement from a single side length.
Octagon formulas
| Measure | Formula (side = a) |
|---|---|
| Area | 2(1 + √2) a² |
| Perimeter | 8a |
| Width across flats | (1 + √2) a |
| Longest diagonal | √(4 + 2√2) · a |
| Circumradius | ½ √(4 + 2√2) · a |
| Inradius | ½ (1 + √2) a |
Worked example
For a side of 5 units, the area is 2(1 + √2) × 25 ≈ 120.71 square units and the perimeter is 40 units.
Where octagons appear
- Stop signs and traffic signage.
- Gazebos, summerhouses and patio designs.
- Tiling, umbrellas and architectural windows.
Results are estimates for general guidance in Canada and may not reflect the latest local rates, fees or rules. Check official sources before making decisions.