Cone Volume Calculator
Enter the base radius and the vertical height of a cone. The calculator returns the volume, slant height and surface areas.
Result
- Slant height
- 9.8489 cm
- Lateral surface area
- 123.7644 cm²
- Base area
- 50.2655 cm²
- Volume in liters
- 0.1508 L
- Volume in US gallons
- 0.0398 gal
Formula
- Volume = π × r² × h ÷ 3
- Slant height l = √(r² + h²)
- Lateral area = π × r × l
- Total surface area = π × r × (r + l)
How the Cone Volume Calculator works
A cone has exactly one third of the volume of a cylinder with the same base and height. Three cones of water fill the matching cylinder.
The slant height runs along the side from the base edge to the tip. It is the hypotenuse of the right triangle formed by the radius and the vertical height.
Worked example
A cone with a radius of 4 cm and a height of 9 cm has a volume of π × 16 × 9 ÷ 3 = 150.7964 cm³. The slant height is √(16 + 81) = 9.8489 cm.
Frequently asked questions
Why is the cone formula divided by 3?
A cone tapers to a point, and integrating its shrinking circular slices gives exactly one third of the enclosing cylinder. The same factor applies to pyramids.
How do I find the volume of a truncated cone?
Volume = π × h ÷ 3 × (R² + R × r + r²), where R and r are the two radii.
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