How it works
Integration or Cavalieri’s principle shows cone volume is one-third of a cylinder with the same base and height.
Formula
V = (1/3)πr²h
How to use Volume of a Cone Calculator
- Enter base radius and perpendicular height (apex to base plane).
- Calculate cubic volume.
- Contrast with cylinder tool using identical r and h.
Worked examples
Concrete numbers and cases you can check against the tool above.
Same r and h as cylinder example
Cone volume is one-third of cylinder → ≈ 0.52 m³.
When to use Volume of a Cone Calculator
Funnels, piles of sand, and ice cream cones share this shape. The ⅓ factor is easy to forget without a calculator.
Common use cases
- Estimate gravel in a conical stockpile.
- Calculus labs verifying V = ⅓πr²h.
- Packaging for tapered containers approximated as cones.
Inputs and outputs
- Radius and height of a right cone
Privacy
This tool runs entirely in your browser. Your data never leaves your device — nothing is uploaded to our servers.
Frequently asked questions
- Does slant height work as h?
- No — h must be perpendicular to the base; slant height is the side edge.
- Truncated cone (frustum)?
- This tool is for full cones; frustums need radii of both ends.
- Same units for r and h?
- Yes — mixing cm radius with m height breaks cubic unit consistency.