A regular octagon’s area and perimeter, computed directly from its side length.
How it works
The area formula (2 times 1 plus the square root of 2, times the side squared) comes from decomposing a regular octagon into simpler triangles and a central square; the perimeter is simply eight times the side.
What this does not include
This does not include irregular octagons — this calculator specifically assumes all eight sides and angles are equal.
How to use this calculator
- Enter the side length.
A worked example
A regular octagon with side length 4: area = 77.254834, perimeter = 8 × 4 = 32.
Side length 1: area = 4.828427 — the base unit octagon’s area.
What the variables mean
| Variable | Meaning |
|---|---|
| Side length | Length of each of the octagon’s eight equal sides |
Edge cases worth knowing
This assumes a regular octagon — eight equal sides and angles, like a stop sign. An irregular octagon needs individual side and angle measurements this single input can’t capture.
Area scales with the square of the side length — quadrupling the side length (1 to 4) multiplies the area by 16, matching 4².
Frequently asked questions
Where do regular octagons appear in real life?
Stop signs, gazebo floor plans, and certain architectural window and tile designs.
Are all eight angles the same in a regular octagon?
Yes — each interior angle measures 135 degrees, and all eight are equal since every side is equal.
Does doubling the side length double the area?
No — area scales with the side length squared, so doubling the side quadruples the area.
