Calculators
Rhombic Pyramid Calculator
Calculate rhombic pyramid volume, surface areas, base side, inradius, and face slant height from diagonals and perpendicular height.
Measure a pyramid with a rhombus base.
Enter rhombus diagonals d₁ and d₂ and pyramid height h. The apex must be directly above the intersection of the base diagonals. Base area B = d₁d₂/2; side s = hypot(d₁/2, d₂/2); perimeter P = 4s; base inradius r = 2B/P. Each triangular face has slant height l = hypot(h, r), so lateral area = Pl/2, total surface area = Pl/2 + B, and volume = Bh/3. For diagonals 6 and 8 and height 10, B = 24, s = 5, r = 2.4, volume = 80 cubic units, and total surface area is approximately 126.839681057 square units. Equal diagonals give a square pyramid. These surface formulas do not apply to an off-center apex. Use consistent length units 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.
Where must the apex be?
Directly above the intersection of the rhombus diagonals. The surface area formula assumes this centered apex.
How is volume calculated?
Multiply half the product of the base diagonals by the perpendicular pyramid height, then divide by three.
Why do all four faces have the same slant height?
A rhombus has an incircle centered at its diagonal intersection. The perpendicular distance from that center to each base side is the same inradius r, so each face slant height is √(h² + r²).
Can I use equal diagonals?
Yes. Equal diagonals give a square base. Enter diagonals, not base side lengths. Total surface area includes the base and four triangular faces.