How to use the cylinder volume calculator
- Enter the radius of the cylinder's circular base.
- Enter the height (the distance between the two bases).
- Optionally type a unit label such as
cm,morinso the results are clearly marked. - The volume, lateral surface area and total surface area appear immediately as you type.
How the cylinder volume formula works
The volume of a cylinder formula multiplies the area of the circular base by the height: V = pi * r^2 * h. The constant pi is approximately 3.14159265. For a cylinder with a radius of 5 cm and a height of 10 cm, the calculation is 3.14159265 * 25 * 10 = 785.398 cm^3.
The lateral surface area covers only the curved side. Its formula is A_lateral = 2 * pi * r * h, which for the same dimensions gives 2 * 3.14159265 * 5 * 10 = 314.159 cm^2. Add the two circular end caps, each with area pi * r^2, to get the total surface area: A_total = 2 * pi * r * h + 2 * pi * r^2.
Common cylinder dimensions reference
This table shows the volume and total surface area for several everyday cylindrical objects. All values are rounded to two decimal places.
| Object | Radius | Height | Volume | Total surface area |
|---|---|---|---|---|
| Soda can | 3.3 cm | 12.2 cm | 417.91 cm³ | 321.27 cm² |
| AA battery | 0.7 cm | 5.0 cm | 7.70 cm³ | 25.15 cm² |
| Standard pencil | 0.35 cm | 18.0 cm | 6.93 cm³ | 40.33 cm² |
| 55-gallon drum | 28.5 cm | 86.0 cm | 219,555.38 cm³ | 20,514.73 cm² |
Practical uses for cylinder volume
Knowing how to find the cylinder volume is useful across many fields. Plumbers and HVAC technicians calculate pipe capacity to size pumps and estimate flow rates. Engineers use it to determine the displacement of pistons in engines, where each cylinder's swept volume directly affects power output.
In packaging, manufacturers compare the volume of cylindrical containers against rectangular boxes to minimize wasted space on pallets. Homeowners filling a round water tank or a cylindrical planter box rely on the same math to know how much liquid or soil to buy.
Diameter versus radius
A frequent mistake when using a volume of a cylinder calculator is entering the diameter instead of the radius. The radius is exactly half the diameter. If you measure a pipe at 10 cm across, the radius is 5 cm. Because the volume of cylinder formula squares the radius, using the diameter by accident makes the result four times too large.
Always double-check whether your measurement spans the full width (diameter) or goes from the center to the edge (radius) before plugging numbers in.
Units and conversions
The calculator labels results with whatever unit you type, but it does not convert between units automatically. If you enter the radius in centimeters and the height in meters, the output will be numerically wrong even though the label says what you typed. Keep both measurements in the same unit before calculating.
When you need to switch between metric and imperial, convert the linear dimensions first, then compute the volume. Cubic conversions are not the same as linear ones: one cubic foot equals 1,728 cubic inches, not 12. You can use dedicated length tools like cm to inches or feet to meters to align your measurements before returning here.
Worked examples
Each result below was produced by the same code the tool runs, so you can check your own numbers against them.
| Example | Input | Result |
|---|---|---|
| Soda can (approximate) | Radius: 3.3; Height: 12.2; Unit label: cm | Volume: 417.385717 cm³; Lateral surface area: 252.96104 cm²; Total surface area: 321.384928 cm² |
| Water pipe section | Radius: 0.05; Height: 3; Unit label: m | Volume: 0.023562 m³; Lateral surface area: 0.942478 m²; Total surface area: 0.958186 m² |
| Large storage tank | Radius: 4; Height: 10; Unit label: ft | Volume: 502.654825 ft³; Lateral surface area: 251.327412 ft²; Total surface area: 351.858377 ft² |
| Pencil barrel | Radius: 0.35; Height: 18; Unit label: cm | Volume: 6.927212 cm³; Lateral surface area: 39.584067 cm²; Total surface area: 40.353758 cm² |
FAQ
What is the formula for the volume of a cylinder?
The volume of a cylinder is V = pi * r^2 * h, where r is the radius of the base and h is the height. Multiply pi (about 3.14159) by the radius squared, then by the height.
How do I find the surface area of a cylinder?
The total cylinder surface area is 2 * pi * r * h + 2 * pi * r^2. The first term is the curved lateral area, and the second term accounts for the two flat circular ends.
Can I use the diameter instead of the radius?
Yes, but divide the diameter by two first. The formula requires the radius. If you substitute the diameter directly, the computed volume will be four times larger than the true value.
Does this tool work for hollow cylinders?
This volume of a cylinder calculator computes the volume of a solid cylinder. For a hollow tube, calculate the outer cylinder volume and subtract the inner cylinder volume using the same formula with the inner radius.
What units should I enter?
Use the same linear unit for both radius and height. The unit label field is cosmetic and simply appends the correct superscript notation to the results. Convert mixed units before calculating.
Is my data sent to a server?
No. The calculator runs entirely in your browser. Nothing you type is uploaded anywhere.