Cylinder Volume Calculator

How to Calculate the Volume of a Cylinder?

The volume of a cylinder equals pi times the radius squared times the height: V = pi r² h. A cylinder with a radius of 5 cm and a height of 10 cm has a volume of pi times 25 times 10 = 785.4 cubic centimeters. If you know the diameter instead of the radius, divide it by 2 first. Enter your measurements in the calculator above to find the volume instantly along with the surface area and lateral area.

Understanding the Cylinder Formula

The formula V = pi r² h makes intuitive sense when you think of a cylinder as a stack of circular discs. Each disc has an area of pi r² (the area of a circle). Stacking h units of these discs gives the total volume. This is the same principle behind integral calculus, where you sum infinitely thin slices to find volume. The formula works for any unit of measurement as long as radius and height use the same unit. The result is in cubic units: cubic centimeters (cm³), cubic inches (in³), cubic feet (ft³), or liters (1 liter = 1,000 cm³).

Surface Area of a Cylinder

The total surface area includes two circular ends plus the curved lateral surface. Total surface area = 2 pi r² + 2 pi r h = 2 pi r (r + h). The lateral (side) surface area alone is 2 pi r h. For a cylinder with radius 5 and height 10: lateral area = 2 times pi times 5 times 10 = 314.2 square units. Total surface area = 2 times pi times 5 times 15 = 471.2 square units. Lateral area is what you need when wrapping a label around a can or calculating insulation for a pipe.

Cylinder Volume in Everyday Life

Drinking glasses, water bottles, cans, pipes, tanks, silos, and swimming pools are all cylindrical or close to it. A standard 12-ounce soda can has a radius of approximately 3.3 cm and height of 12.2 cm, giving a volume of about 417 cm³ (417 ml). A 55-gallon steel drum has an interior volume of approximately 208 liters. Water towers, fuel tanks, and industrial storage vessels are sized using the cylinder volume formula. Knowing the volume helps you calculate capacity, weight of contents, and fill times.

How to Find the Radius or Height from Volume?

Rearranging the formula: radius = square root of (V / (pi h)) and height = V / (pi r²). If a cylindrical tank holds 500 liters (500,000 cm³) and has a height of 100 cm, the radius is square root of (500,000 / (pi times 100)) = square root of 1,591.5 = 39.9 cm (diameter of about 80 cm). These reverse calculations help when designing containers to specific volume requirements or when determining the dimensions of existing tanks.

Hollow Cylinders and Pipes

A hollow cylinder (pipe or tube) has an outer radius R and inner radius r. Its volume is pi h (R² - r²). This gives the volume of the material in the pipe wall, useful for calculating weight, material cost, and thermal properties. A pipe with outer diameter 10 cm, inner diameter 8 cm, and length 200 cm has a wall volume of pi times 200 times (25 - 16) = 5,655 cm³. Plumbers, engineers, and HVAC technicians use this for pipe weight estimates, fluid flow calculations, and insulation requirements.

Oblique Cylinders

An oblique cylinder leans to one side, like a tilted can. Its volume is the same as a right cylinder with the same base area and perpendicular height: V = pi r² h, where h is the vertical height (not the slant length). This is a consequence of Cavalieri's principle, which states that two solids with equal cross-sectional areas at every height have equal volumes. The surface area of an oblique cylinder is more complex to calculate and depends on the angle of tilt.

Cylinder Volume Unit Conversions

Common volume conversions for cylindrical tanks and containers: 1 cubic meter = 1,000 liters = 264.2 US gallons. 1 cubic foot = 28.317 liters = 7.481 US gallons. 1 US gallon = 3.785 liters = 231 cubic inches. When calculating pool, tank, or pipe volumes, measure the radius and height in the same unit, compute the volume, then convert. A cylindrical swimming pool 5 meters in diameter and 1.5 meters deep holds pi times 2.5² times 1.5 = 29.45 cubic meters = 29,452 liters = 7,779 US gallons. Knowing these conversions helps you estimate water costs, chemical treatment quantities, fill times, and pump sizing for any cylindrical container.

Frequently asked questions