Cylinder volume calculator.
Find the volume of a cylinder. Enter the radius of the base and the height and the calculator returns the volume, the base area, the total surface area and the diameter.
Cylinder dimensions
LiveVolume equals pi times the radius squared times the height. The units come out cubed, so a radius and height in cm give a volume in cubic cm.
Volume
785.398
pi times r squared times h
Assumes a right circular cylinder. Units match whatever unit you enter. Calculations run in your browser; nothing you enter is stored.
How it works
Base area times height
A cylinder is a circle extruded straight up, so its volume is simply the area of the circular base multiplied by the height. The base area is pi times the radius squared, so the volume is pi times the radius squared times the height.
With a radius of 5 and a height of 10, the base area is about 78.54 and the volume is that times 10, roughly 785.40. Double the height and the volume doubles; double the radius and it quadruples.
Reference
Cylinder volume examples.
The volume for a few radius and height combinations, using pi.
| Radius, height | Volume |
|---|---|
| r 5, h 10 | 785.40 |
| r 3, h 8 | 226.19 |
| r 10, h 20 | 6283.19 |
| r 2, h 5 | 62.83 |
| r 7, h 7 | 1077.57 |
The full guide
The complete guide to cylinder volume.
How the formula works, how surface area differs, and where it is used.
The volume formula
A cylinder’s volume is the area of its circular base times its height. Since the base is a circle of area pi r squared, the volume is pi r squared h. It is one of the most useful solid-volume formulas because so many real objects, from cans to pipes, are cylinders.
Keep the radius and height in the same units and the volume comes out in those units cubed.
Radius, diameter and height
The radius is the distance from the centre of the base to its edge; the diameter is twice that. If you only know the diameter, halve it first. The height is the straight distance between the two circular ends.
Because volume depends on the radius squared, the radius matters far more than the height: a small change in radius has a big effect.
Volume versus surface area
Volume measures the space inside the cylinder, while surface area measures the material to cover it. The total surface area is two circular ends, 2 pi r squared, plus the curved side, 2 pi r h. The calculator reports both so you can size contents and packaging.
For an open tube, you would drop one or both end caps from the surface area.
Where it is used
Cylinder volume shows up everywhere: tanks, cans, pipes, silos, drinking glasses and engine bores. Converting the result to litres or gallons is common, since one litre is 1000 cubic cm.
For a sphere or a circle, use the related volume and circumference calculators.
The formula
Pi r squared
times h.
A cylinder’s volume is its circular base area, pi r squared, multiplied by its height.
Sphere volume ›# Cylinder
volume = pi × r^2 × h
surface = 2 pi r^2 + 2 pi r h
# r=5, h=10
V = 785.40Questions
Cylinder questions.
How do I calculate the volume of a cylinder?
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Multiply pi by the radius squared by the height. Enter the radius and height above and the calculator returns the volume along with the surface area.
What is the formula for cylinder volume?
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V equals pi r squared h, where r is the base radius and h is the height. It is the base area, pi r squared, times the height.
How do I find the volume in litres?
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Work in centimetres, then divide the cubic-centimetre volume by 1000, since one litre equals 1000 cubic centimetres.
What is the surface area of a cylinder?
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The total surface area is 2 pi r squared plus 2 pi r h: the two circular ends plus the curved side. The calculator shows this too.
Is this cylinder volume calculator free?
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Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The cylinder volume calculator reports the volume, base area, surface area and diameter.