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Octagon Area Calculator

Work out octagon area instantly with clear inputs, formula shown and shareable results.

About Octagon Area Calculator

A regular octagon has 8 equal sides. Splitting it into 8 isosceles triangles from the centre gives A = 8s² / (4·tan(π/8)), which evaluates to 2(1+√2)·s² ≈ 4.828427·s².

Formulas

Area

A = 8s² / (4·tan(π/8)) = 2(1+√2)·s² ≈ 4.828427·s²

Apothem

a = s / (2·tan(π/8))

Worked example

With the default values below, Octagon Area Calculator returns Area of one octagon of 173.8234. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side lengthminimum 0
6
Number of shapesminimum 1
1

Results

Area of one octagon
173.8234
Perimeter
48.0000
Apothem
7.2426
Total area of all shapes
173.8234

Step by step

  1. 1Values used
  2. 2Area
  3. 3Apothem
  4. 4Area of one octagon= 173.8234
  5. 5Perimeter= 48.0000
  6. 6Apothem= 7.2426
  7. 7Total area of all shapes= 173.8234

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is the interior angle of a regular octagon?

(8 − 2) × 180° / 8 = 135°.

Does the formula need a regular octagon?

Yes. For an irregular octagon use the shoelace formula on its vertex coordinates instead.

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