Volume of a cylinder calculator

The volume of a cylinder is V = πr²h: the area of the circular end, πr², times the height. A cylinder is a prism with a round cross-section, and every prism has the same rule: the area of the slice times how many slices are stacked. For a radius of 3 cm and a height of 10 cm, the end has an area of π × 3² = 9π cm², and ten centimeters of those stacked up is 90π cm³, about 282.743 cm³.

The answer is in cubic units because it multiplies three lengths: r, r and h. Centimeters in give cubic centimeters out, and a cubic centimeter is a milliliter, so this cylinder holds about 282.7 mL, or 0.2827 liters. In US units, a cubic foot is 1,728 cubic inches and a US gallon is exactly 231, so a cubic foot holds about 7.48 gallons. A round tank 2 feet in radius and 5 feet tall holds 20π, about 62.83 cubic feet, which is about 470 gallons.

The mistake that matters is the diameter. Most real cylinders are measured across, and the formula wants half of that. Put the 6 cm diameter in as the radius and the answer is 360π, about 1,131 cm³. That is four times too big, because the radius is squared. If you only have the diameter, either halve it first or use V = πd²h / 4. The second slip is mixing units: a radius in inches and a height in feet give a number that is neither, so convert both to one unit before multiplying.

The formula does not care whether the cylinder leans. An oblique cylinder, like a stack of coins pushed sideways, has the same volume as the upright one with the same radius and vertical height, because every slice still has area πr². Measure the height straight up, not along the slanted side.

A hollow cylinder, such as a pipe or a tube, is the outer cylinder minus the inner one: V = π(R² - r²)h. A pipe 10 cm long with an outer radius of 3 cm and an inner radius of 2 cm contains π(9 - 4) × 10 = 50π, about 157.08 cm³ of material. For the water inside it, use the inner radius alone.

The cylinder is also the yardstick for the round solids next to it. A cone with the same base and height is exactly a third of it, 30π here. A sphere that fits snugly inside a cylinder (radius r, height 2r) is exactly two-thirds of that cylinder, which is how Archimedes found the sphere's formula. For paint, label or sheet-metal questions you want the surface area instead, which this calculator shows under the volume: 2πr² for the two ends plus 2πrh for the side.