How to Use This Calculator
- Enter the side length of your octagon in the first input field (required).
- Optionally, you can enter the apothem (the distance from the center to a side) if you know it.
- Click the "Calculate" button to compute the circumradius and inradius.
- The results will be displayed in the respective fields.
Understanding Octagon Geometry
An octagon is a polygon with eight sides. In this calculator:
- Circumradius (R): The radius of the circumscribed circle that passes through all eight vertices of the octagon.
- Inradius (r): The radius of the inscribed circle that touches all eight sides of the octagon.
Formulas Used
The calculator uses these formulas:
Circumradius: R = s / (2 × sin(π/8))
Inradius: r = s / (2 × tan(π/8))
Where s is the side length of the octagon.
Practical Applications
This calculator can be used for:
- Designing regular octagonal structures (like stop signs, windows, or decorative elements)
- Calculating material requirements for octagonal shapes
- Understanding geometric properties of octagons in engineering and architecture