Calculators

Square Bipyramid Calculator

Calculate square bipyramid volume, exterior surface area, and face slant heights from a shared square side and two perpendicular heights.

Two right square pyramids share one base, with tips on opposite sides directly above and below its center. Enter the square side and each perpendicular tip-to-base height in the same unit, from 1e-50 to 1e50. Exterior area includes eight triangular faces and excludes the internal square. All calculations stay in your browser.

Measure two square pyramids joined at their bases.

A square bipyramid has eight triangular exterior faces. Both tips must lie on the perpendicular line through the shared square center, on opposite sides. For square side a and perpendicular heights h₁ and h₂, shared internal area B = a²; volume V = a²(h₁ + h₂)/3. Face slant heights are l₁ = hypot(h₁, a/2) and l₂ = hypot(h₂, a/2). Exterior area A = 2a(l₁ + l₂), excluding the internal square. Tip-to-tip height is h₁ + h₂. For a = 6 and both heights = 4, volume is 96 cubic units, slant heights are 5 units, and exterior area is 120 square units. Unequal heights are supported. Equal heights a/√2 give a regular octahedron. Off-center tips need different surface formulas. Use consistent positive 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 two tips be?

On opposite sides of the square, directly above and below its center. Heights are perpendicular distances to the shared base plane, not slanted edges.

Is the shared square included in surface area?

No. The square is internal. Exterior surface area is the sum of the eight triangular faces: 2a times the sum of the two face slant heights.

Can the two heights differ?

Yes. Each pyramid has its own perpendicular height and face slant height. Their volumes and exterior areas are added.

When is this a regular octahedron?

When both heights equal the square side divided by √2. Equal heights alone do not guarantee equilateral faces.

What units and precision should I use?

Use one length unit for all inputs. Areas are in square units and volumes in cubic units. Positive lengths from 1e-50 to 1e50 are supported, with results rounded to 12 significant digits.