Hexagon calculator
Online calculator and formulas for a regular hexagon
This function calculates various parameters of a hexagon.
To perform the calculation, select the required parameter in the menu and enter its value. Then click the 'Calculate' button.
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Properties of a hexagon
A regular hexagon is a polygon consisting of six corners and six sides. If all six sides are the same length, we speak of an equilateral hexagon. Even if all the angles at the six corners are the same size, the hexagon is called a regular hexagon.
For a regular hexagon, the diagonals that connect opposite vertices are all the same length and all interior angles of the regular hexagon are equal and 120 degrees.
The sum of the interior angles of a regular hexagon is 720° (4 x 180°). This comes from a general formula for polygons, in which the number of vertices of the polygon is used as a variable \(n\):
\((n-2)· 180\ \ \ = (6-2) · 180 \ \ = 4 · 180 =720°\)
The value of an interior angle of 120° is therefore given by the formula:
\(\displaystyle \frac{180·(n-2)}{n} \ \ =\frac{180·(6-2)}{6} =120° \)
These two formulas apply to all regular polygons. The number of corners is used for n.
Formulas for the equilateral hexagon
Perimeter (\(\small{P}\))
\(\displaystyle P = a · 6 \)
Area (\(\small{A}\))
\(\displaystyle A =\frac{a^2 ·\sqrt{3} · 3}{2} \) \(\displaystyle ≈\frac{a^2 ·5.2}{2} \)
Short diagonal (\(\small{e}\))
\(\displaystyle e = a · \sqrt{3} \)
Long diagonal (\(\small{f}\))
\(\displaystyle f = 2 · a \)
Incircle radius (\(\small{r_i}\))
\(\displaystyle r_i=\frac{ \sqrt{3} · a}{2}\)
Edge length (\(\small{a}\))
\(\displaystyle a = \frac{f}{2} \) \(\displaystyle \ \ \ = \frac{e}{\sqrt{3}} \) \(\displaystyle \ \ \ = \frac{P}{6} \)
Height (\(\small{h}\))
Height (\(\small{h}\)) = short diagonal (\(\small{e}\))
More polygons
Triangle • Square • Pentagon • Hexagon • Heptagon • Octagon • Nonagon • Decagon • Hendecagon • Dodecagon • Hexadecagon • N-Gon • Polygon ring • Concave hexagon • Axial Symmetric Pentagon • Irregular, stretched Hexagon • Irregular, stretched Octagon • Pentagram • Hexagram • Octagram • Star of Lakshmi
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