Frustum Volume Calculator

Quickly find the volume of a conical frustum (a truncated cone) by entering its height, top radius, and bottom radius. Perfect for geometry homework or practical applications.

Height (h)

Enter the perpendicular height of the frustum.

Bottom Radius (R)

Enter the radius of the larger, bottom base.

Top Radius (r)

Enter the radius of the smaller, top base.

Please enter a positive number for the height.

How it works

Quickly find the volume of a conical frustum (a truncated cone) by entering its height, top radius, and bottom radius. Perfect for geometry homework or practical applications.

The Formula

V = (1/3) * π * h * (R² + Rr + r²)
Where:
V = Volume
h = Height of the frustum
R = Radius of the bottom base
r = Radius of the top base

Worked Example

Example: A Conical Frustum
Imagine a bucket (a frustum) that is 30 cm tall. The bottom opening has a radius of 15 cm, and the top opening has a radius of 10 cm. To find its volume: Height (h) = 30 cm Bottom Radius (R) = 15 cm Top Radius (r) = 10 cm V = (1/3) * π * 30 * (15² + 15*10 + 10²) V = 10 * π * (225 + 150 + 100) V = 10 * π * 475 V ≈ 14922.56 cm³

Tips, Assumptions & Limitations

Ensure all measurements (height, radii) are in the same unit before calculating.
A frustum is essentially a cone with its top cut off by a plane parallel to its base.
This calculator specifically handles conical frustums. For pyramidal frustums, a different formula involving base areas is needed.

FAQ

A frustum is a portion of a solid (usually a cone or pyramid) that remains after cutting off the top part by a plane parallel to the base. Think of a lampshade or a bucket – these are common examples of conical frustums.

The volume of a conical frustum is calculated using the formula V = (1/3) * π * h * (R² + Rr + r²), where 'h' is the height, 'R' is the radius of the bottom base, and 'r' is the radius of the top base. This formula accounts for the tapering shape.

No, this specific calculator is designed for conical frustums only. Pyramidal frustums, which have polygonal bases, require a different formula that involves the areas of their top and bottom bases.