Calculate the volume and surface area of a square-based pyramid from its base side length and height.
A square pyramid has a square base and four triangular faces that meet at a single apex point directly above the center of the base. It is defined by the side length of its base (a) and its vertical height (h).
Base Area: Abase = a²
Volume: V = (1/3) × a² × h
Slant Height (apex to base edge midpoint): s = √(h² + (a/2)²)
Lateral Surface Area: Alateral = 2 × a × s
Total Surface Area: Atotal = a² + 2 × a × s
1. Enter the length of one side of the square base (a).
2. Enter the vertical height (h) from the base to the apex.
3. Choose your unit and click Calculate.
For a pyramid with a = 6 cm and h = 9 cm:
Base area = 6² = 36 cm²
Volume = (1/3) × 36 × 9 = 108 cm³
Slant height = √(81 + 9) = 9.49 cm
Lateral area = 2 × 6 × 9.49 = 113.84 cm²
Total area = 36 + 113.84 = 149.84 cm²
Volume = (1/3) × base area × height; surface area sums base plus triangular lateral faces.
The volume formula works for any pyramid base shape, as long as you use the correct base area formula.
The Great Pyramid of Giza is a classic square-based pyramid example.