Octagon Calculator

Category: Geometry
- July 01, 2025
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Calculate various properties of a regular octagon based on your input. A regular octagon has 8 equal sides and 8 equal internal angles of 135°.

Enter one parameter and the calculator will determine all other measurements of the octagon.

Input Parameter

units

Display Options

About Regular Octagons

A regular octagon is an eight-sided polygon with all sides and all interior angles equal. It's a highly symmetrical shape found in architecture, design, and everyday objects.

Key Properties
  • Number of sides: 8
  • Interior angle: 135° (Sum of interior angles: 1080°)
  • Exterior angle: 45°
  • Number of diagonals: 20
  • Area: 2(1 + √2) × side²
  • Perimeter: 8 × side
Applications

Regular octagons appear in:

  • Road signs (e.g., stop signs)
  • Architecture and interior design
  • Islamic geometric patterns
  • Tiling and tessellation
  • Camera aperture designs
  • Coins in some countries

Understanding the Octagon Calculator

The Octagon Calculator is your handy tool for crunching numbers related to regular octagons. This calculator allows you to quickly find various properties of an octagon based on just one input. Whether you know the side length, perimeter, or another measurement, this tool simplifies the process of understanding octagons.

What is a Regular Octagon?

A regular octagon is a shape with eight equal sides and angles. Each interior angle measures 135 degrees, creating a balanced and symmetrical form. Regular octagons are common in design and architecture, making them familiar to many. Key characteristics include:

  • Sides: 8
  • Interior Angle: 135°
  • Exterior Angle: 45°
  • Diagonals: 20

Inputting Your Data

The Octagon Calculator is user-friendly. You start by selecting what you know about the octagon. Options include side length, perimeter, inradius, circumradius, and area. By entering just one value, the calculator can work out the rest for you, making calculations straightforward and quick.

What Can You Calculate?

This tool calculates several key properties of a regular octagon. After entering your chosen measurement, the calculator provides results for:

  • Side Length
  • Perimeter
  • Area
  • Inradius (Apothem)
  • Circumradius
  • Interior Angle

decimal precision and Display Options

The Octagon Calculator offers flexibility in how results are presented. You can choose the number of decimal places for accuracy. This way, whether you need a rough estimate or precise measurements, the calculator can meet your needs. Additionally, there’s an option to show the formulas used in the calculations, which can help you understand the Math behind the results.

Visualizing the Octagon

Alongside results, the calculator provides a visual representation of the octagon. This helps you see how the properties relate to the shape. The canvas shows the octagon based on your input, enhancing your understanding of its dimensions and proportions. A visual can be incredibly useful for grasping geometric concepts.

Learning More About Octagons

Octagons aren't just simple shapes; they have real-world applications. You see them in various contexts, like road signs and architectural designs. Here are some interesting uses:

  • Road signs (like stop signs)
  • Design elements in buildings
  • Tiling patterns
  • Coins in some countries

Why Use the Octagon Calculator?

Using the Octagon Calculator saves time and simplifies math for students, designers, and anyone needing quick calculations. It’s a practical tool that makes learning about octagons engaging and accessible. With its clear interface and helpful features, you’ll find understanding octagonal Geometry easier than ever.