Octagon Radius Calculator

Calculate Octagon Radius

Formula

To calculate the Radius (R):

\[ R = \frac{S}{2 \times \sin\left(\frac{\pi}{8}\right)} \]

Where:

What is an Octagon Radius?

An octagon radius is the distance from the center of the octagon to any of its vertices. It is a crucial measurement in various fields such as architecture, carpentry, and mathematics, especially when constructing objects with octagonal shapes or when calculating areas and perimeters of octagons.

Example Calculation 1

Let's assume the following value:

Using the formula:

\[ R = \frac{10}{2 \times \sin\left(\frac{\pi}{8}\right)} = \frac{10}{2 \times 0.382683} = \frac{10}{0.765367} = 13.07 \text{ units} \]

The Radius is 13.07 units.

Example Calculation 2

Let's assume the following value:

Using the formula:

\[ R = \frac{5}{2 \times \sin\left(\frac{\pi}{8}\right)} = \frac{5}{2 \times 0.382683} = \frac{5}{0.765367} = 6.54 \text{ units} \]

The Radius is 6.54 units.