Calculators
Hexagonal Bipyramid Calculator
Calculate centered hexagonal bipyramid volume, twelve-face exterior surface area, and slant heights from a regular hexagon side and two heights.
Measure two pyramids sharing a regular hexagon.
Two pyramids share a regular hexagon with tips on opposite sides directly above and below its center. Enter side a and perpendicular heights h₁ and h₂ in the same unit. The base apothem is r = √3 a/2 and internal base area B = 3√3 a²/2. Volume V = B(h₁ + h₂)/3. Face slant heights are ℓ₁ = hypot(h₁, r) and ℓ₂ = hypot(h₂, r). Exterior area A = 3a(ℓ₁ + ℓ₂) includes twelve triangular faces and excludes the internal hexagon. For a = 2 and both heights = 3, B = 6√3, V = 12√3 ≈ 20.7846096908 cubic units, and A = 24√3 ≈ 41.5692193817 square units. Unequal heights are supported; oblique tips and irregular bases are not. Use positive lengths from 1e-50 to 1e50; scientific notation is accepted. Results use browser floating-point arithmetic rounded to 12 significant digits. All inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do I calculate hexagonal bipyramid volume?
Multiply the regular hexagon area 3√3 a²/2 by the sum of the two perpendicular heights, then divide by 3.
Does surface area include the shared hexagon?
No. The shared hexagon lies inside the solid. Exterior area includes only the twelve triangular faces: 3a(ℓ₁ + ℓ₂).
Can the two heights be different?
Yes. Each tip must be directly above or below the center on opposite sides of the base plane. Enter each perpendicular height separately.
What units should I use?
Use the same length unit for all three inputs. Volume is in cubic units and areas are in square units. The calculator does not convert units.
Is this always a solid with equilateral faces?
No. A regular hexagonal base does not make the triangular faces equilateral. Their slant heights depend on each pyramid height.
What are the input and precision limits?
Enter positive lengths from 1e-50 to 1e50. Scientific notation is supported. Results are approximate with 12 significant digits. Processing happens entirely in your browser.