A cone with its pointed tip cut off flat — a shape common in buckets, lampshades, and tapered tanks.
How it works
The formula combines both radii and the height into a single expression derived from the difference between two full-cone volumes.
What this does not include
This does not include a full, uncut cone — for that simpler shape, use this site’s general volume calculator instead.
How to use this calculator
- Enter the bottom radius, top radius, and height.
A worked example
A truncated cone (frustum) with bottom radius 5, top radius 3, height 6: volume = 307.876.
Bottom and top radius both 5, height 6 (no taper — a plain cylinder): volume = 471.239, matching the standard cylinder volume formula exactly.
What the variables mean
| Variable | Meaning |
|---|---|
| Bottom radius | Radius of the wider (or equal) end |
| Top radius | Radius of the narrower (or equal) end |
| Height | Perpendicular distance between the two flat ends |
Edge cases worth knowing
Equal top and bottom radii turn the frustum into a plain cylinder — the formula naturally reduces to the cylinder volume formula in that case, confirming it as a generalization rather than a separate rule.
A bottom radius of zero makes the shape degenerate at one end, so the calculator declines to show a result — use the full cone volume calculator instead for a shape with one pointed end.
Frequently asked questions
What happens if the top radius equals the bottom radius?
The shape becomes a plain cylinder, and this formula correctly reduces to the standard cylinder volume formula in that case.
What’s a real-world example of a truncated cone?
A bucket, a lampshade, or a traffic cone with its tip removed — any tapered container that doesn’t come to a full point.
What happens if the top radius is zero?
The shape becomes a full, uncut cone, and this formula correctly reduces to the standard cone volume formula.
