The Octagon is one of the most versatile shapes in construction. Bridging the gap between the square and the circle, it offers the structural stability of straight lines with the ergonomic efficiency of a round shape. You see it everywhere: the red STOP sign, the UFC fighting cage, garden gazebos, and even poker tables.

The Octagon Area Calculator is built for carpenters, tilers, and designers. Whether you are pouring a concrete slab for a hot tub or tiling a bathroom floor, this tool computes the Area, Perimeter, and Span (Width) instantly.

How to Use This Calculator

Select the dimension you have measured:

1. Side Length (Edge)

The length of one of the 8 flat outer edges. This is the most common measurement for carpentry (e.g., cutting deck boards).

2. Inradius (Span / Flat-to-Flat)

The distance from the center to the middle of an edge. Often called the "Apothem." Essential for sizing tables or gazebos to fit in a specific square space.

3. Circumradius (Corner-to-Corner)

The distance from the center to a sharp outer point (vertex). Useful for marking layout stakes on the ground.

The Math Behind the Shape

For a valid Regular Octagon with side length :

• Area:
• Perimeter:
• Span (Width):

Why Octagons Matter

Carpentry (Gazebos)

Building an octagonal deck or gazebo? You need the Area to order maintenance-free decking boards and the Perimeter for railings. The Span tells you exactly how wide the roof trusses need to be.

Tiling

Victorian-style bathrooms often use small hexagonal or octagonal tiles. Calculating the exact area helps you buy the right amount of mosaic sheets, accounting for the "Dot" inserts often used in these patterns.

Martial Arts

The UFC "Octagon" is a regulated fighting surface. Knowing the area (approx 750 sq ft for a standard cage) determines the canvas size and padding requirements.

Frequently Asked Questions (FAQ)

1. What is the angle of an octagon?

Each internal angle of a regular octagon is 135 degrees. This means you need to set your miter saw to 22.5 degrees (half of the 45-degree exterior angle) to cut perfectly tight frame joints.

2. How do I layout an octagon on the ground?

Start with a square. Measure the diagonal. The side of your octagon will be related to the span. Or, use the "Circumradius" mode to drive a center stake and measure 8 equal distances to the corners.

3. Can I calculate an Irregular Octagon?

Yes! If your 8 sides are different lengths (e.g., a stretched dining table), switch to "Irregular" mode (Coordinate Geometry) to solve it accurately.

Final Words

From elegant architecture to rugged fighting cages, the octagon is a shape of strength. The Octagon Area Calculator ensures your cuts are sharp, your angles are true, and your project is solid.