Calculators
Octagonal Bipyramid Calculator
Calculate centered octagonal bipyramid volume, sixteen-face exterior surface area, and slant heights from a regular octagon side and two heights.
Measure two pyramids sharing a regular octagon.
Two pyramids share a regular octagon with their tips directly above and below its center on opposite sides. Enter side a and perpendicular heights h₁ and h₂ in the same unit. Apothem r = a/(2 tan(π/8)), internal base area B = 4ar = 2(1 + √2)a², and volume V = B(h₁ + h₂)/3. Face slant heights are ℓ₁ = hypot(h₁, r) and ℓ₂ = hypot(h₂, r). Exterior surface area A = 4a(ℓ₁ + ℓ₂) includes sixteen triangular faces and excludes the shared internal octagon. For a = 2 and both heights = 3, B ≈ 19.313708499 square units, V ≈ 38.627416998 cubic units, and A ≈ 61.6123148724 square units. Unequal heights are supported. These formulas require a regular base and centered tips. Use positive lengths from 1e-50 to 1e50; scientific notation is accepted. Browser floating-point results are rounded to 12 significant digits. Inputs remain in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is octagonal bipyramid volume calculated?
The shared regular octagon has area B = 2(1 + √2)a². Multiply B by the sum of the two perpendicular heights and divide by 3.
Does exterior surface area include the octagon?
No. The octagon is internal. The exterior consists of sixteen triangular faces with total area 4a(ℓ₁ + ℓ₂).
Can the two pyramid heights differ?
Yes. Enter each height separately. Both tips must lie on the perpendicular line through the octagon center on opposite sides of its plane.
Which measurements and units should I use?
Enter the regular octagon side and the two perpendicular heights in the same unit. Slant heights are calculated, not entered. Areas use square units and volume uses cubic units.
What are the input limits?
Use positive lengths from 1e-50 to 1e50. Scientific notation is accepted. Results are approximate to 12 significant digits and all processing stays in your browser.