What is the formula for the area of a regular octagon?

The area formula is A = 2(1+√2)s², where s is the length of one side. The constant 2(1+√2) is approximately 4.8284. This formula applies only to regular octagons — those with all sides equal and all interior angles equal to 135°.

Does this work for irregular octagons?

No. The formula A = 2(1+√2)s² is valid only for regular octagons. An irregular octagon (with unequal sides or angles) requires a different approach, such as dividing it into triangles or using the shoelace formula with vertex coordinates.

What units does the calculator use?

You can enter the side length in millimeters, centimeters, meters, inches, or feet. The result is displayed in the corresponding square unit (e.g., cm² if you enter centimeters).

How accurate is the result?

The calculation uses JavaScript's full floating-point precision (IEEE 754 double). Results are displayed rounded to 6 significant figures, which is sufficient for virtually all practical applications.

What is the perimeter of a regular octagon?

The perimeter is simply 8 × s, since a regular octagon has eight equal sides. This calculator shows the perimeter alongside the area for convenience.

Area of an Octagon Calculator

Name: Area of an Octagon Calculator
Availability: InStock
Author: Nham Vu

Enter the side length of a regular octagon to instantly calculate its area using the formula A = 2(1+√2)s².

Input

Side Length (s)

Formula

A = 2(1 + √2) × s²

where s = side length

Constant ≈ 4.828427

Result

Enter a side length and click Calculate

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Summary

Enter the side length of a regular octagon to instantly calculate its area using the formula A = 2(1+√2)s².

How it works

Enter the side length of the regular octagon in the input field.
Choose your preferred unit (millimeters, centimeters, meters, inches, or feet).
The area is calculated instantly using the formula A = 2(1+√2)s².
View the step-by-step breakdown showing intermediate values.
Copy the result or reset the form to start over.

Use cases

Calculating floor area for octagonal room layouts or tiles.
Estimating material for octagonal garden beds or patio sections.
Architecture and engineering projects involving octagonal structures.
Homework and exam preparation for geometry courses.
Verifying manual calculations for DIY projects.
Computing stop-sign shaped surface areas for signage or art.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu