Cone Volume Calculator
The volume of a cone from its base radius and height — exactly one third of the cylinder around it.
A cone holds ⅓πr²h: precisely a third of the cylinder with the same base and height.
How the cone volume calculator works
A cone holds ⅓πr²h: precisely a third of the cylinder with the same base and height. Pour three cones of water into that cylinder and it fills exactly. The height must be the perpendicular one from base to tip, not the slant along the side — the slant is longer and belongs to surface area, not volume.
Formula: cone ⅓πr²h; pyramid ⅓lwh; torus 2π²Rr²; hemisphere ⅔πr³; ellipsoid ⁴⁄₃πabc
Worked examples
| Inputs | Volume | Note |
|---|---|---|
| Radius 5, height 12 | 314.1593 | 314.16 |
| An ice-cream cone, radius 2.5, height 12 cm | 78.5398 | 78.5 cm³ |
| A traffic cone, radius 15, height 50 cm | 11,780.9725 | 11,781 cm³, about 11.8 litres |
FAQFrequently asked questions
What is the volume of a cone?
⅓πr²h — a third of the cylinder with the same base and height.
Which height do I use?
The perpendicular height from the base to the tip. The slant height is longer and is only used for surface area.
How many litres is that?
Work in centimetres and divide by 1,000 — 11,781 cm³ is 11.78 litres.
Why one third?
It holds for any solid tapering to a point, whatever the base shape — Archimedes proved it for the cone and sphere together.
What if the cone leans?
The volume is unchanged, as long as the perpendicular height is the same.
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)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.