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Octagon Calculator.

Calculate regular octagon area, perimeter, and apothem from its side length.

On-device calculationNo signup
01

Set your values

Results update as you type.

area: 120.710678

area

120.710678
perimeter: 40

perimeter

40.000000
apothem: 6.035534

apothem

6.035534

Results update automatically as you type.

Use Cases

Geometry Homework and Learning

Students can verify their manual calculations for octagon properties. It's a quick way to check answers and understand the relationships between side length, area, perimeter, and apothem.

Example: Check the area of an octagon with side length 3 cm to confirm your textbook solution.

Frequently Asked Questions

What is an apothem of a regular octagon?
The apothem is the distance from the center to the midpoint of any side. It is also the radius of the inscribed circle. For a regular octagon, it can be calculated from the side length using the formula: apothem = side / (2 * tan(π/8)).
How do I calculate the area of a regular octagon?
The area of a regular octagon can be found using the formula: area = 2 * (1 + √2) * side². Alternatively, you can use the apothem and perimeter: area = (perimeter * apothem) / 2.
What is the perimeter of a regular octagon?
The perimeter is the total distance around the octagon. For a regular octagon, it is simply 8 times the side length. For example, if the side length is 5 units, the perimeter is 40 units.

Tips & Common Mistakes

Tips

  • Ensure the side length is measured in the same unit for all calculations. The results will be in square units for area and linear units for perimeter and apothem.
  • For a regular octagon, all sides and angles are equal. If your shape is irregular, this calculator will not be accurate.
  • Use the apothem value to find the radius of the inscribed circle, which is useful for fitting a circle inside the octagon.
  • Double-check your side length input for typos, as a small error can significantly affect the area and perimeter results.

Common Mistakes to Avoid

  • Using the diameter of the circumscribed circle instead of the side length. The calculator expects the side length, not the distance across the octagon.
  • Confusing the apothem with the radius of the circumscribed circle. The apothem is the distance to a side, not to a vertex.
  • Forgetting to square the side length when calculating the area. The area formula requires side², not just side.

Last updated: August 13, 2026