Octagon Calculator

Category: Geometry
- April 18, 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

What Is the Octagon Calculator?

The Octagon Calculator is an easy-to-use tool designed to help you calculate important measurements of a regular octagon. A regular octagon is a shape with 8 equal sides and 8 equal angles. This calculator allows you to enter just one known value—such as side length, area, perimeter, inradius (apothem), or circumradius—and it will instantly calculate all the other properties for you.

Who Can Benefit From This Calculator?

Whether you're a student working on geometry assignments, an architect creating floor designs, or someone simply curious about octagonal shapes, this tool offers quick and reliable calculations. It complements popular geometry tools like the Triangle Calculator, Area Calculator, Volume Calculator, and Polygon Calculator.

How to Use the Octagon Calculator

  • Step 1: Select the measurement you know from the dropdown menu (e.g., Side Length, Area).
  • Step 2: Enter the value in the input box provided.
  • Step 3: Choose how many decimal places you'd like the results to display.
  • Step 4: Click the Calculate button to see all related properties.
  • Step 5: View the results, formulas, and a dynamic visual of the octagon.

What Does It Calculate?

Once you input a single value, the calculator determines:

  • Side Length
  • Perimeter
  • Area
  • Inradius (Apothem)
  • Circumradius
  • Interior Angle (Always 135°)

Octagon Formulas Used

Perimeter: \( P = 8s \)
Area: \( A = 2(1 + \sqrt{2}) \cdot s^2 \)
Inradius (r): \( r = \frac{s}{2 \cdot \tan(\pi/8)} \)
Circumradius (R): \( R = \frac{s}{2 \cdot \sin(\pi/8)} \)
Side from Area: \( s = \sqrt{\frac{A}{2(1 + \sqrt{2})}} \)
Interior Angle: \( \frac{(n - 2) \cdot 180^\circ}{n} = 135^\circ \)

Why Use This Calculator?

This tool eliminates the need for manual calculations, making it ideal for quick checks or complex planning. Instead of solving each formula by hand, get all the answers in a few clicks. It's especially helpful in areas like:

  • Engineering and CAD design
  • Geometry homework or test preparation
  • Building layout or tile work involving octagonal shapes

Frequently Asked Questions (FAQ)

Can I use this calculator for irregular octagons?

No, this calculator is made for regular octagons where all sides and angles are equal.

What units should I use?

You can use any unit (inches, centimeters, meters, etc.), as long as you're consistent. The results will be in the same unit.

Does it include a diagram?

Yes! After calculation, a visual diagram shows the octagon with side labels and radius lines, helping you better understand the geometry.

Can I hide the formulas?

Yes, there's a checkbox labeled “Show formulas” which lets you turn this feature on or off based on your preference.

Is this like a triangle geometry tool?

In a way, yes. Like a triangle solver or right triangle calculator, this tool uses known formulas to compute unknown values. It’s just focused on octagons instead of triangles.

Other Useful Geometry Tools

If you're working on geometry problems or projects, you might also find these calculators useful:

  • Triangle Calculator: Solve triangle dimensions, angles, and area.
  • Pythagorean Theorem Calculator: Find the hypotenuse and triangle sides quickly.
  • Area Calculator: Calculate the surface area of different shapes.
  • Volume Calculator: Get the volume of 3D objects like cubes, cones, and cylinders.
  • Polygon Calculator: Measure properties of various multi-sided shapes.

Conclusion

The Octagon Calculator is a practical and visual tool for quickly solving octagonal measurements. It saves time, reduces error, and helps anyone working with shapes get accurate results. Give it a try for your next geometry challenge or creative project!