How is frustum volume calculated?

Volume = (1/3) × π × h × (R² + Rr + r²), where R and r are the two radii and h is the height between them.

Where is this shape commonly seen?

Buckets, lampshades, and some drinking cups are classic real-world examples of a cone frustum shape.

Cone Frustum Calculator - CalculatorLabs.net

Q: What is a cone frustum?

It's the shape left when the top of a cone is sliced off parallel to its base — like a bucket or lampshade shape, with two different circular radii.

Cone Frustum Calculator

A cone frustum is what's left of a cone once the pointed top is sliced off with a cut parallel to the base — think of a bucket, a lampshade, or a paper cup.

Bottom Radius (R)

Top Radius (r)

Height (h)

Instant Result

Volume -

Lateral Surface Area -

Total Surface Area -

Slant Height -

What Is a Cone Frustum Calculator?

A cone frustum is what's left of a cone once the pointed top is sliced off with a cut parallel to the base — think of a bucket, a lampshade, or a paper cup. This calculator finds the volume, lateral (side) surface area, total surface area, and slant height from the two radii and the height.

How to Use This Cone Frustum Calculator

Measure the bottom (larger) radius R and the top (smaller) radius r.
Measure the vertical height h between the two flat faces.
Enter R, r, and h into the fields above.
Click Calculate to get the volume, surface areas, and slant height.

Formula

Slant Height = √((R − r)² + h²)
Volume = (1/3) × π × h × (R² + Rr + r²)
Lateral Surface Area = π × (R + r) × slant
Total Surface Area = π(R² + r²) + Lateral Surface Area

Worked Example

A bucket has a bottom radius of 15 cm, a top radius of 20 cm, and stands 30 cm tall. Slant = √((20−15)² + 30²) ≈ 30.41 cm. Volume = (1/3)π(30)(15²+15×20+20²) ≈ 27,489 cm³. Lateral Surface Area = π(35)(30.41) ≈ 3,344 cm².