A pyramid volume calculator computes the space inside a pyramid — a shape with a polygon base and triangular faces meeting at an apex. Enter base side and height.
A pyramid is a 3D solid with a polygonal base and triangular faces that converge at a single point called the apex. Pyramids are named by their base shape: square pyramid (Egyptian pyramids), triangular pyramid (tetrahedron), hexagonal pyramid, etc.
The Great Pyramid of Giza has a square base with sides of ~230.4 m and a height of ~146.5 m, giving it a volume of approximately 2,583,283 m³.
Pyramid volume = (1/3) × base area × height.
For a square pyramid: V = (1/3) × a² × h.
Example: Square base side 6 cm, height 10 cm: V = (1/3) × 36 × 10 = 120 cm³.
The 1/3 factor means a pyramid holds exactly one-third the volume of a prism with the same base and height.
Base 230.4 m, height 146.5 m: V = (1/3)×230.4²×146.5 ≈ 2,583,283 m³.
Base 5 cm, height 7 cm: V = (1/3)×25×7 = 58.33 cm³.
Base 8 m square, height 3 m: V = (1/3)×64×3 = 64 m³ of attic space.
Base 10 cm, height 15 cm: V = (1/3)×100×15 = 500 cm³ = 0.5 L.
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Answers to common questions about the pyramid volume calculator.
V = (1/3) × Base Area × Height. For a square pyramid: V = (1/3)a²h. For any polygon base, calculate the base area first.
A cube can be divided into exactly 3 identical pyramids. This geometric proof, known since ancient Egypt, shows that any pyramid is ⅓ the volume of a prism with the same base and height.
For a square pyramid: slant height = √(h² + (a/2)²) where h is the pyramid height and a is the base side length.
A triangular pyramid is called a tetrahedron. If all 4 faces are equilateral triangles, it is a regular tetrahedron with V = (a³√2)/12.
h = 3V / (base area). For a square pyramid: h = 3V / a². If V = 300 cm³ and a = 10 cm: h = 900/100 = 9 cm.