Calculators
Pentagonal Bipyramid Calculator
Calculate centered pentagonal bipyramid volume, ten-face exterior surface area, and slant heights from a regular pentagon side and two heights.
Measure two pyramids sharing a regular pentagon.
Two pyramids share a regular pentagon, with their tips on opposite sides directly above and below its center. Enter the shared side a and perpendicular heights h₁ and h₂ in the same length unit. The pentagon apothem is r = a/(2 tan(π/5)) and its area is B = 5ar/2. Volume = B(h₁ + h₂)/3. Each face slant height is ℓ = √(h² + r²); exterior surface area = 5a(ℓ₁ + ℓ₂)/2. The shared pentagon is internal and excluded from exterior area. Unequal heights are supported; these formulas require centered tips and a regular pentagon. For side 2 and both heights 3, B ≈ 6.88190960236 and volume ≈ 13.7638192047 cubic units. 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.
What measurements are required?
Enter the shared regular pentagon side and the two perpendicular tip-to-base heights in the same unit. Tips must lie directly above and below the pentagon center.
How is volume calculated?
With pentagon apothem r = a/(2 tan(π/5)), base area B = 5ar/2. Total volume is B(h₁ + h₂)/3.
Does surface area include the shared pentagon?
No. Exterior area includes ten triangular faces only. Each half has area 5a√(h² + r²)/2.
Can the two heights differ?
Yes. Each pyramid has its own positive height and face slant height. Equal heights produce a symmetric bipyramid.
What inputs and precision are supported?
Use positive lengths from 1e-50 to 1e50, including scientific notation. Results use browser floating-point arithmetic and 12 significant digits.
Are measurements uploaded?
No. Calculation, reset, and result copying run locally in your browser.