Octagon Area Calculator

Need to calculate the area of an octagon but don’t want to mess with complex math? Whether you're designing a space, solving homework, or just curious, our Octagon Area Calculator is here to make things fast and simple. With a few inputs, you'll get precise results—and maybe learn a few surprising things about this unique shape along the way.

What Is an Octagon?

Let’s start with the basics. An octagon is a polygon with eight sides and eight angles. It comes in two main types:

• Regular octagon: All sides and angles are equal.

• Irregular octagon: Sides and angles vary in length and degree.

When most people talk about calculating octagon area, they usually mean regular octagons—the kind you’ll find in architecture, game boards, and even stop signs.

But why eight sides? The number eight gives the octagon a symmetrical balance that’s both functional and beautiful. It's a shape that's easy to recognize, easy to work with, and surprisingly common in everyday life.

If you imagine an octagon, you probably picture something like a stop sign. That’s a regular octagon, and it has some cool math behind it. To find its area, you’ll need either a side length or the distance across the flat edges (known as the apothem in geometry-speak).

Try out Triangle Square Footage Calculator

Formula for Octagon Area

To calculate the area of a regular octagon—one where all sides and angles are equal—you can use this reliable formula:

Area = 2 × (1 + √2) × a²

Let’s break that down a bit.

• The letter "a" represents the length of one side of the octagon.

• The square (a²) means you're multiplying the side length by itself.

• The constant (1 + √2) comes from geometric derivations specific to eight-sided polygons.

• Multiply everything by 2 to scale it properly for all eight sides.

This formula only works for regular octagons, which are the most common type in practical applications—think stop signs, game tiles, and certain architectural layouts.

Example:

Let’s say each side of your octagon is 5 centimeters long.

Here’s how you calculate the area:

1. Square the side length: 5 × 5 = 25

2. Find the value of (1 + √2), which is approximately 2.414

3. Multiply everything: 2 × 2.414 × 25 = 120.7

Result: The area of a regular octagon with 5 cm sides is approximately 120.7 square centimeters.

The Ancient Temple with an Octagonal Secret

Long before calculators—or even algebra—ancient builders were already mastering geometric design. One of the most fascinating examples? The Dome of the Rock in Jerusalem.

Built around 691 AD, this iconic Islamic shrine is one of the earliest examples of monumental Islamic architecture. But here’s the hidden twist: its foundation is an octagon.

Why an octagon? It wasn't just for looks. The number eight has long carried spiritual and symbolic meaning across many cultures. In this case, the octagon serves as a transition between a square base (symbolizing Earth) and a circular dome (symbolizing Heaven). That geometric decision wasn’t just artistic—it was deeply symbolic and structurally functional.

From a mathematical standpoint, the regularity of the octagon made it easier for ancient architects to distribute weight evenly and guide the eye upward. This clever use of geometry created not just balance, but beauty.

And they did it all without an Octagon Area Calculator.

So the next time you plug numbers into a calculator for something as ordinary as a tile layout or game design, remember: you're tapping into a design tradition that dates back more than 1,300 years.

Geometry isn’t just math—it’s history, symbolism, and art all rolled into one elegant shape.

Try out Pentagon Area Calculator

Fun Facts About Octagons

Think an octagon is just a fancy stop sign shape? Think again. Here are some surprising—and genuinely fun—facts about this eight-sided figure that might just change how you see it:

1. Stop Signs Are Octagons for a Reason
You’ve probably seen hundreds of stop signs, but have you ever wondered why they’re octagonal? The unique shape isn’t just for style. In traffic design, an octagon is used exclusively for stop signs because it’s instantly recognizable—even from behind. That eight-sided shape signals “STOP” before you even read the word.

2. Octagons Are Common in Coins
Some countries use octagon-shaped coins because the shape is easier to grip and distinguish by touch. The Hong Kong $2 coin, for example, has an octagonal design, combining both form and function.

3. Sacred Geometry Uses the Octagon
In religious architecture, the octagon is often used as a symbolic transition between earth (square) and heaven (circle), just like in the Dome of the Rock. This geometric form appears in temples, cathedrals, and even baptismal fonts throughout history.

4. The UFC Fighting Ring Is Called “The Octagon”
Yes, The Octagon is also the name of the world-famous UFC fighting ring. Its eight sides create a more dynamic and evenly balanced space for fighters—less predictable than a square ring and more strategic.