How do you calculate the area of a regular octagon?

For a regular octagon with side length s, the area is A = 2(1 + √2)s². This calculator applies that formula and converts units.

What if I only know the perimeter of the octagon?

Divide the perimeter by 8 to get the side length, then use A = 2(1 + √2)s². The tool does that automatically.

Can I get the octagon that fits in a square?

Yes. If a square of side S is cut equally at corners to form a regular octagon, then the octagon’s side is s = S(√2 − 1). This tool can compute both S from s and s from S.

Octagon Calculator (Area, Perimeter, Side, Inradius, Circumradius)

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Value

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Side length

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Perimeter

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Area

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Inradius (apothem)

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Circumradius

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Square side (if cut)

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Steps

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Regular octagon formulas

For a regular octagon with side \( s \):

Area: \( A = 2(1 + \sqrt{2})s^2 \)

Perimeter: \( P = 8s \)

Inradius (apothem): \( r = \frac{s}{2 \tan(\pi/8)} \)

Circumradius: \( R = \frac{s}{2 \sin(\pi/8)} \)

Numerically, \( 2(1 + \sqrt{2}) \approx 4.82842712 \), so \( A \approx 4.82842712 s^2 \).

Octagon obtained by cutting the corners of a square

If you start from a square of side \( S \) and cut equal isosceles right triangles from each corner so that a regular octagon remains, the octagon side is:

\( s = S(\sqrt{2} - 1) \)

and so \( S = \dfrac{s}{\sqrt{2} - 1} \)

FAQ

Is this only for regular octagons?

Yes. Irregular octagons need coordinates or side-angle data; this tool follows the regular case like the common online calculators.

What unit should I use?

Use whatever you measure in (mm, cm, m, in, ft). We convert everything internally and show some alternative units.