Regular Hexagon Calculator — Area, Perimeter, Diagonals
Find every measurement of a regular hexagon from any single known value — side length, apothem, perimeter or area. The calculator computes area, perimeter, both diagonals, inradius and circumradius instantly.
Known measurement
Area = (3√3 / 2) × a²
- 1
a²
5 × 5 = 25 - 2
3√3 ÷ 2
2.598076Area coefficient for a regular hexagon (= sum of 6 equilateral triangle areas). - 3
Area
2.5981 × 25 = 64.9519
How does this calculator work?
For a regular hexagon with side a: Area = (3√3/2)a², Perimeter = 6a, Apothem = (√3/2)a, Long diagonal = 2a, Short diagonal = √3·a. Enter any one known measurement and the calculator derives all the others.
Formula
How this is calculated
A regular hexagon has six equal sides of length a and six equal interior angles of 120°. Because of this high symmetry, every measurement can be derived from any single known dimension. The area formula (3√3/2)a² comes from dividing the hexagon into six equilateral triangles, each with area (√3/4)a², and summing them. The perimeter is simply 6a.
The apothem (also called the inradius) is the perpendicular distance from the centre to the midpoint of any side: a × (√3/2). The circumradius (distance from centre to any vertex) is exactly equal to the side length a — a unique property of the regular hexagon. The long diagonal (vertex to opposite vertex) is 2a, and the short diagonal (midpoint of one side to the opposite midpoint, also the flat-to-flat width) is a × √3.
To solve from a known apothem (ap), side length = ap × 2/√3. From known area (A), side = √(2A/(3√3)). All formulas assume a perfect regular hexagon; irregular hexagons require the individual side and angle measurements.
Frequently asked questions
The apothem is the perpendicular distance from the centre to the midpoint of a side — equal to (√3/2) × a for a regular hexagon. It is also called the inradius and equals half the flat-to-flat width.
The long diagonal connects two opposite vertices (= 2a). The short diagonal connects two vertices with one vertex between them, or equivalently crosses the flat-to-flat width (= √3 × a). For a = 5, the long diagonal is 10 and the short diagonal is ≈ 8.66.
When you draw lines from the centre to every vertex, you divide the hexagon into six equilateral triangles. Each triangle has all sides equal to the radius of the circumscribed circle — which must therefore equal the side length a. This holds only for the regular hexagon.
Also known as
TG we-Calculate Editorial Team. (2026). Regular Hexagon Calculator — Area, Perimeter, Diagonals [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hexagon-calculator
TG we-Calculate Editorial Team. "Regular Hexagon Calculator — Area, Perimeter, Diagonals." TG we-Calculate. 2026. https://we-calculate.com/calculator/hexagon-calculator.
TG we-Calculate Editorial Team, "Regular Hexagon Calculator — Area, Perimeter, Diagonals," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hexagon-calculator
@misc{wecalculate_hexagon_calculator, title = {Regular Hexagon Calculator — Area, Perimeter, Diagonals}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hexagon-calculator}}, year = {2026}, note = {TG we-Calculate} }
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