Square Pyramid Volume Calculator

Square Pyramid Volume

Work out the space inside a pyramid with a square base using the standard school formula. Enter the side length of the square base and the perpendicular height from the base to the apex (same units throughout). Works for revision, lesson checks, and comparison with cones and prisms.

Base side (s)

Side length of the square base; same unit as height.

Perpendicular height (h)

Vertical distance from the base to the apex.

Base side and height must be greater than zero.

How it works

Work out the space inside a pyramid with a square base using the standard school formula. Enter the side length of the square base and the perpendicular height from the base to the apex (same units throughout). Works for revision, lesson checks, and comparison with cones and prisms.

The Formula

For a pyramid with a square base of side length s and perpendicular height h (both in the same length units),

V = (1/3) × (base area) × h = (1/3) × s² × h.

The result is in cubic units (e.g. cm³ if s and h are in cm).

Worked Example

Worked example (metres)
If the base side is s = 4 m and the height is h = 9 m, the base area is 4² = 16 m². Then V = (1/3) × 16 × 9 = 48 m³. That is the same idea as stacking one third of a prism with the same base and height.

Tips, Assumptions & Limitations

Use the perpendicular height from the base to the tip, not the slant height along a face.
Keep every length in the same unit before you multiply; the answer is always in cubic units.
Compare with a cone: both use V = (1/3) × base area × height when the base is flat.

FAQ

It is V = (1/3) × s² × h, where s is the side of the square base and h is the perpendicular height. That is one third of the volume of a prism with the same square base and height.

Use the perpendicular (vertical) height from the base to the apex. Slant height appears on triangular faces but is not used directly in this volume formula unless you first convert geometry to find h.

Yes. It applies the standard pyramid rule taught in many US and UK courses. Always state your units and show s² and the factor of one third in your working.

Both are pyramids in a broad sense: V = (1/3) × (base area) × height. A cone uses a circular base (πr²); this tool uses a square base (s²).