Math
Hexagon Calculator
Calculate side, perimeter, area, apothem, and both diagonals of a regular hexagon from any one measurement.
Regular hexagon dimensions
Pick which dimension you have. The rest are derived.
Area
259.8076
- Side (s)
- 10
- Perimeter
- 60
- Apothem
- 8.6603
- Long diagonal
- 20
- Short diagonal
- 17.3205
- Circumradius
- 10
- Inradius
- 8.6603
Area formula
A = (3 sqrt(3) / 2) s^2
Apothem formula
a = s sqrt(3) / 2
Long diagonal formula
d_long = 2s
Frequently Asked Questions about the Hexagon Calculator
What is the area formula for a regular hexagon?
A regular hexagon with side length s has area A = (3 sqrt(3) / 2) s^2, which equals about 2.598076 times s squared. For s = 10, the area is about 259.81 square units.
What is the difference between the long and short diagonal?
The long diagonal connects two opposite vertices and equals 2s, the same as the diameter of the circumscribed circle. The short diagonal connects two opposite flat sides and equals s sqrt(3), the same as twice the apothem.
How do I find the side length from the area?
Rearrange the area formula: s = sqrt(A / (3 sqrt(3) / 2)) = sqrt(A / 2.598076). For example, an area of 100 square units gives a side of about 6.204 units.
What is the apothem of a regular hexagon?
The apothem is the perpendicular distance from the center to the midpoint of any side. For a regular hexagon, apothem a = (s sqrt(3)) / 2, which is also the inradius (radius of the inscribed circle).
Why does the circumradius equal the side length?
A regular hexagon is made of six equilateral triangles meeting at the center, so the distance from the center to any vertex equals the side length s. That distance is the circumradius and the radius of the circumscribed circle.