Pyramid Volume Calculator

Pyramid Geometry & Derivation

A pyramid is formed by connecting a polygonal base with an apex point. The vertical distance between the base plane and the apex is the altitude or height h.

Governing Formulas

1. General Pyramid Volume: V = (1/3) × Base Area × Height

2. Square Base Pyramid (base side a, height h):

   • Volume = (1/3) × a² × h
   • Slant Height s = √(h² + (a / 2)²)
   • Lateral Area = 2 × a × s
   • Total Surface Area = a² + 2 × a × s

3. Rectangular Base Pyramid (length l, width w, height h): Volume = (1/3) × l × w × h

4. Regular Tetrahedron (all edge lengths equal to a):

   • Volume = a³ / (6 × √2) ≈ 0.11785 × a³
   • Total Area = √3 × a² ≈ 1.732 × a²

Square pyramid – calculation example

Let’s calculate the volume of the Great Pyramid of Giza (original base side 230.3 meters and height 146.6 meters):

1. Base side length: base side = 230.3 m.
2. Vertical height: height = 146.6 m.
3. Compute base area: base area = 53,038 m².
4. The calculation results are available for you: volume = 2,592,447 m³ (approx 91.5 million cubic feet).
5. Slant height: slant height = 186.4 m.

💡 The volume of any pyramid is always exactly one-third the volume of a prism with the identical base dimensions and vertical height.