Hexagon Calculator
From a single side length, get the area, the perimeter, the apothem, and both diagonals — every measurement that describes a regular six-sided polygon.
One input, five answers
Enter the side length and the calculator returns the area ((3√3/2)s²), the perimeter (6s), the apothem ((√3/2)s), and the long and short diagonals at once.
Regular hexagons only
These formulas assume all six sides and all six angles are equal. An irregular six-sided shape needs a different method, and your answers come back in the same unit you typed in (squared for the area).
What is a hexagon calculator?
One side in, the whole hexagon out
A hexagon calculator turns a single measurement — the length of one side — into every number that describes a regular hexagon: the area it covers, the distance around it (perimeter), the apothem (centre to the middle of an edge), and the long and short diagonals. Because a regular hexagon is perfectly symmetric, all six sides are equal, so that one input fixes everything else. Hexagons are everywhere once you look: honeycomb cells, nuts and bolts, floor and bathroom tiles, snowflakes, and the classic board-game grid. Whether you are tiling a floor, sizing a bolt, or finishing a geometry worksheet, the side length is all you need.
Enter one side length in any unit to get the area, perimeter, apothem, and both diagonals instantly.
A handful of short formulas, all built from the side length s and the square root of 3 (≈ 1.732).
area = (3 × √3 / 2) × s²A regular hexagon is six equilateral triangles fanned out from the centre, which is where the √3 comes from. The perimeter is simply 6 × s. The apothem — the distance from the centre to the middle of any side — is (√3 / 2) × s. The long diagonal joins two opposite corners and equals 2 × s; the short diagonal joins corners one apart and equals √3 × s.
Suppose you have a regular hexagon with a side of 6.
Perimeter
6 × 6 = 36 — the distance all the way around.
Apothem and diagonals
apothem = (√3 / 2) × 6 = 5.196152, long diagonal = 2 × 6 = 12, short diagonal = √3 × 6 = 10.392305.
Area
(3 × √3 / 2) × 6² = 93.530744 square units — the surface inside.
The outputs answer different practical questions. The area (about 93.530744 square units for s = 6) is how much surface the hexagon covers — the tile you need to lay, the felt you would cut, the cross-section of a hex bolt. The perimeter (36 here) is the edging or trim that runs around it. The apothem (about 5.196152) is the centre-to-edge distance, the radius of the largest circle that fits inside; it is exactly what you measure across the flats of a nut, so a hex bolt's "width across flats" is twice the apothem. The long diagonal (12) is the width across opposite corners — the largest straight span — and is always exactly twice the side. The short diagonal (about 10.392305) joins corners one step apart. A useful rule of thumb: a regular hexagon's long diagonal equals two sides, so the corner-to-corner width is double the edge, while the flat-to-flat width is a little less (√3 × s).
The formulas are exact, but a couple of practical points are worth keeping in mind.
Regular hexagons and consistent units
These formulas describe a perfect regular hexagon — six equal sides and six equal 120° angles. An irregular hexagon (sides or angles that differ) will not match these results; split it into triangles instead. The side length is also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a side in centimetres gives an area in square centimetres and an apothem in centimetres, never a mix.