Octagon Area Calculator
The area of a regular octagon from its side length — about 4.828 times the side squared.
A regular octagon is a square with its corners cut off at 45°, which is the easiest way to see its area: 2(1 + √2)a², roughly 4.
How the octagon area calculator works
A regular octagon is a square with its corners cut off at 45°, which is the easiest way to see its area: 2(1 + √2)a², roughly 4.828 a². Its interior angles are 135°, and the distance across the flats is a(1 + √2) — the measurement that matters when an octagonal shape has to fit an opening.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Side 10 | 482.8427 | 482.84 |
| Side 1 | 4.8284 | 4.828 |
| A stop sign, side 300 mm | 434,558.4412 | about 434,558 mm² |
FAQFrequently asked questions
What is the area of a regular octagon?
2(1 + √2) times the side squared, about 4.828 a².
What are its interior angles?
135° each, adding to 1,080°.
What is the width across the flats?
a(1 + √2), about 2.414 times the side.
How is an octagon related to a square?
It is a square with its four corners cut off at 45°, which is how the formula is most easily derived.
Do octagons tile?
Not alone — but octagons and squares together tile perfectly, a pattern found on countless floors.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.