Frustum Volume Calculator
The volume of a frustum — a cone with the top cut off, the shape of a bucket, a plant pot or a lampshade.
A frustum is what is left when a cone is sliced parallel to its base.
How the frustum volume calculator works
A frustum is what is left when a cone is sliced parallel to its base. Its volume is ⅓πh(R² + Rr + r²), which looks odd until you see it as the big cone minus the small one that was removed. The middle term Rr is what stops you being able to just average the two ends — a common shortcut that gives the wrong answer.
Formula: cone ⅓πr²h; pyramid ⅓lwh; torus 2π²Rr²; hemisphere ⅔πr³; ellipsoid ⁴⁄₃πabc
Worked examples
| Inputs | Volume | Note |
|---|---|---|
| Radii 8 and 5, height 12 | 1,621.0618 | 1,621.1 — that is 516π |
| A bucket, 18 cm top, 15 cm bottom, 30 cm deep | 25,729.6438 | about 25.7 litres |
| A plant pot, 14 and 10, 20 deep | 9,131.5626 | 9,131 cm³, a little over 9 litres |
FAQFrequently asked questions
What is a frustum?
A cone or pyramid with the top sliced off parallel to the base — a bucket, a plant pot, a lampshade.
What is the formula?
⅓πh(R² + Rr + r²), where R and r are the two radii.
Why not just average the two ends?
Because area grows with the square of the radius, so averaging the radii underestimates. The Rr term is the correction.
How do I get litres from centimetres?
Divide cubic centimetres by 1,000.
Does it work upside down?
Yes — enter the wider radius as the bottom whichever way up it sits.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.