Short Diagonal Of Hexagon Given Circumradius Calculator

Short Diagonal of Hexagon Formula:

\[ d_{short} = \sqrt{3} \times r_c \]

Short Diagonal of Hexagon (d_short):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Short Diagonal of Hexagon?

The Short Diagonal of a Hexagon is the length of the line joining any vertex of the Hexagon to one of the vertices which are next to adjacent vertices. It represents the distance between non-adjacent vertices that are separated by one vertex.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{short} = \sqrt{3} \times r_c \]

Where:

\( d_{short} \) — Short Diagonal of Hexagon (m)
\( r_c \) — Circumradius of Hexagon (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732051)

Explanation: The formula derives from the geometric properties of a regular hexagon, where the short diagonal is related to the circumradius through the square root of 3.

3. Importance of Short Diagonal Calculation

Details: Calculating the short diagonal is important in geometry, engineering, and architectural design where hexagonal shapes are used. It helps in determining spacing, structural integrity, and aesthetic proportions in hexagonal patterns and constructions.

4. Using the Calculator

Tips: Enter the circumradius of the hexagon in meters. The value must be positive and greater than zero. The calculator will compute the short diagonal using the mathematical relationship between these two properties.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between short diagonal and long diagonal?
A: The short diagonal connects vertices separated by one vertex, while the long diagonal connects opposite vertices through the center of the hexagon.

Q2: How is this formula derived?
A: The formula comes from the trigonometric relationships in a regular hexagon, where internal angles are 120 degrees and the circumradius forms specific triangles with the sides and diagonals.

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

Q4: What are practical applications of this calculation?
A: This calculation is used in engineering design, architecture, material science, and any field dealing with hexagonal patterns like honeycomb structures, bolt heads, or tile designs.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular hexagons. The accuracy depends on the precision of the input circumradius value.