Hexagon Calculator
Type the side length of a regular hexagon. The calculator returns the area, perimeter, apothem, long diagonal, width across the flats and circumradius — all from one input.
Area
259.8076 square units
- Perimeter (6s)
- 60
- Apothem (√3/2 · s) — inradius
- 8.66
- Long diagonal (2s) — vertex to opposite vertex
- 20
- Width across flats (√3 · s) — opposite parallel sides
- 17.32
- Circumradius (R = s) — centre to vertex
- 10
A regular hexagon with side s has six equilateral triangles meeting at the centre. Area A = (3√3/2)·s². Perimeter P = 6s. The apothem (distance from centre to side midpoint) is a = (√3/2)·s. The long diagonal joins opposite vertices and equals 2s; the short diagonal (between vertices separated by one) equals √3·s. The circumradius — centre to vertex — is simply s.
How to use this calculator
Enter the side length of your hexagon — any unit will do (cm, m, in, ft). The calculator immediately returns the area in square units, the perimeter, the apothem (centre-to-side distance), both diagonals and the circumradius. All outputs use the same unit as the input.
How the calculation works
A regular hexagon is six identical equilateral triangles meeting at the centre, so its geometry collapses to a single number — the side length s. Area A = (3√3/2)·s² ≈ 2.598·s², the sum of the six triangles each with area (√3/4)·s². Perimeter P = 6s. The apothem (perpendicular distance from centre to the midpoint of a side) is a = (√3/2)·s ≈ 0.866·s. The long diagonal — joining opposite vertices — is exactly 2s, and the width across the flats (the perpendicular gap between two parallel sides) is √3·s ≈ 1.732·s. The circumradius — centre to any vertex — is the side length itself: R = s.
Worked example
Take a hexagon with side s = 10. Perimeter P = 6·10 = 60. Area A = (3√3/2)·100 = 150√3 ≈ 259.808 square units. Apothem a = 5√3 ≈ 8.660. Long diagonal = 2·10 = 20. Width across flats = 10√3 ≈ 17.321. Circumradius R = 10. Whether the unit is centimetres, metres or inches, the numbers and ratios stay the same.
Frequently asked questions
What does "regular" hexagon mean?
A regular hexagon has six sides of equal length and six interior angles all equal to 120°. Most hexagons people care about — honeycomb cells, nuts and bolts, stop signs in some countries, gaming tiles — are regular, so a single side length s defines the whole shape.
Why is the area formula (3√3/2)·s²?
A regular hexagon is six congruent equilateral triangles meeting at the centre. Each triangle has area (√3/4)·s², so the hexagon has area 6 · (√3/4)·s² = (3√3/2)·s². The √3 appears because the height of an equilateral triangle with side s is (√3/2)·s.
What is the apothem, and why does it matter?
The apothem is the perpendicular distance from the centre of the hexagon to the midpoint of any side — it is the inradius (radius of the largest circle that fits inside the hexagon). For a regular hexagon, a = (√3/2)·s. It is useful any time you fit a hexagon inside a circle, lay out hex tiles or work out the size of a nut by its "across the flats" measurement, which equals 2·a.
What's the difference between the long diagonal and the width across the flats?
The long diagonal joins two opposite vertices through the centre and equals 2s — the same as the diameter of the circle that passes through all six vertices. The width across the flats is the perpendicular distance between two opposite parallel sides and equals √3·s ≈ 1.732·s. So the long diagonal is always a little longer than the across-flats width (by a factor of 2/√3 ≈ 1.155).
Why does R = s for a hexagon?
The circumradius R is the distance from the centre to any vertex. In a regular hexagon, joining the centre to two adjacent vertices forms an equilateral triangle — all three sides equal — because the central angle is exactly 360°/6 = 60°. So R = s. This is unique to the hexagon among regular polygons.
Can I use any units?
Yes. The formulas are scale-invariant: enter the side in centimetres and you get a perimeter in cm, an area in cm², an apothem in cm and so on. Centimetres, metres, inches and feet all work — just keep track of your unit, especially for area which is the squared unit.