Enter the known measurements; all results update as you type, with the formula and steps.
About this calculator
This calculator works out the volume and lateral area of a cone frustum (truncated cone) from the bottom radius, the top radius and the height. It shows the volume, the slant height, the lateral area and the volume in litres when lengths are in cm, with the formula used.
Enter the values in the same unit; results come out in that unit, squared for areas and cubed for volumes.
When to use it
- Measuring a bucket or a pot.
- Making a lampshade pattern.
- Geometry homework and exams.
- DIY, building and craft projects.
How to read the result
V = π h (R² + R r + r²) / 3; slant height = √(h² + (R − r)²).
Buckets, flower pots and lampshades are frustums.
Mistakes to avoid
- Using diameters instead of radii.
- Mixing units, such as centimetres and metres.
- Using a diameter where a radius is asked.
Formula
V = π h / 3 × (R² + R r + r²)
Worked example
R = 5, r = 3, h = 6 cm: V = 307.9 cm³, about 0.31 L.
Frequently asked questions
How do I find the volume of a bucket?
Measure the top and bottom radii and the height, in cm, then divide cm³ by 1,000 for litres.
What is the slant height?
The length of the sloping side.
Which units should I use?
Any unit, as long as every length uses the same one; areas are in that unit squared and volumes in that unit cubed.
Is a bucket a frustum?
Yes, usually.
Which unit should I use?
Any, as long as all lengths use the same one.
Is π rounded?
No, the full value of π is used.
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Results are estimates for information only. Check important figures with a professional.