Volume Tronco de Pirâmide
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
V = (h/3)(A₁+A₂+√(A₁A₂))
About this calculator
The truncated pyramid volume calculator allows you to compute the volume of a solid geometric shape formed by a pyramid cut parallel to its base. The volume is obtained by the formula V = (h/3) × (A₁ + A₂ + √(A₁ × A₂)), where h is the height of the frustum, A₁ is the area of the larger base, and A₂ is the area of the smaller base. This tool is useful for geometry students, engineers, and professionals working with frustum-shaped structures.
It works simply: enter the height, larger base area, and smaller base area in the respective fields. The calculator automatically applies the formula and displays the volume. Ensure that the areas are in the same unit (e.g., cm²) and the height in the corresponding linear unit (cm). The result will be in cubic units (cm³).
Use this calculator in situations such as sizing reservoirs, calculating earth volumes in road cuts, or architectural projects involving truncated pyramid shapes. It avoids manual errors and speeds up calculations, especially with complex measurements.
Caution: verify that the areas are in the same unit and the height is perpendicular to the bases. Remember that the formula applies only to frustums of regular or irregular pyramids, provided the bases are parallel. For non-parallel bases, a different calculation is needed.
Frequently asked questions
What is a truncated pyramid?
It is the part of a pyramid between the base and a cross-section parallel to it, obtained by cutting the pyramid with a plane parallel to the base.
How to measure the height of the frustum?
The height is the perpendicular distance between the two parallel bases. Measure it with a ruler or tape, ensuring it is the shortest distance between the base planes.
Can I use this calculator for conical frustums?
No, the formula is specific to pyramid frustums. For conical frustums, use V = (πh/3)(R² + Rr + r²).
What if the bases are not parallel?
The standard formula does not apply. In that case, volume must be calculated by integration or numerical methods. Consult an engineer for specific solutions.