Cone Volume Calculator
From a radius and a height, get the volume, the slant height, and the lateral surface area — the three numbers that describe any right circular cone.
Two inputs, three answers
Enter the base radius and the height and the calculator returns the volume ((1/3)πr²h), the slant height (√(r²+h²)), and the lateral surface (πrl) at once.
Keep units consistent
The radius and height are unit-agnostic — your answers come back in the same unit (squared for the surface, cubed for the volume), so don't mix centimetres with inches.
What is a cone volume calculator?
Radius and height in, full cone out
A cone volume calculator turns two measurements — the base radius and the vertical height — into the numbers that describe a whole right circular cone: how much it holds (volume), the length of its slanted side (slant height), and the area of its curved wall (lateral surface). Each one is fixed once you know the radius and height, because every cone shares the same constant π (pi). That makes those two inputs all you need for ice-cream cones, funnels, piles of sand or gravel, party hats, and any geometry homework where a cone shows up.
Enter the radius and height in any length unit to get the volume, slant height, and lateral surface instantly.
Three short formulas, all built from the radius, the height, and the constant π (about 3.14159).
volume = (1/3) × π × r² × hThe slant height is the diagonal side from the base rim up to the apex; by the Pythagorean theorem it is √(r² + h²). The lateral surface — the curved wall, not counting the base — is π × r × l, where l is that slant height. The volume, the space inside, is (1/3) × π × r² × h: a cone holds exactly one-third of a cylinder with the same base and height.
Suppose you have a cone with a radius of 3 and a height of 4.
Slant height
√(3² + 4²) = √(9 + 16) = √25 = 5 — the diagonal side (a classic 3-4-5 triangle).
Lateral surface
π × 3 × 5 = 47.123890 square units — the curved wall.
Volume
(1/3) × π × 3² × 4 = 37.699112 cubic units — the space inside.
The three outputs answer three different everyday questions. The volume (about 37.699112 cubic units for r = 3, h = 4) is how much the cone holds — the ice cream in a cone, the sand in a conical pile, the water a funnel can buffer. The single most useful insight is that a cone is exactly one-third of the cylinder with the same base and height: three full cones fill the matching cylinder, which is why a scoop pressed into a cone goes a long way. The slant height (5 here) is the diagonal side you would measure down the outside of the cone; because it is the hypotenuse of the radius-and-height triangle, it is always longer than the vertical height — never confuse the two when cutting a party hat or a funnel template. The lateral surface (about 47.123890 square units) is the curved wall you would paper or paint, useful for wrapping a cone or estimating material; add the base area π × r² if you need the full outside surface. π is the thread tying it all together — the same constant links the radius and height to the volume and the surface of every cone, large or small.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Right circular cones and consistent units
These formulas describe a perfect right circular cone — a circular base with the apex straight above its centre. An oblique cone (tip off to one side), a truncated cone (a frustum, with the tip cut off), or a real pile with sloping, uneven sides will differ from the computed value. The radius and height are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a radius and height in centimetres give a volume in cubic centimetres and a lateral surface in square centimetres, never a mix.