Find the volume of a cylinder.
The circular base area is multiplied by the height.
Volume: π × radius² × height
A cylinder has two equal circular ends joined by a curved side, like a water tank, a gas cylinder, a drum, a pipe or a tin can. The cylinder volume calculator takes the radius of the circular base and the height, and returns the volume πr²h, which is how much the cylinder can hold.
In India this is one of the most practical formulas of all. It tells you the capacity of a Sintex-style vertical water tank, the water in a borewell casing or a circular well, the concrete in a round column, or the milk in a steel can. The volume comes out in cubic units of whatever you entered; from cubic centimetres, divide by 1,000 to get litres. It is a core part of Class 9 and 10 surface area and volume chapters.
1. Measure the radius r of the circular base. If you know the diameter, halve it.
2. Measure the height h, the perpendicular distance between the two circular ends.
3. Put r and h in the same unit.
4. Find the base area: πr².
5. Multiply by the height: V = πr²h.
6. Convert to litres if needed: 1,000 cm³ = 1 litre and 1 m³ = 1,000 litres.
Imagine the cylinder as a pile of very thin coins, each a circle of area πr². Stacking them to height h gives total volume equal to base area × height. The same principle, known as Cavalieri's principle, says that any two solids with equal cross-sectional areas at every height have equal volumes. So a slanted, oblique cylinder with the same base and vertical height has the same volume as an upright one, even though it looks different.
The radius is squared, so it matters far more than the height. Doubling the height doubles the volume, but doubling the radius makes it four times as large. A tank of radius 60 cm and height 1 m holds about 1,131 litres, while one of radius 120 cm and the same height holds about 4,524 litres. When choosing a container, a small increase in diameter adds more capacity than the same increase in height.
Volume measures what is inside. The curved surface area, 2πrh, measures the side wall, and the total surface area, 2πr(r + h), adds both ends. For a pipe or hollow column with outer radius R and inner radius r, the material volume is π(R² − r²)h, the difference of two cylinders. This calculator gives the volume of a solid or fully filled cylinder, so work out hollow shapes by subtracting two results.
Suresh has a vertical cylindrical water tank on his roof with an inner radius of 55 centimetres and a height of 140 centimetres.
Answer: Volume 13,30,464.4888
Entering the diameter as the radius, which makes the volume four times too large.
Mixing units, such as radius in centimetres and height in metres.
Converting cm³ to litres by dividing by 100 instead of 1,000.
Using outer dimensions for capacity when the walls have noticeable thickness.
Using the slant length of a tilted cylinder instead of its perpendicular height.
Finding the capacity of water tanks, drums and gas cylinders in litres.
Estimating the volume of concrete in round columns and pillars.
Calculating the water held in a well or borewell of known depth.
Sizing tins, cans and bottles in packaging design.
Solving Class 9 and 10 mensuration problems.
How is this related to circle area?
A cylinder's volume is just its circular cross-section (πr²) repeated all the way through its height — the same circle-area formula is hidden inside it.