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# Hexagon calculator - diagonals, area, perimeter, sides

Hexagon calculator will help you calculate the long diagonal of the hexagon, the short diagonal of the hexagon, the side length, height, area of the hexagon, the radius of the circumscribed circle and the radius of the circle inscribed in a regular hexagon.

## Longer diagonal of regular hexagon

$$P_{d}=2\cdot a=2\cdot R$$

## Shorter diagonal or height of regular hexagon

$$P_{k}=h=2\cdot r=S_a=a\cdot sqrt{3}$$

## Perimeter of regular hexagon

$$L=6\cdot a=6\cdot R$$

## Area regular hexagon

$$S=\frac{3\cdot a^2\cdot \sqrt{3}}{2}$$

## Radius of the circle inscribed in a regular hexagon

$$r={\frac {a{\sqrt {3}}}{2}}$$

Regular hexagon - information

Hexagon - a polygon with six sides and six interior angles. The sum of the angle measures in any hexagon is 720 °. Regular hexagon is a convex hexagon with all sides of equal length and all angles of equal length.

Regular hexagon has the following properties ( a , is the side length of the hexagon):
1. It is a regular polygon that can be constructed with a compass and a ruler.
2. Its every inside angle has a measure $${\displaystyle {\frac {2}{3}}\pi =120^{\circ }.\,}$$
3. The center angle of the circumscribed circle, based on the side, has a measure $${\displaystyle {\frac {\pi }{3}}=60^{\circ }.\,}$$
4. Radius of the circumscribed circle: $${\displaystyle R=a.\,}$$
5. Radius of the inscribed circle: $${\displaystyle r={\frac {a{\sqrt {3}}}{2}}.}$$
6. Area regular hexagon: $${\displaystyle S={\frac {3a^{2}{\sqrt {3}}}{2}}=a^{2}{\sqrt {6{,}75}}\approx 2{,}59808\cdot a^{2}.}$$
7. Perimeter: $${\displaystyle 6a.\,}$$
8. Longer diagonal: $${\displaystyle 2a.\,}$$
9. Shorter diagonal: $${\displaystyle a{\sqrt {3}}.}$$