Calculate the missing side length, height, or volume of a hexagonal prism from any two values with meters, cm, inches, feet, liters, and cubic units.
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Hexagonal Volume Formula
The calculator uses the volume formula for a regular hexagonal prism. The base is a regular hexagon, meaning all six sides are equal, and the height is the perpendicular distance through the prism.
V = \frac{3\sqrt{3}}{2}a^2h- V = volume of the hexagonal prism
- a = length of one side of the regular hexagonal base
- h = height of the prism
When you enter the side length and height, the calculator finds the volume using the formula above.
a = \sqrt{\frac{2V}{3\sqrt{3}h}}- a = missing side length
- V = known volume
- h = known height
When you enter the volume and height, the calculator rearranges the formula to solve for the side length.
h = \frac{2V}{3\sqrt{3}a^2}- h = missing height
- V = known volume
- a = known side length
When you enter the volume and side length, the calculator rearranges the formula to solve for the height. Length inputs are converted to meters internally, volume inputs are converted to cubic meters internally, and the result is converted back to the unit you selected.
Common Unit Conversions for Hexagonal Volume
| Unit | Equivalent in base units | Used for |
|---|---|---|
| 1 cm | 0.01 m | Side length or height |
| 1 in | 0.0254 m | Side length or height |
| 1 ft | 0.3048 m | Side length or height |
| 1 L | 0.001 m³ | Volume |
| 1 cm³ | 0.000001 m³ | Volume |
| 1 ft³ | 0.0283168 m³ | Volume |
Regular Hexagon Base Measurements
| Measurement | Formula using side length a | Meaning |
|---|---|---|
| Base area | A = (3√3 / 2)a² | Area of the regular hexagonal face |
| Volume | V = Ah | Base area multiplied by prism height |
| Perimeter of base | P = 6a | Total distance around the hexagonal base |
Example Problems
Example 1: Find the volume
Suppose the side length is 4 cm and the height is 10 cm.
V = \frac{3\sqrt{3}}{2}(4)^2(10)V \approx 415.692194\text{ cm}^3The volume is about 415.692 cm³.
Example 2: Find the height
Suppose the volume is 1000 in³ and the side length is 8 in.
h = \frac{2(1000)}{3\sqrt{3}(8)^2}h \approx 6.014065\text{ in}The height is about 6.014 in.
FAQ
What shape does this hexagonal volume calculator assume?
It assumes a regular hexagonal prism. That means the base is a regular hexagon with six equal sides, and the height is measured straight through the prism, perpendicular to the hexagonal base.
Can this be used for an irregular hexagon?
No. The formula V = (3√3 / 2)a²h only works for a regular hexagonal base. If the hexagon is irregular, you need the actual area of the hexagonal base first, then use V = base area × height.
Why do I need to enter exactly two values?
The formula has three main variables: side length, height, and volume. If you provide any two of them, the missing one can be calculated. If more than one value is missing, there is not enough information to solve the problem.
