A frustum is a cone with its tip cut off by a plane parallel to the base. Enter the bottom radius, the top radius and the vertical height to get the volume, the slant height, the side area and the total surface area. The page also covers a square frustum.
24 solids in six groups. Enter the dimensions and the model updates instantly.
Prices are in whatever currency you use. The material price needs a material or density above.
Export the shape at your real size for 3D printing, or print a flat net you can cut out and fold into a paper model.
Enter r₁ for the bottom and r₂ for the top, then the straight height between them. Use Diameter mode if you measured across the circles. For a square base, pick Square frustum from the shape list.
This page is the cone frustum view of the full 3D Shape Calculator, which covers 24 solids. Every shape button is still available, so you can compare solids without leaving the page.
In every formula, r is a radius, h is a height or depth, and all measurements must use the same unit. The result is in that unit cubed for volume and squared for area.
A bucket has a bottom radius of 10 cm, a top radius of 14 cm and a height of 25 cm. Its volume is (π × 25 / 3) × (100 + 140 + 196) ≈ 11,414 cm³, about 11.4 litres. The working capacity is a little less because a bucket is never filled to the brim.
Frustums describe buckets, flower pots, lampshades, paper cups, speaker cones, cooling towers, concrete footings and sand castles. Knowing the volume lets you size a pot for a plant or order the right amount of concrete for a tapered footing.
What is a frustum? A frustum is the part of a cone or pyramid that remains between the base and a plane parallel to it, after the top has been cut off.
Is the height the slanted side? No. Use the straight vertical distance between the two circular faces. The slant height is calculated for you and used for the side area.
How do I find the frustum volume from diameters? Switch the input to Diameter and type the bottom and top diameters. The calculator halves them for you before applying the formula.
How does a frustum compare with a cylinder? If both radii are equal the frustum becomes a cylinder and the formula reduces to π × r² × h. If the top radius is zero it becomes a cone.