Frustum Volume Calculator
A frustum (also called a truncated cone) is a cone with its top cut off by a plane parallel to the base, resulting in a solid shape with two parallel circular bases of different sizes. The volume formula for a frustum accounts for both base areas and their interaction: V = (π * h / 3) * (r1² + r1*r2 + r2²), where r1 is the radius of the top base, r2 is the radius of the bottom base, and h is the perpendicular height between them. The slant height is the distance along the sloped surface from one base to the other, calculated as l = sqrt(h² + (r2 - r1)²). The lateral surface area (curved side only) is π * l * (r1 + r2). The total surface area includes both bases and the lateral surface. This calculator computes the volume, slant height, and both lateral and total surface areas from the two radii and height.
Frustum volume formulas
Volume = (π * h / 3) * (r1² + r1*r2 + r2²)
Slant Height = √(h² + (r2 - r1)²)
Lateral Surface Area = π * l * (r1 + r2)
Total Surface Area = π*r1² + π*r2² + π*l*(r1 + r2)
Reference volumes
| Top Radius | Bottom Radius | Height | Volume |
|---|---|---|---|
| 2 cm | 4 cm | 5 cm | 113.10 cm³ |
| 3 cm | 5 cm | 10 cm | 471.24 cm³ |
| 5 cm | 10 cm | 12 cm | 2,199.11 cm³ |
| 1 m | 2 m | 3 m | 6.60 m³ |
| 2 m | 3.5 m | 8 m | 132.08 m³ |
Frustum volume calculator: frequently asked questions
What is a frustum?
A frustum is a cone with its top cut off by a plane parallel to the base. It has two parallel circular bases of different sizes connected by a curved side surface. A frustum can also refer to a pyramid with its top cut off, but usually refers to a truncated cone.
What is the formula for frustum volume?
The volume of a frustum is V = (π * h / 3) * (r1² + r1*r2 + r2²), where r1 is the top radius, r2 is the bottom radius, and h is the height between the two bases. This formula accounts for both circular base areas and their interaction.
What is the slant height of a frustum?
Slant height is the distance along the sloped surface from the edge of the top circle to the edge of the bottom circle. It is calculated using the Pythagorean theorem: l = sqrt(h² + (r2 - r1)²).
How do I find the lateral surface area?
The lateral (side) surface area of a frustum is π * l * (r1 + r2), where l is the slant height and r1 and r2 are the two radii.
What are examples of frustums?
Common frustums include traffic cones, buckets, cups, lampshades, cooling towers, exhaust pipes, and truncated rooflines on buildings.
Official sources
- Khan Academy: Volume and surface area of solids.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.