Cone Volume Calculator
Compute the volume of a cone: V = ⅓ × π × r² × h.
Calculator
Use the Cone Volume Calculator
Result
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Formula
V = ⅓ × π × r² × h
Step-by-step
- 1
Enter radius and height
The circular base plus the tip height.
- 2
Read the volume
Exactly one third of the matching cylinder.
Worked example
Example input: a: 2, b: 9
Result: 37.6991
Related tools
- Cylinder Volume
Three cones make a cylinder.
Frequently asked questions
What is the volume formula for a cone?
V = one third x pi x r-squared x h. Radius 2 with height 9 gives 37.699 cubic units, the example shown above: one third of the matching cylinder would be the same number. The water-pour classroom trick confirms the one third within a millimeter.
Why is a cone one third of a cylinder?
A cone with the same base and height packs exactly one third of the cylinder around it. Fill one with water and pour: after three pours the cylinder is full — the classic classroom test.
Where do cone calculations show up?
Ice cream cones, funnels, traffic cones, and sand or grain piles heaped by pouring — anything tapering to a point over its base share the same one-third math.
What is the volume of a cone with radius 3 and height 5?
About 47.12 cubic units. V = ⅓ × π × 3² × 5 = 15π ≈ 47.1239 — exactly one third of the same-size cylinder. Enter radius 3 and height 5 above to see it.