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Cylinder Volume Calculator
Use this cylinder volume calculator to find the volume of any cylinder — a tank, pipe, drum or can — from its radius or diameter and its height. It also gives the curved surface area, the total surface area and, for metric units, the volume in litres.
| Volume (π r² h) | |
| Curved surface area (2π r h) | |
| Total surface area (2π r(r + h)) | |
| Base area (π r²) | |
| Volume in litres |
How to use this cylinder volume calculator
- Say whether you know the radius or the diameter of the circular end.
- Enter that measurement, then the height (the length of the cylinder).
- Pick the unit — cm, m, inches or feet. Both measurements must be in this unit.
- Read the volume, both surface areas, and the litres figure if you are working in cm or m.
How cylinder volume works
A cylinder is just a circle extended in a straight line. Everything about it comes from the circle at its end: find that circle's area, then multiply by how far the shape stretches — its height. That is the whole idea; the three standard results below are all built from the base circle.
Volume is the space inside: how much water a tank holds, how much concrete a round column needs. It grows fast — double the radius and the volume becomes four times bigger, because the radius is squared. Double the height and the volume only doubles.
Curved surface area is the area of the side wall alone, ignoring the ends. Imagine unrolling the wall of a can: it becomes a rectangle whose width is the circumference (2πr) and whose height is h. Use it for painting or wrapping the outside of a pipe.
Total surface area adds the two circular ends to the wall: 2πr² for the two bases plus 2πrh for the wall, which tidies up into 2πr(r + h). Use it when the cylinder is closed, like a sealed drum. For an open-top tank, the right figure is the curved area plus just one base — the calculator's rows let you add that up yourself.
For water tanks, litres are the practical unit: 1 litre = 1,000 cm³, and 1 m³ = 1,000 litres. The calculator shows litres automatically for centimetre and metre inputs.
Worked example
A steel drum has a radius of 5 cm (a small model) and a height of 10 cm. Find its volume and surface areas.
Step 1: Base area = π × r² = 3.14159 × 5² = 78.54 cm².
Step 2: Volume = base area × height = 78.54 × 10 = 785.40 cm³ (about 0.79 litres).
Step 3: Curved surface area = 2 × π × r × h = 2 × 3.14159 × 5 × 10 = 314.16 cm².
Step 4: Total surface area = 2 × π × r × (r + h) = 2 × 3.14159 × 5 × 15 = 471.24 cm².
Enter radius 5 and height 10 in centimetres and the calculator shows exactly these numbers.
Volumes of some common cylinders
| Object (approx.) | Radius | Height | Volume | In litres |
|---|---|---|---|---|
| Small drum (worked example) | 5 cm | 10 cm | 785.40 cm³ | 0.79 L |
| Paint tin | 10 cm | 20 cm | 6,283.19 cm³ | 6.28 L |
| Household water tank | 50 cm | 100 cm | 7,85,398.16 cm³ | 785.40 L |
| Large tank (1 m radius) | 100 cm | 100 cm | 31,41,592.65 cm³ | 3,141.59 L |
Notice the pattern: the 50 cm tank holds a thousand times more than the 5 cm drum, because its radius is 10 times bigger (100 times the base area) and its height is 10 times bigger again.
FAQ
How do you calculate the volume of a cylinder?
Multiply the area of the circular base by the height: V = π × r² × h, where r is the radius and h is the height. For a cylinder with a radius of 5 cm and a height of 10 cm, V = 3.14159 × 25 × 10 = 785.40 cm³. If you know the diameter instead, halve it first to get the radius.
What is the difference between curved surface area and total surface area?
The curved surface area (2 × π × r × h) counts only the side wall of the cylinder — the part you could wrap with a sheet of paper. The total surface area adds the two circular ends: 2 × π × r × (r + h). For a radius of 5 cm and height of 10 cm, the curved area is 314.16 cm² and the total is 471.24 cm². For an open tank, use the curved area plus one base, not the total.
How many litres is a cylinder of radius 50 cm and height 100 cm?
Its volume is π × 50² × 100 = 7,85,398 cm³. Since 1 litre is 1,000 cm³, that is 785.40 litres — which is why a standard 500-litre or 1,000-litre water tank is roughly this size. This calculator shows litres automatically when you work in centimetres or metres.
What units can I use in this cylinder calculator?
Centimetres, metres, inches and feet. The radius and height must be in the same unit; the volume then comes out in cubic units of that unit (cm³, m³, in³ or ft³) and the areas in square units. Do not mix units — a radius in cm with a height in inches gives a wrong answer.
How do I find the volume if I only know the diameter?
Divide the diameter by 2 to get the radius, then use V = π × r² × h. Or pick 'Diameter' in this calculator and enter the diameter directly — it does the halving for you. A pipe with a diameter of 20 cm and length 100 cm holds π × 10² × 100 = 31,415.93 cm³, about 31.42 litres.