Cylinder Volume Calculator

Cylinder formulas

A cylinder’s volume is its base area stacked up to its height, so the formula is the area of a circle, πr², times h. The side area is a rectangle rolled up: its width is the circumference 2πr and its height is h. Add the two round ends for the total. If you know the diameter instead of the radius, halve it first — a 6-inch pipe has a 3-inch radius — or choose d and h and the calculator does it for you.

Working backwards from a volume

When the volume is fixed — a tank that must hold a certain amount, a can of a given size — the calculator finds the missing size:

• Height from radius and volume: h = V ÷ πr². A volume of 1,000 with a radius of 6 needs a height of 8.84194.
• Radius from height and volume: r = √(V ÷ πh). A volume of 500 in a height of 12 needs a radius of 3.64183.

Enter the volume in cubic units of the length you picked. For a tank sized in gallons, convert first: 1 gallon is 231 cubic inches, so 100 gallons is 23,100 in³. To convert between gallons and liters directly, use gallons to liters.

Cans, pipes, drums and tanks

The drum shows why rated capacity is less than the geometric volume: a “55-gallon” drum holds about 57.7 gallons filled to the top, and the rating leaves headspace. A can holds less than its volume for the same reason. For pipes, the water inside a run of pipe is the cylinder volume of the inside diameter times the length — useful for flushing a line or sizing a fill. For round concrete footings and columns, the volume in cubic yards is what you order; see the concrete calculator, which handles round forms and adds waste.

Surface area for paint, labels and insulation

The side area is what a label, a sheet of insulation or a coat of paint covers on a pipe or tank; the ends add 2πr² if they are covered too. A tank 4 feet across and 6 feet tall has 75.4 square feet of side and 25.1 square feet of ends, about 100.5 square feet in all. A can’s label is the side area alone: 2π × 1.3 × 4.83 = 39.5 square inches.

Cylinders, spheres and cones

A sphere that fits exactly inside a cylinder has two-thirds of the cylinder’s volume, and a cone with the same base and height has one-third — a result Archimedes was proud enough of to want on his tombstone. For balls and round tanks, use the sphere calculator. To check powers and square roots by hand, the scientific calculator has both.