About this calculator
The Hexagon Calculator finds area, perimeter, short diagonal, long diagonal, and apothem for a regular hexagon. It is useful for geometry revision, tiling patterns, honeycomb designs, board games, and regular polygon work.
hexagon calculator method
A regular hexagon has six equal sides and can be split into six equilateral triangles. That structure gives the standard formulas for area, diagonals, and apothem.
- Area = (3sqrt(3) / 2) x s^2
- Perimeter = 6s
- Short diagonal = s sqrt(3)
- Long diagonal = 2s
- Apothem = s sqrt(3) / 2
How to use the hexagon calculator
- Enter the side length.
- Multiply by 6 for perimeter.
- Use the area formula for a regular hexagon.
- Calculate short and long diagonals.
- Calculate the apothem.
- Round curved or square-root results only at the end.
Worked examples
Side length 6
Input: s = 6
Calculation: Perimeter = 6 x 6; area = (3sqrt(3)/2) x 36
Result: Perimeter 36, area about 93.53
Long diagonal
Input: s = 8
Calculation: Long diagonal = 2s
Result: 16 units
Regular hexagons only
These formulas apply to regular hexagons, where every side is the same length and every interior angle is equal.
Practical geometry checks
- Use one unit system
- Keep all lengths in the same unit before calculating. Mixing centimetres, metres, inches, or feet in the same formula will produce misleading results.
- Perimeter vs area
- Perimeter is a distance around the outside. Area is the amount of flat space inside a shape. Surface area is the total outside covering of a 3D shape.
- Rounded answers
- Pi, square roots, and trigonometric values are often irrational, so decimal answers are approximations. Keep extra decimal places until the final result.
Edge cases
- Zero or negative dimensions do not describe a real physical shape.
- Regular polygon formulas assume all sides and angles are equal.
- Circle and ellipse formulas use pi, so most decimal answers are rounded.
- A trapezoid/trapezium perimeter needs all four side lengths, not just the parallel sides and height.
Limitations
This calculator is for educational and planning use. For construction, manufacturing, surveying, engineering, or safety-critical work, confirm dimensions, tolerances, and rounding rules with the appropriate professional method or specification.
Frequently asked questions
What units should I enter?
Use any length unit you like, but keep every length in the same unit. If you enter metres, area is in square metres and surface area is also in square metres.
Why are some answers approximate?
Calculations involving pi, square roots, or curved shapes often produce irrational numbers. The calculator rounds the displayed decimal result.
What is the difference between area and surface area?
Area measures a flat 2D region. Surface area measures the total outside area of a 3D object.
Can I use these calculators for homework?
Yes. They are useful for checking answers and understanding formulas, but you should still show the working required by your class or exam.
Do regular polygon formulas work for irregular polygons?
No. Regular polygon formulas assume equal sides and equal angles. Irregular polygons usually need to be split into simpler shapes.
Related calculators
- Polygon Calculator
- Area Calculator
- Perimeter Calculator