Truncated Cone (Frustum) Calculator

V = πh/3(R² + Rr + r²).

How the Math Works

A truncated cone, or frustum, is a cone with its top portion cut off by a plane parallel to its base. To calculate its volume, we use the formula V = (1/3)πh(R² + Rr + r²), where h is the height, R is the radius of the larger base, and r is the radius of the smaller top base. This formula essentially takes the average of the areas of the two bases and multiplies by the height, then scales appropriately - it's like averaging the bottom and top circular areas and treating the shape as a cylinder with that average area.

Practical Applications

Use this calculator when working with any object shaped like a bucket, cup, flower pot, or truncated pyramid. Simply measure the height of the frustum and the radii (or diameters divided by 2) of both the top and bottom circular faces. Enter these three measurements and the calculator will give you the exact volume. This is especially useful for determining how much liquid a container can hold, calculating material quantities for construction projects, or finding the capacity of custom-made containers.

Day-to-Day Use

In everyday life, this calculation helps you determine how much paint, concrete, or fertilizer a circular or conical pile can hold. It's useful for sizing containers like buckets, planters, or buckets correctly, or for calculating how much ice cream fits in a cone that's been cut off. Whether you're DIY-ing a home project, cooking with unusual-shaped bowls, or just curious about volume, this tool makes geometric calculations quick and accessible without needing to remember complex formulas.

FAQ