BYTETOOLS

Hexagon Calculator

Solve a regular hexagon from any single measurement — side, area, perimeter, apothem, circumradius or either diagonal — and see how many tile a given area.

10
Side
259.8076
Area
60
Perimeter
8.6603
Apothem

Every measurement

  • Side s = 10
  • Perimeter = 6s = 60
  • Area = (3√3/2)s² = 259.807621
  • Apothem (inradius) = (√3/2)s = 8.660254
  • Circumradius = s = 10
  • Short diagonal (across the flats) = √3·s = 17.320508
  • Long diagonal (corner to corner) = 2s = 20
  • Interior angle = 120°, exterior angle = 60°, interior angles sum to 720°

Shape

Solid line: circumradius (equal to the side). Dashed line: apothem, the perpendicular distance to a side.

How many hexagons tile an area?

Enter an area above to see how many hexagons of this size it takes to fill it.

What is the Hexagon Calculator?

The ByteTools Hexagon Calculator works backwards from whichever measurement you happen to have. Give it a side, a perimeter, an area, an apothem, a circumradius, the short diagonal across the flats or the long corner-to-corner diagonal, and it recovers the side length first, then reports every other measurement.

  • Solves from side, perimeter, area, apothem, circumradius or either diagonal
  • Exact regular-hexagon relationships, including area (3√3/2)s²
  • Short and long diagonals reported separately, since they differ by √3 versus 2
  • Diagram marking the circumradius against the apothem
  • Tiling count for any area you want to cover
  • Runs entirely in your browser — private and offline-friendly

How to use the Hexagon Calculator

  1. 1

    Pick which measurement you already know from the dropdown.

  2. 2

    Type its value in the field beside it.

  3. 3

    Read the side, area, perimeter and apothem in the summary tiles.

  4. 4

    Check the full measurement list for both diagonals, the circumradius and the angles.

  5. 5

    Enter an area to cover at the bottom to see how many hexagons fill it.

About the Hexagon Calculator

The ByteTools Hexagon Calculator works backwards from whichever measurement you happen to have. Give it a side, a perimeter, an area, an apothem, a circumradius, the short diagonal across the flats or the long corner-to-corner diagonal, and it recovers the side length first, then reports every other measurement.

The relationships used are the exact ones for a regular hexagon: area (3√3/2)s², apothem (√3/2)s, circumradius equal to the side, short diagonal √3·s and long diagonal 2s, with interior angles of 120°. A drawing marks the circumradius and the apothem so the two are never confused.

There is also a tiling helper: enter an area to cover and the tool divides by the hexagon area to say how many tiles it takes, since regular hexagons fill a plane with no gaps. Everything is calculated in your browser, with nothing uploaded, so it works offline.

Frequently asked questions

What is the area of a regular hexagon?

It is (3√3/2) times the side squared, roughly 2.598s². A hexagon with 10-unit sides has an area of about 259.81 square units. The formula comes from splitting the hexagon into six equilateral triangles of side s.

What is the apothem of a hexagon?

The apothem is the perpendicular distance from the center to the middle of a side, equal to (√3/2)s, or about 0.866 times the side. It is the inradius of the hexagon, so it is also the radius of the largest circle that fits inside.

Why does a hexagon have two different diagonals?

The short diagonal connects vertices two apart and measures √3·s, about 1.732 times the side. The long diagonal passes through the center to the opposite vertex and measures exactly 2s. Suppliers usually quote hex bar stock by the short diagonal, the across-flats size.

Is the circumradius of a hexagon the same as its side?

Yes, and that is unique to the hexagon among regular polygons. Because the six triangles formed with the center are equilateral, the distance from the center to any corner equals the side length exactly.

How many hexagons do I need to cover an area?

Divide your total area by the area of one hexagon and round up — regular hexagons tessellate perfectly, so no area is wasted in the middle of the field. Add a cutting allowance for the edges, where hexagons have to be trimmed to meet a straight boundary.

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