Hexagonal Prism Volume
Calculator
Results
- Volume
- 415.692193
- Base area
- 41.569219
- Lateral surface area
- 240
- Total surface area
- 323.138438
Results
| Volume | 415.692193 |
| Base area | 41.569219 |
| Lateral surface area | 240 |
| Total surface area | 323.138438 |
formula-map diagram
- Volume
- 415.692193
- Base area
- 41.569219
- Lateral surface area
- 240
- Total surface area
- 323.138438
Formula map
Formula
V = (3√3 ÷ 2) × a² × h= 415.69219381653
Note
Simplified model: these are the exact results of the stated idealised geometric formulas, assuming perfect shapes, exact inputs and consistent units. Real measurements carry error, and results such as the cyclic-quadrilateral area only hold when the figure truly satisfies the stated condition. Verify independently before relying on these figures.
More in Advanced geometry
See all →Frequently asked questions
What is the formula for the volume of a hexagonal prism?+
Volume equals the area of the regular hexagonal base times the height: V = ((3√3)/2)s² × h, where s is the hexagon's side length and h is the prism's height. The (3√3/2)s² term is simply the standard area formula for a regular hexagon.
Why does a regular hexagon's area formula include √3?+
A regular hexagon can be divided into six equilateral triangles, and an equilateral triangle's area formula inherently involves √3 (from its 60-degree angles and the Pythagorean relationship in its height). Summing the six triangles' areas produces the (3√3/2)s² hexagon formula.
Do I need the hexagon's side length or its width across to use this calculator?+
The formula needs the side length (s), the length of one of the six equal edges, not the width across the hexagon (the distance between two opposite flat sides or two opposite vertices). If you only know the width, it can be converted to side length using the hexagon's known geometric ratios.
Why are hexagonal prisms common in real-world objects like pencils and bolts?+
A regular hexagon tiles a plane with no gaps and gives a shape that's easy to grip and turn with a wrench, which is why hex nuts and pencils use this cross-section. The hexagonal prism volume formula is directly useful for calculating material usage in manufacturing these objects.
How does a hexagonal prism's volume compare to a rectangular prism circumscribing it?+
A regular hexagon fills a smaller fraction of its circumscribing rectangle than you might expect, since the hexagon's corners cut into the rectangle's area, so the hexagonal prism holds noticeably less volume than a rectangular box of the same overall width and height. This matters for packing and material efficiency comparisons.