Octagon Radius Calculator helps you find the circumradius of a regular octagon using side length. Includes formula, examples, and easy-to-use geometry math.
An octagon is a polygon with eight equal sides and eight equal angles when it is regular. In many real-world applications—such as construction layouts, tile design, CNC cutting, and geometry tools—you may need to calculate the radius of a regular octagon.
This calculator helps you find the circumradius (outer radius), which is the distance from the center of the octagon to any of its vertices.
What Is the Radius of an Octagon?
The radius of a regular octagon usually refers to the circumradius. This is the radius of the circle that passes through all eight vertices of the octagon.
To calculate this value, you only need one input:
- Side length of the octagon
Formula to Calculate Octagon Radius
Perimeter of a Regular Octagon
Formula
The perimeter P of a regular octagon is the sum of all its sides.
P=8a
Area of a Regular Octagon
Formula
The area A of a regular octagon with side length a is:
A=2(1+2)a2
Diameter of a Regular Octagon
The diameter is twice the circumradius (distance from one vertex to the opposite vertex).
Formula
D=2R
Using side length directly:
D=sin(8π)a
How the Calculator Works
- The user enters the side length of the octagon
- The calculator applies the circumradius formula
- The result is the radius from the center to a vertex
Example Calculation
Given:
- Side length: a = 10 units
Radius
R=2sin(8π)10
R≈13.07
Perimeter
P=8×10=80
Area
A=2(1+2)×102
A≈482.84
Diameter
D=2×13.07
D≈26.14
Final Output Summary (for Calculator)
- Radius: 13.07 units
- Diameter: 26.14 units
- Perimeter: 80 units
- Area: 482.84 square units
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