Hexagon Calculator
Compute regular hexagon properties: area, perimeter, diagonals, circumradius, and apothem from side length. Free online 2D geometry calculator for students.
About This Calculator
The Hexagon Calculator is a free online geometry tool that computes all key properties of a regular hexagon from a single side length input. Whether you are a student learning polygon geometry, a teacher preparing classroom materials, an architect designing hexagonal tiles or structures, or a hobbyist working on a craft project, this calculator provides instant and accurate results for area, perimeter, diagonals, circumradius, and apothem (inradius).
A regular hexagon is a six-sided polygon where all sides are equal and all interior angles measure exactly 120 degrees. The hexagon is one of the most efficient and stable shapes found in nature, from honeycomb cells and snowflake crystals to the molecular structure of graphene and the Giant's Causeway basalt columns. The calculator uses standard mathematical formulas: area A = (3sqrt3/2) x a^2, perimeter P = 6a, long diagonal D = 2a, short diagonal d = sqrt3 x a, circumradius R = a, and apothem r = (sqrt3/2) x a.
Regional Notes
This calculator is unit-agnostic and works with any measurement system (metric or imperial). Simply enter your side length in consistent units -- centimeters, meters, inches, or feet -- and all computed results will be in the same units (area in square units, linear measurements in the same unit). The hexagon calculator is used worldwide by students, architects, engineers, and designers across India, the United States, the United Kingdom, and beyond.
Hexagonal shapes appear in numerous practical applications: floor and wall tiling, bolt and nut heads, pencil cross-sections, telescope mirrors (like the James Webb Space Telescope's segmented mirror), cellular network tower layouts, and chemical compound diagrams. Understanding hexagon geometry is essential in fields ranging from civil engineering and architecture to graphic design and materials science.
Frequently Asked Questions
What is a regular hexagon?
A regular hexagon is a six-sided polygon where all sides are equal in length and all interior angles are 120 degrees. The six equilateral triangles that form a regular hexagon make it one of the most efficient shapes in nature, found in honeycombs, snowflake crystals, and molecular structures.
How do you calculate the area of a regular hexagon?
The area of a regular hexagon is calculated using the formula A = (3sqrt3/2) x a^2, where a is the side length. This formula comes from dividing the hexagon into six equilateral triangles, each with area (sqrt3/4) x a^2, and summing them. For a hexagon with side length 5 units, the area would be approximately 64.95 square units.
What is the apothem of a regular hexagon?
The apothem (also called inradius) of a regular hexagon is the distance from the center to the midpoint of any side. It is calculated as r = (sqrt3/2) x a, where a is the side length. For a hexagon with side 10 cm, the apothem is approximately 8.66 cm. The apothem is also the radius of the inscribed circle.
What are the long and short diagonals of a hexagon?
A regular hexagon has two types of diagonals. The long diagonal connects opposite vertices and equals twice the side length (D = 2a). The short diagonal connects vertices with one vertex between them and equals sqrt3 times the side length (d = sqrt3 x a). A regular hexagon has 3 long diagonals and 6 short diagonals, totaling 9 diagonals.
What is the circumradius of a regular hexagon?
The circumradius of a regular hexagon is the radius of the circumscribed circle that passes through all six vertices. Remarkably, for a regular hexagon, the circumradius R equals the side length a. This means the distance from the center to any vertex is exactly the same as the length of each side, making the hexagon unique among regular polygons.
Why are hexagons so common in nature?
Hexagons appear frequently in nature because the 120-degree interior angle provides structural efficiency and stability. Honeybees use hexagonal cells to maximize storage space while minimizing wax usage. The hexagonal pattern also appears in snowflake crystals, basalt columns (like Giant's Causeway), insect eyes, and molecular structures like graphene and benzene rings.
How do you find the perimeter of a hexagon from side length?
The perimeter of a regular hexagon is simply six times the side length: P = 6a. Since all six sides are equal in a regular hexagon, you multiply the side length by 6. For irregular hexagons, you would add all six side lengths individually.
What is the sum of interior angles in a hexagon?
The sum of interior angles in any hexagon is 720 degrees. In a regular hexagon, each interior angle is 120 degrees (720 deg ÷ 6). The exterior angle of a regular hexagon is 60 degrees. This can be verified using the formula (n-2) x 180 deg where n is the number of sides: (6-2) x 180 deg = 720 deg.