Hexagonal Prism Volume Calculator
Calculate the volume of a hexagonal prism by entering its side length and height.
Formula:
Volume=3√32× a² × h
Where:
- a = Side length of the hexagonal base
- h = Height (length) of the prism
Unit of Measurement:
cm
The side length of the hexagonal base
cm
The height of the prism
Result
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About Hexagonal Prism Volume
A hexagonal prism is a three-dimensional solid with two congruent hexagonal bases and six rectangular side faces:contentReference[oaicite:0][index:0]:contentReference[oaicite:1][index:1]. It has 8 faces, 18 edges, and 12 vertices. The volume of a prism is the product of the base area and the height. For a regular hexagonal base with side length a and height h, the base area is (3√3/2)×a²:contentReference[oaicite:2][index:2], giving the volume formula V = (3√3/2) × a² × h.
For example, if the side length is 4 cm and the prism height is 8 cm: base area = (3√3/2)×4² ≈ 41.57 cm², so volume ≈ 41.57 × 8 = 332.56 cm³.
How to Calculate Hexagonal Prism Volume
Step 1: Measure the Side Length
Measure the side length of the hexagonal base (the distance of one edge of the hexagon). This is the value a in the formula.
Step 2: Measure the Height
Measure the height h of the prism, which is the perpendicular distance between the two hexagonal bases.
Step 3: Apply the Formula
Use the formula V = (3√3/2) × a² × h. First compute a², then multiply by (3√3/2), and then by the height h. For example, with a = 4 and h = 8: V = (3√3/2)×4²×8.
Practical Applications
Engineering & Construction
Hexagonal prism shapes are used in building designs and structural elements, such as columns and supports:contentReference[oaicite:3][index:3].
Hardware & Manufacturing
Many nuts and bolts have a hexagonal prism shape. Understanding hex prism volume helps in designing these fasteners:contentReference[oaicite:4][index:4].
Stationery & Crafts
Pencils and wooden rods often have a hexagonal cross-section. Artists and designers also use hexagonal prisms for packaging and decorative projects:contentReference[oaicite:5][index:5].
Packaging
Hexagonal boxes and containers (like gift boxes or canisters) take advantage of this shape for efficient packing and an attractive appearance.
Tips and Common Mistakes
- Using diameter instead of side: Ensure you use the side length a in the formula, not the diameter of the hexagon.
- Regular vs Irregular: The formula V = (3√3/2)a²h assumes a regular hexagonal base. For an irregular base, calculate the actual base area first.
- Unit consistency: Make sure the side length and height use the same units (e.g. both in cm) before calculating volume.
- Height measurement: The height h must be the perpendicular distance between the bases, not a slanted edge.
Frequently Asked Questions
A hexagonal prism is a 3D shape with two parallel hexagonal bases and six rectangular lateral faces. It has 8 faces, 18 edges, and 12 vertices:contentReference[oaicite:6][index:6]:contentReference[oaicite:7][index:7].
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.
Need Help?
Check out our guide on how to use this calculator properly and understand the concepts behind it.
Learn how to calculate volume