Square Pyramid Volume Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
The volume of a square pyramid is calculated with V = (1/3) × side² × height. For a base with a 6 cm side and a height of 4 cm, the volume is 48 cm³.
Explanation
A regular square pyramid is formed by a square base and four identical isosceles triangles meeting at an apex located exactly above the center of the base. Its volume follows the same logic as that of a cone or a cylinder: one third of the base area times the height for any pyramid or cone, versus the base area multiplied directly by the height for a cylinder or prism, whose volume does not taper to a single point. The slant height — the distance between the apex and the midpoint of a base edge, not to be confused with the lateral edge connecting the apex to a corner — is obtained by the Pythagorean theorem: it forms the hypotenuse of a right triangle whose two legs are the pyramid height and half the base side. This slant height is then used to calculate the area of each of the four triangular faces, and therefore the total lateral area and total area of the pyramid, useful for example to estimate the amount of material needed to cover its faces.
Example: base 6 cm, height 4 cm
Inputs
Base side: 6 cm. Pyramid height: 4 cm.
Calculation
Base area = 6² = 36 cm². Slant height = √(4² + 3²) = √(16+9) = √25 = 5 cm. Volume = (1/3) × 36 × 4 = 48 cm³. Lateral area = 2 × 6 × 5 = 60 cm². Total area = 36 + 60 = 96 cm².
Result
This pyramid has a volume of 48 cm³, a lateral area of 60 cm², and a total area of 96 cm².
Frequently asked questions
What is the difference between the slant height and the lateral edge?
The slant height connects the apex to the midpoint of a base edge (perpendicular to that edge) and is used to calculate the area of a triangular face. The lateral edge connects the apex to a corner of the base — a different, longer distance that does not appear in this volume or lateral area calculation.
Why divide by 3 in the volume formula?
This factor of 1/3 is a general property of all cones and pyramids: at equal base area and height, a pyramid (or cone) holds exactly one third of the volume of the corresponding prism (or cylinder), because its cross-section shrinks progressively to a single point at the apex, instead of staying constant over the whole height.
Does this formula apply to a pyramid with a rectangular (non-square) base?
The volume, yes: V = (1/3) × length × width × height works for any right pyramid with a rectangular base. The lateral area, however, becomes more complex, because the four triangular faces are then no longer identical in pairs (they split into two pairs of triangles of different sizes) — this calculator, deliberately limited to the square base, stays in the case where a single slant height is enough.