Octagon Calculator

Category: Geometry
- June 19, 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 a useful tool designed to help you find various properties of a regular octagon. With eight equal sides and equal internal angles of 135°, this shape is common in many areas. By entering just one known value, you can easily calculate others, making it a convenient choice for students, architects, and anyone interested in Geometry.

Inputting Your Data

To begin using the Octagon Calculator, you simply need to select a parameter you know. The tool allows you to choose from options such as side length, perimeter, inradius (or apothem), circumradius, and area. After you enter the value for your chosen parameter, the calculator will automatically determine the rest of the octagon’s properties.

What Properties Can You Calculate?

This calculator can provide you with a range of octagon properties. Here are some of the key measurements you can find:

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

Adjusting Display Options

The calculator also lets you customise how results are displayed. You can choose the number of decimal places for your answers, ensuring accuracy in your calculations. Furthermore, you have the option to show the formulas used for the calculations, providing a clearer understanding of how each result is derived.

Visual Representation of Octagons

One of the exciting features of the Octagon Calculator is its visual representation of the octagon. After calculating the properties, you can view a canvas drawing of the octagon based on your inputs. This visual aid can be particularly helpful for grasping the dimensions and angles of your octagon.

Learning About Regular Octagons

Regular octagons have some fascinating properties. They have eight sides, and their interior angles each measure 135°. The sum of all interior angles in an octagon is 1080°. Here are some more interesting facts:

  • Exterior angle: 45°
  • Number of diagonals: 20
  • Area formula: 2(1 + √2) × side²
  • Perimeter formula: 8 × side

Practical Uses of Octagons

Octagons are not just shapes studied in classrooms; they are widely used in the real world. Regular octagons can be found in various contexts such as:

  • Road signs, like stop signs
  • Architectural designs
  • Islamic geometric patterns
  • Tiling and tessellation
  • Camera apertures
  • Coins in some countries

Start Using the Octagon Calculator Today!

With the Octagon Calculator, you can quickly and accurately determine the properties of a regular octagon. Whether you’re working on a school project, designing a building, or just exploring geometry, this calculator is a handy tool that simplifies complex calculations and enhances your learning experience. Give it a try and see how easy it is to work with octagons!