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Hexagon Calculator

Solve a regular hexagon — six equal sides and six 120° corners — from any one measurement: its side, perimeter, apothem, width across flats, width across corners or area. You get all the others back.

Quick examples
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Area93.53 in²
Side length
6 in
Perimeter
36 in
Apothem
5.1962 in
Width across corners (long diagonal)
12 in
Width across flats (short diagonal)
10.3923 in

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    Results you calculate here are kept on this device so you can come back to them.

      Formula

      Area = (3 × √3 ÷ 2) × side² ≈ 2.598 × side²
      Perimeter = 6 × side
      Apothem = (√3 ÷ 2) × side ≈ 0.866 × side
      Width across corners = 2 × side
      Width across flats = √3 × side ≈ 1.732 × side

      How to use it

      1. Choose which measurement you know.
      2. Enter its value and unit.
      3. Read the area, side, perimeter, apothem and both widths.

      Worked examples

      A 6-inch side: 93.53 in² (0.0603 m²), 36 in around, 12 in corner to corner

      Area
      93.53 in²
      Perimeter
      36 in
      Apothem
      5.1962 in
      Width across corners (long diagonal)
      12 in
      Width across flats (short diagonal)
      10.3923 in

      An apothem of 5 m

      Side length
      5.7735 m
      Area
      86.6 m²
      Perimeter
      34.64 m
      Width across corners (long diagonal)
      11.547 m
      Width across flats (short diagonal)
      10 m

      A hexagon of 100 in²: each side is 6.204 in (0.1576 m)

      Side length
      6.204 in

      Flats and corners

      A hexagon has two widths. Across flats — from the middle of one side to the middle of the opposite side — is the size a wrench or socket is named for, and equals twice the apothem. Across corners is the longest diagonal and equals exactly two side lengths.

      Six triangles

      A regular hexagon is six equilateral triangles meeting at the center. That is why the distance from the center to a corner equals the side length, and why the area is six times the area of one of those triangles.

      Questions people ask

      What is the area of a hexagon with 6-inch sides?

      2.598 × 6² = 93.53 square inches.

      How do I find the side of a hexagon from its width across flats?

      Divide by √3 (about 1.732). A hexagon 10 units across flats has sides of 5.77.

      What are the interior angles of a regular hexagon?

      Each is 120°, and the six add up to 720°.

      Related calculators

      Area CalculatorArea of a rectangle, triangle, circle, trapezoid and more.Perimeter CalculatorDistance around a rectangle, triangle, circle, polygon or ellipse.Triangle Area CalculatorArea from base and height, three sides, or two sides and an angle.Circle CalculatorRadius, diameter, circumference and area from any one of them.Trapezoid Area CalculatorArea of a trapezoid from its two parallel sides and height.