A truncated pyramid (frustum) is the part of a pyramid between its base and a cutting plane parallel to the base.
Formula
The volume of a truncated pyramid is V = 1/3 * H * (S₁ + √(S₁ * S₂) + S₂), where S₁ and S₂ are the areas of the bottom and top bases
Example
A pit with a 1 × 1 m bottom, a 2 × 2 m top and 3 m depth: S₁ = 4 m², S₂ = 1 m², V = 1/3 × 3 × (4 + √(4 × 1) + 1) = 7 m³.
Units
The volume comes out in cubic units of the dimensions you enter: centimetres give cm³, metres give m³. Use the same unit for all dimensions. Conversion: 1 L = 1 dm³ = 1000 cm³, 1 m³ = 1000 L, 1 mL = 1 cm³.
Good to know
- The bases must be similar (same shape, different size), otherwise the formula is inexact.
- With S₂ = 0 it is a pyramid, with S₁ = S₂ a prism.
Where it is used
- Excavations and trenches with slopes, ponds, spoil heaps and embankments.
- Spread footings and piers, hoppers and chutes.
- Boxes and containers with sloped sides, planters, podiums.
How to use
Enter the dimensions (decimals with a dot or comma) and press “Calculate”. You get the formula with your numbers and the result with a copy button, and the 3D model is redrawn to your dimensions.