Cylinder Volume vs Cone

Cylinder Volume vs Cone is a comparison calculator that shows the relationship between the volume of a cylinder and a cone with the same base radius and height. This tool exists because the 3:1 volume ratio between cylinders and cones is one of the most fundamental relationships in geometry, and seeing it calculated with real numbers makes it concrete.

A cone holds exactly one-third the volume of a cylinder with the same base and height: V_cone = (1/3)πr²h vs V_cylinder = πr²h. This means it takes exactly 3 cones to fill 1 cylinder. This tool lets you verify this with any dimensions.

This calculator is used by math students, teachers creating demonstrations, ice cream container designers, funnel manufacturers, and anyone who needs to understand or compare cylindrical and conical volumes.

A cone tapers from a full circular base (area πr²) to a point (area 0). The cross-sectional area at height y from the base is:

A(y) = π(r(1 − y/h))² = πr²(1 − y/h)²

Integrating from 0 to h: V = ∫₀ʰ πr²(1 − y/h)² dy = πr² × h/3 = (1/3)πr²h

The (1 − y/h)² factor — the squared linear taper — is what produces the 1/3. A cylinder has A(y) = πr² (constant), so its integral gives πr²h. The ratio is 1:3.

Ice cream cones: A cone-shaped wafer holds about 1/3 the volume of a cylindrical cup of the same width and height. That's why cone-shaped cups look tall but hold less.

Funnels: A conical funnel's volume helps determine how much liquid it holds while draining. For a funnel with r = 5 cm, h = 10 cm: V = (1/3)π × 25 × 10 = 261.8 cm³.

Traffic cones, party hats, volcanic cinder cones — they all follow the same 1/3 relationship with their equivalent cylinders.