Cone Volume Calculator
Calculate a cone's volume from its radius and height, plus slant height and surface area.
Volume
37.6991
Volume = ⅓ × π × r² × h. A radius of 3 and height of 4 hold about 37.7 cubic units.
Slant height
5
Surface area
75.3982
How it works
A cone's volume is one third of a cylinder with the same base and height — a tidy result that surprises people the first time they meet it. The formula is one third times pi times radius squared times height.
From the radius and height the tool also derives the slant height using the Pythagorean theorem, then uses it to work out the full surface area including the circular base.
Enter the two measurements and everything updates together, which is handy for anything cone-shaped, from an ice cream cone to a funnel to a pile of gravel.
Frequently asked questions
How do you find the volume of a cone?
Multiply one third by pi, by the radius squared, by the height. It is exactly a third of the cylinder that would enclose it.
What is slant height?
It is the distance from the tip of the cone straight down the sloping side to the edge of the base. It equals the square root of radius squared plus height squared.
Does the surface area include the base?
Yes, the total surface area here includes both the curved side and the circular base. The curved part alone is pi times radius times slant height.