Calculators
Triangular Bipyramid Calculator
Calculate triangular bipyramid volume, six-face exterior area, and slant heights from an equilateral base side and two perpendicular heights.
Measure two pyramids joined at an equilateral triangle.
Two pyramids share an equilateral triangle of side a, with centered tips on opposite sides. Heights h₁ and h₂ are perpendicular distances to the base plane. Shared internal area B = √3 a²/4; inradius r = a/(2√3); face slant heights l₁ = hypot(h₁, r) and l₂ = hypot(h₂, r). Volume V = B(h₁ + h₂)/3. Exterior area A = 3a(l₁ + l₂)/2 excludes the internal triangle. Tip-to-tip height is h₁ + h₂. For a = 6 and both heights = 4, volume is approximately 41.5692193817 cubic units and exterior area is 78.4601809837 square units. Unequal heights are supported. These formulas require an equilateral base and centered tips. Use consistent 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.
What shape is supported?
Two pyramids sharing an equilateral triangle with tips on opposite sides directly above and below its center. Perpendicular heights may differ.
Does surface area include the shared triangle?
No. Only the six exterior triangular faces are included. The shared base is internal.
Which formulas are used?
Two pyramids share an equilateral triangle of side a, with centered tips on opposite sides. Heights h₁ and h₂ are perpendicular distances to the base plane. Shared internal area B = √3 a²/4; inradius r = a/(2√3); face slant heights l₁ = hypot(h₁, r) and l₂ = hypot(h₂, r). Volume V = B(h₁ + h₂)/3. Exterior area A = 3a(l₁ + l₂)/2 excludes the internal triangle. Tip-to-tip height is h₁ + h₂. For a = 6 and both heights = 4, volume is approximately 41.5692193817 cubic units and exterior area is 78.4601809837 square units. Unequal heights are supported. These formulas require an equilateral base and centered tips. Use consistent 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.
Can I use slanted edges as heights?
No. Heights must be perpendicular to the shared base plane. Off-center tips require different surface formulas.