Calculators
Rhombic Bipyramid Calculator
Calculate rhombic bipyramid volume, exterior surface area, and two face slant heights from shared rhombus diagonals and perpendicular heights.
Measure two pyramids joined at a rhombus base.
Two pyramids share a rhombus base with tips on opposite sides, on the perpendicular line through the diagonal intersection. Enter diagonals d₁ and d₂ and positive heights h₁ and h₂ in one length unit. Internal base area B = d₁d₂/2; side s = hypot(d₁/2, d₂/2); perimeter P = 4s; inradius r = 2B/P. Volume V = B(h₁ + h₂)/3. Face slant heights are l₁ = hypot(h₁, r) and l₂ = hypot(h₂, r). Exterior surface area A = P(l₁ + l₂)/2 excludes the internal rhombus and includes all eight triangular faces. Tip-to-tip height is h₁ + h₂. For diagonals 6 and 8 and both heights 3, B = 24, s = 5, r = 2.4, V = 48 cubic units, and A ≈ 76.8374908492 square units. Unequal heights are supported. Equal diagonals give a square bipyramid. Off-center tips require different surface formulas. Use lengths from 1e-50 to 1e50; scientific notation is accepted. Results use browser floating-point arithmetic 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.
Where must the tips lie?
On opposite sides of the shared base, directly above and below the intersection of the rhombus diagonals. Off-center tips need different surface area formulas.
Does exterior surface area include the rhombus?
No. The shared rhombus lies inside the solid. Exterior area includes only the eight triangular faces.
Can the heights differ?
Yes. Enter a positive perpendicular height for each pyramid. Volume is half the product of the diagonals times the sum of the heights, divided by three.
What happens when the diagonals are equal?
The shared base is a square, giving a square bipyramid. The diagonal inputs are not side lengths.
Which units and input ranges are supported?
Use one consistent length unit with values from 1e-50 to 1e50. Scientific notation is accepted. Areas use squared units and volume uses cubed units. Calculations run entirely in your browser.