1. What is the Circumradius of Hexagon?

The Circumradius of a Hexagon is the radius of the circumscribed circle that passes through all six vertices of the regular hexagon. It represents the distance from the center of the hexagon to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the Circumradius formula:

Where:

• \( r_c \) — Circumradius of Hexagon (m)
• \( P \) — Perimeter of Hexagon (m)

Explanation: For a regular hexagon, the circumradius is equal to the side length, and since the perimeter is 6 times the side length, the circumradius equals the perimeter divided by 6.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry, engineering, and design applications involving hexagonal shapes. It helps determine the size of the circumscribed circle and is used in various construction and manufacturing processes.

4. Using the Calculator

Tips: Enter the perimeter of the hexagon in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and side length?
A: For a regular hexagon, the circumradius equals the side length (\( r_c = a \)).

Q2: Can this formula be used for irregular hexagons?
A: No, this formula applies only to regular hexagons where all sides and angles are equal.

Q3: How is circumradius different from inradius?
A: Circumradius is the distance from center to vertices, while inradius is the distance from center to sides.

Q4: What are practical applications of circumradius calculation?
A: Used in bolt circle patterns, honeycomb structures, architectural designs, and mechanical engineering components.

Q5: How does circumradius relate to area calculation?
A: The area of a regular hexagon can also be expressed in terms of circumradius: \( Area = \frac{3\sqrt{3}}{2} r_c^2 \).