Regular Hexagon Area Calculator
Compute the area of a regular hexagon from a single side length measurement. Useful for tile layouts, honeycomb design, board game hex grids, and any engineering application involving six-sided symmetry.
About this calculator
A regular hexagon has six equal sides and six equal interior angles of 120°. Because it can be divided into exactly six equilateral triangles, its area follows directly from the equilateral triangle area formula scaled by six. The result is: Area = (3√3 / 2) × s², where s is the length of one side. The factor 3√3/2 ≈ 2.598 accounts for the geometry of the six equilateral triangles packed inside the hexagon. This formula only applies to regular (equilateral and equiangular) hexagons; irregular hexagons require decomposition into simpler shapes. Regular hexagons are the most area-efficient polygon for tiling a flat plane, which is why honeycombs and many engineering grids use them.
How to use
Suppose you are designing hexagonal floor tiles with a side length of 4 cm each and need to know how much area each tile covers. Using the formula: Area = (3√3 / 2) × 4² = (3 × 1.7321 / 2) × 16 = 2.598 × 16 ≈ 41.57 cm². Enter 4 in the Side Length field. The calculator returns approximately 41.57 square units per tile, so you can divide your total floor area by 41.57 to find out how many tiles to order.
Frequently asked questions
How do I find the area of a regular hexagon if I know the apothem instead of the side length?
The apothem (a) is the perpendicular distance from the centre to the midpoint of any side. It relates to the side length by a = (√3 / 2) × s, so s = 2a / √3. Substituting into the main formula gives Area = (3√3 / 2) × (2a/√3)² = 2√3 × a². Alternatively, the area can be computed directly as Area = 3 × a × s, using both the apothem and side length. Knowing this is useful when measurements are taken from centre to wall rather than corner to corner.
Why does the regular hexagon area formula contain the square root of 3?
The √3 comes from the geometry of equilateral triangles. A regular hexagon is made of six identical equilateral triangles, and each equilateral triangle with side s has a height of (√3/2)s. That height feeds directly into each triangle's area — (1/2) × base × height = (√3/4)s² — and multiplying by six gives (3√3/2)s². So √3 is intrinsic to any shape built from 60° angles, and it cannot be avoided in exact hexagon area calculations.
What is the difference between a regular hexagon and an irregular hexagon?
A regular hexagon has all six sides equal in length and all six interior angles equal to exactly 120°, giving it perfect six-fold rotational symmetry. An irregular hexagon has sides or angles that differ, and no single formula covers all cases. For irregular hexagons, you must break the shape into triangles or use the shoelace formula with coordinate geometry. Most practical applications — tiles, nuts, bolts, hex grids — use regular hexagons because their symmetry simplifies both calculation and manufacturing.