What makes an octagon regular?

All eight sides and angles are equal, each interior angle measuring 135°.

Where are regular octagons commonly seen?

Stop signs are a familiar real-world example.

Octagon Calculator - CalculatorLabs.net

Q: What formulas does this calculator use for a regular octagon?

Area = 2(1+√2) × side²; Perimeter = 8 × side.

Octagon Calculator

Calculate the area, perimeter, and apothem of a regular octagon.

What Is the Octagon Calculator?

A regular octagon has eight equal sides and angles — the shape of a classic stop sign. This calculator finds its area, perimeter, and apothem from a single side length.

Regular octagon — 8 equal sides

Formula Used

Area = 2 × (1 + √2) × side²
Perimeter = 8 × side
Apothem = (side ÷ 2) × (1 + √2)

These formulas apply to a regular octagon where all eight sides and interior angles (135° each) are equal.

How to Use This Calculator

Enter the length of one side of the octagon.
Click Calculate to see the area, perimeter, and apothem.

Worked Example

A regular octagon with side length 6 has an area of 2×(1+√2)×6² ≈ 173.82 square units, a perimeter of 8×6 = 48 units, and an apothem of (6÷2)×(1+√2) ≈ 7.24 units.