Volume of a cone calculator
Enter the dimensions of a cone and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.
Volume
56.548 668m³
- Surface area
- 91.497 666
- Slant height
- 6.708 203 9
- Curved surface only
- 63.223 333
- Half angle at the apex
- 26.5651 degrees
Show the working
- Base radius = 3
- Height = 6
- Volume = pi * 3^2 * 6 / 3 = 56.5487
- Surface area = pi * 3 * (3 + hypot(3, 6)) = 91.4977
- Slant height = hypot(3, 6) = 6.7082
- Curved surface only = pi * 3 * hypot(3, 6) = 63.2233
- Half angle at the apex = 6 > 0 ? deg(atan(3/6)) : 0 = 26.5651
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
Scenarios & local history
Compare a saved scenario
Recent calculations
The formula
- volume = pi r^2 h / 3
- slant height = sqrt(r^2 + h^2)
- lateral surface = pi r l
A cone holds exactly one third of the cylinder that encloses it.
Switch the volume unit to litres or US gallons to read the capacity directly.
Related calculators
- Volume of a sphere
- Volume of a cylinder
- Volume of a rectangular box
- Volume of a cube
- Volume of a ellipsoid
- Volume of a hemisphere
- Volume of a hexagonal prism
- Volume of a hollow cylinder
- Volume of a rectangular pyramid
- Volume of a regular dodecahedron
- Volume of a regular icosahedron
- Volume of a regular octahedron
- All geometry calculators →