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A frustum is what's left of a cone after slicing off the top with a cut parallel to the base — think of a bucket, lampshade, or traffic cone with the tip removed — and its volume formula accounts for both radii, not just one.
This calculator finds a frustum's volume, slant height, and lateral surface area from its two radii and height.
How it works
Enter the top radius, bottom radius, and height. The calculator applies the frustum volume formula, then separately finds the slant height (using the Pythagorean theorem on the height and radius difference) to compute the lateral surface area.
- Enter top radius.
- Enter bottom radius.
- Enter height.
- Click Calculate to see your results.
Examples
Top radius 3, bottom radius 6, height 10
This frustum has a volume of about 659.73, a slant height of about 10.44, and a lateral surface area of about 295.19.
Who should use it
- Calculating the volume of a bucket, lampshade, or traffic-cone-shaped object.
- Checking frustum geometry coursework.
Industry applications
- Manufacturing and industrial design (buckets, funnels, lampshades)
- Geometry education
Advantages
- Calculates volume, slant height, and lateral surface area together.
- Correctly handles the full-cone special case (top radius = 0).
Limitations
- Only handles a right circular frustum (symmetric, straight axis) — oblique or non-circular frustums need a different approach.
Common mistakes to avoid
- Confusing slant height (the sloped distance) with vertical height (the straight-up distance) — they're only equal when the top and bottom radii are the same (i.e., a cylinder, not a frustum).
- Setting the top radius equal to or larger than the bottom radius when a genuine frustum (narrowing shape) was intended.
Best practices
- For a full cone (no flat top), set the top radius to 0 — the formula handles this correctly as a special case.
Tips
- Setting the top and bottom radii equal turns the frustum formula into the standard cylinder volume formula (πr²h) — a useful sanity check for the formula's correctness.