Key takeaways
- The volume of a cylinder is V = π × r² × h.
- Only the radius gets squared, never the height.
- A cylinder holds exactly 3 times as much as a cone with the same radius and height.
- Volume measures what a cylinder holds; surface area measures the material to build it.
In this guide
What is the volume of a cylinder?
A cylinder is a 3D shape with two flat circular ends connected by a curved side, like a soda can or a water pipe. Volume measures how much space is inside it, in cubic units such as cm³ or liters. This is different from surface area, which measures the material to build the can, not what fits inside it.
Why does the volume of a cylinder matter?
It tells you exactly how much a tank, can, or pipe can actually hold — a crucial number whenever liquid or gas is involved.
A cylinder with radius 3 m and height 4 m holds about 113.1 m³ — exactly three times as much as a cone with that same radius and height, which holds only about 37.7 m³. Same base, same height, one-third the volume.
The formula
| Symbol | What it means | Example |
|---|---|---|
| V | The volume, space inside the cylinder | 502.65 m³ |
| π (pi) | A fixed number, about 3.14159 | 3.14159 |
| r | The radius of the circular base | 4 m |
| h | The height: distance between the two circular ends | 10 m |
How to find the volume step by step
- 1Measure the radius of the circular base. If you know the diameter, divide it by 2.
- 2Square the radius.
- 3Multiply by π. This gives the area of the circular base.
- 4Multiply that base area by the height.
- 5Add cubic units. Such as cm³ or m³.
Now try it yourself. Change the radius and height in the calculator below and watch the volume update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Confusing volume with surface area. Volume is how much the cylinder holds inside; use the surface area of a cylinder calculator if you need the material to build or wrap it instead.
- Squaring the whole `(r × h)` instead of just r. Only the radius gets squared, not the height.
- Forgetting cubic units. Volume is always in units³, such as m³ or ft³.
Tips and tricks
- Doubling the height doubles the volume, since height only appears once. Doubling the radius instead multiplies volume by 4, since the radius is squared.
- For a similar shape that tapers to a point, compare with the volume of a cone calculator — a cone always holds exactly one-third as much.
Where you'll use it in real life
- Home and garden: working out how much water a cylindrical tank holds.
- Cooking: estimating how much soup fits in a can.
- Kitchenware: checking how much a drinking glass can carry.
- Engineering: calculating the capacity of pipes and cylindrical containers.
Quick summary
To find the volume of a cylinder, square the radius, multiply by π to get the base area, then multiply by the height. A cylinder always holds exactly three times as much as a cone with the same radius and height. Use the calculator above to check your own cylinder instantly.
Worked example
You're filling a cylindrical water tank with a radius of 4 meters and a height of 10 meters. How much water can the tank hold?
- 01V = πr²h
- 02V = π(4)²(10)
- 03V = π(16)(10)
- 04V = 160π
- 05V = 502.65 m³
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the volume of a cylinder from its diameter?
Divide the diameter by 2 to get the radius, then use V = πr²h.
What's the difference between the volume and surface area of a cylinder?
Volume (πr²h) tells you how much the cylinder can hold, in cubic units. Surface area (2πr² + 2πrh) tells you how much material covers its outside, in square units. Use the [surface area of a cylinder calculator](/calculator/surface-area-cylinder) for the outer covering.
How do I convert cylinder volume to liters?
Find the volume in cubic centimeters (cm³), then divide by 1000, since 1 liter equals 1000 cm³.
Does doubling the height double the volume?
Yes, since height appears only once in the formula. But doubling the radius instead multiplies the volume by 4, since the radius is squared.
