HesapHanem

Pyramid Volume Calculator

Find the volume and surface area of a pyramid.

Result

48.00
96.00

How it is calculated

The tool models a right pyramid with a square base. Inputs are the base edge a and the vertical height h, which is the perpendicular distance from the base to the apex, not the slanted edge. Volume is V = a² × h / 3. For the surface area the engine first finds the slant height of a triangular face, s = √((a/2)² + h²), then adds the base and the four triangles: S = a² + 2 × a × s. Both inputs must be above zero. The result has no built-in unit: if a and h are in centimetres, volume is in cm³ and surface area in cm², so keep both inputs in the same unit. Results are rounded to two decimals.

Worked example

Take a pyramid with a base edge of 6 and a height of 4. The base area is 6² = 36, so the volume is 36 × 4 / 3 = 48.00. For the surface, half the base edge is 3, and the slant height is √(3² + 4²) = √25 = 5. The four triangular faces add up to 2 × 6 × 5 = 60, and the base adds 36. The total surface area is 36 + 60 = 96.00. The volume is 48.00 cubic units.

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Common mistakes

  • Entering the slant height (the sloped edge of a face) as the height. The tool needs the vertical height, otherwise volume comes out too large.
  • Forgetting the division by 3 in volume by hand. A pyramid holds exactly one third of the prism with the same base and height.
  • Mixing units, like a base in metres and a height in centimetres.
  • Using the tool for a rectangular or triangular base. The engine assumes a square base, so other base shapes need a different formula.

Sources

About this calculator

This calculator finds the volume and surface area of a square-based pyramid from its base side length and height, using volume = (1/3) × base area × height and adding up the base and the four triangular lateral faces for surface area.

It's used in geometry classes covering 3D solids, in architecture and engineering when estimating material for a pyramidal roof or structure, and in general knowledge or history contexts — like estimating the volume of stone in a monument such as the Great Pyramid of Giza from its known base and height. The 1/3 factor is the key thing students often need to check, since a pyramid holds exactly a third of the volume of a prism with the same base and height.

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Comments (1)

  • Editorial team

    The height asked for is the vertical one, from the apex straight down to the centre of the base, not the length along a sloping face. If you only measured the slant height s along a face, convert it first: h = √(s² − (a/2)²). A base edge of 10 with a slant of 13 gives h = 12. The surface figure is the base plus the four triangular faces. What are you measuring, a model, a roof or a monument?

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