Find the volume of a right circular cone when you know the base radius and perpendicular height. The result is in cubic units matching the length unit you use (millimetres give mm³, inches give in³, and so on).
Half of the base diameter, in any length unit.
Perpendicular distance from the base to the tip, same unit as r.
Find the volume of a right circular cone when you know the base radius and perpendicular height. The result is in cubic units matching the length unit you use (millimetres give mm³, inches give in³, and so on).
Let r be the radius of the circular base and h the perpendicular height from the base to the apex. V = (1/3) π r² h A cone with the same base and height as a cylinder has exactly one-third of that cylinder’s volume.
If r = 4 cm and h = 9 cm, then r² = 16 and V = (1/3)π × 16 × 9 = 48π ≈ 150.8 cm³. A cylinder with the same r and h would hold about 452.4 cm³, three times as much.
Use V = (1/3)πr²h with the radius r and the perpendicular height h. Slant height is only needed for surface-area questions, not this volume formula.
For a fixed base area and height, the cone’s interior tapers linearly from base to apex, which geometrically accounts for the factor of one-third compared with a full prism or cylinder of the same base and height.
Yes. Enter r and h in the same unit; the volume appears in the matching cubic unit (ft³, m³, etc.). This is an educational model of a right circular cone, not a construction or engineering certification.
Cone Volume Calculator: The (1/3)πr²h Formula for School Maths
Cone volume questions appear constantly in UK and US school geometry: traffic cones, paper cups, and lab glassware are all modelled as right circular cones. Once you measure the base radius and the perpendicular height in the same unit, one compact formula gives the interior space in cubic units.
A right circular cone has a flat circular base of radius r and a single apex directly above the centre of that circle. The perpendicular height h is the vertical drop from apex to base, not the slant distance down the side. The volume counts three-dimensional space inside, so area at the base (πr²) is scaled by height and then reduced by the tapering shape, giving the classical factor of one-third.
Let r be the base radius and h the perpendicular height. Then V = (1/3)πr²h. If only the diameter d is known, substitute r = d/2 before squaring.
Suppose r = 5 inches and h = 12 inches. Then r² = 25 and V = (1/3)π × 25 × 12 = 100π ≈ 314.16 in³. In centimetres the same numeric idea applies: r = 5 cm and h = 12 cm would give about 314.16 cm³—always keep length units consistent.
Open the Cone Volume Calculator page, type a positive radius and a positive perpendicular height using the same length unit throughout, then read the output lines. They restate the formula, echo your inputs, give V in cubic units, and remind you that a cylinder sharing the same r and h would be three times larger—useful when you revise related solid problems.
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