A truncated cone (frustum) is the part of a cone between its base and a cutting plane parallel to the base.
Formula
The volume of a truncated cone is V = 1/3 * π * H * (R2 + R * r + r2), where R and r are the radii of the bottom and top bases, π = 3.141592
Example
A bucket with a 10 cm bottom radius, 15 cm top radius and 30 cm height: V = 1/3 × 3.141592 × 30 × (15² + 15 × 10 + 10²) = 10π × 475 ≈ 14,922.6 cm³ ≈ 14.9 L.
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
- Which base is the bottom does not matter: the formula is symmetric in R and r.
- With r = 0 it is a cone, with r = R a cylinder.
Where it is used
- Buckets, cups, flower pots, lampshades.
- Concrete cone rings, hoppers, silos, cooling towers.
- Ponds and pools with sloped walls, filament for 3D printing.
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.