Square Pyramid Calculator

Instantly find the volume and surface area of a square-based pyramid. This tool handles the Pythagorean relationship between height, slant height, and base width.

Volume (V) = (1/3)a²h Slant Height (s) = √((a/2)² + h²) Surface Area (A) = a² + 2as
For a pyramid with a 6 cm base side and 4 cm height: • Slant Height: √(3² + 4²) = 5 cm • Volume: (1/3) * 36 * 4 = 48 cm³ • Total Area: 36 + (2 * 6 * 5) = 96 cm²

What is a square pyramid?

A square pyramid is a 3D shape with a square base and four triangular faces that meet at a single point called the apex.

How is the slant height different from the actual height?

The height (h) is the vertical distance from the center of the base to the apex. The slant height (s) is the distance from the apex to the midpoint of any side of the base. They form a right triangle with half of the base side length (a/2).

What is the volume formula for a square pyramid?

The volume is one-third of the base area times the height: V = (1/3)a²h, where a is the base side length and h is the height.

How do I calculate the surface area?

The total surface area includes the base (a²) plus the four triangular sides (2as). Formula: A = a² + 2a√((a/2)² + h²).