Área Octógono Regular
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
2·(1+√2)·l²
About this calculator
The regular octagon area calculator determines the area of an octagon with all sides equal. The calculation uses the formula 2·(1+√2)·l², where 'l' is the side length. This tool is useful for construction projects, floor design, or octagonal objects.
To use the calculator, enter the side length in meters or centimeters. The result is given in the same unit squared. The formula derives from decomposing the octagon into isosceles triangles and a central square, but the calculation is simplified for direct use.
When to use: when planning an octagonal table, calculating the area of a garden or pavement, or in geometry problems. Cautions: ensure the octagon is regular (all sides equal). The formula does not apply to irregular octagons. Rounding may be needed for irrational values.
Frequently asked questions
What is a regular octagon?
It is an eight-sided polygon with all sides and internal angles equal (135° each).
Can I use the calculator for irregular octagons?
No, the formula is specific to regular octagons. For irregular ones, you need to decompose the shape into triangles or use other methods.
What unit should I use for the side?
Any unit of length, as long as consistent. The area will be in the squared unit (m², cm², etc.).
How do I get the side if I have the circumradius?
The side l = R * √(2 - √2), where R is the circumradius. But this calculator only uses the side.
Does the formula consider the apothem?
Not directly. The area can also be calculated as (perimeter * apothem)/2, but the formula used here is equivalent.