Cone Frustum Volume Calculator
Calculate the volume of a cone frustum using bottom radius, top radius, and perpendicular height. Get accurate results with our free online volume calculator.
What Is a Cone Frustum?
A frustum is the portion of a cone that remains after the top has been sliced off by a plane parallel to its base.
Common examples include buckets, tapered cups, lampshades, hoppers, and many mechanical or architectural parts.
Volume of a Cone Frustum Formula
Formula Variables Explained:
The radius of the larger circular base.
The radius of the smaller circular top face.
The perpendicular distance between the two parallel circular faces.
A cone frustum has two parallel circular faces with different radii. Its volume is found from the height and the three radius terms R², R × r, and r².
The standard formula is V = (1/3) × π × h × (R² + R × r + r²), where R is the larger radius, r is the smaller radius, and h is the perpendicular height.
How to find the volume of a Cone Frustum?
- 1Measure the larger bottom radius R, the smaller top radius r, and the perpendicular height h.
- 2Compute the radius expression R² + R × r + r².
- 3Multiply that result by the height h.
- 4Multiply by π and divide by 3.
- 5Write the final result in cubic units such as cm³, m³, in³, or ft³.
Example: Calculate the Volume of a Cone Frustum
Example 1: Calculate cone frustum volume with radii 6 m and 3 m, height 10 m
Problem: A tapered storage hopper has a bottom radius of 6 meters, a top radius of 3 meters, and a vertical height of 10 meters. Find its volume.
- Formula: V = (1/3) × π × h × (R² + R × r + r²)
- Substitute R = 6, r = 3, h = 10
- R² + R × r + r² = 36 + 18 + 9 = 63
- V = (1/3) × π × 10 × 63 = 210π
- V ≈ 659.73 m³
Frequently Asked Questions (FAQ)
Q: What is the difference between a cone and a frustum?
A cone narrows to a single apex point, while a frustum is a truncated cone with the top removed, leaving two parallel circular faces.
Q: Can the top radius be zero?
Yes. If the top radius r = 0, the cone frustum formula simplifies to the standard cone volume formula V = (1/3) × π × R² × h.
Q: Do I use slant height or vertical height?
Use the perpendicular vertical height between the two circular faces, not the slant height along the side.