1. What is Circumradius of Hexagon?

The Circumradius of Hexagon is the radius of the circumcircle of the Hexagon or the circle that contains the Hexagon with all vertices lying on that circle. 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 formula:

Where:

• \( rc \) — Circumradius of Hexagon (m)
• \( dLong \) — Long Diagonal of Hexagon (m)

Explanation: The circumradius of a regular hexagon is exactly half the length of its long diagonal, as all vertices of a regular hexagon lie on a circle whose radius equals half the longest diagonal.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is essential in geometry and various engineering applications, particularly in designing hexagonal structures, patterns, and understanding spatial relationships in hexagonal grids.

4. Using the Calculator

Tips: Enter the long diagonal 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: In a regular hexagon, the circumradius equals the side length (\( rc = a \)).

Q2: How does circumradius relate to short diagonal?
A: The circumradius is \( \frac{\sqrt{3}}{2} \) times the short diagonal of a regular hexagon.

Q3: Can this formula be used for irregular hexagons?
A: No, this formula applies only to regular hexagons where all sides and angles are equal.

Q4: What are practical applications of circumradius calculation?
A: Used in mechanical engineering, architecture, material science, and any field dealing with hexagonal patterns or structures.

Q5: How is circumradius different from inradius?
A: Circumradius is the radius of the circle passing through all vertices, while inradius is the radius of the circle inscribed within the hexagon touching all sides.