Quick answer
Cylinder volume V = πr²h. A cylinder with radius 3 and height 5 has a volume of 141.3717.
Enter the radius and height. The calculator returns the volume.
Related tools: Hollow Cylinder Volume Calculator: Volume of material in a pipe or tube. Sphere Volume Calculator: Volume and surface area of a sphere. Volume of a Hemisphere Calculator: Volume and surface area of a hemisphere.
How to use the Cylinder Volume Calculator
- Enter radius (above 0).
- Enter height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Radius | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
V = πr²h
IEEE-754 double precision; shown to at most 6 decimal places.
Base area times height.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Radius = 3; Height = 5.
| Result | Value |
|---|---|
| Volume | 141.371669 |
Example 2
Inputs: Radius = 1; Height = 1.
| Result | Value |
|---|---|
| Volume | 3.141593 |
The first line is the headline result (volume). IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
Base area π × 9 = 28.274; multiplied by the height 5 gives 141.37. Doubling the radius quadruples the volume; doubling the height only doubles it.
Capacity
For liquids use the inside dimensions: a tank of 141.37 L when dimensions are in decimetres. 1 dm³ is 1 litre. Add the surface area if you need paint or insulation, which is 2πr(r + h).
Units and the radius mistake
The result is in cubic units of whatever you entered. For radius 3 and height 5 the volume is about 141.37; in centimetres that is 141.37 cm³, equal to 141.37 mL, and in inches 141.37 in³ is about 0.61 US gallons (1 gal = 231 in³).
The most common mistake is typing the diameter as the radius, which makes the volume four times too large: radius 6 instead of 3 gives about 565.49.
How the result changes with radius
Holding every other input at the first worked example, this table changes only radius. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Radius | Volume |
|---|---|
| 1.5 | 35.342917 |
| 3 | 141.371669 |
| 6 | 565.486678 |
| 12 | 2,261.946711 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Radius: entering "0" shows "Radius must be greater than 0." beside that field and no result.
Choosing between the Cylinder Volume Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Hollow Cylinder Volume Calculator](/math/hollow-cylinder-volume/) | outer radius, inner radius and length | Volume |
| [Sphere Volume Calculator](/math/sphere-volume-calculator/) | radius | Volume |
| [Volume of a Hemisphere Calculator](/math/volume-of-hemisphere/) | radius | Volume |
| [Cone Volume Calculator](/math/cone-volume-calculator/) | radius and height | Volume |
| [Pyramid Volume Calculator](/math/pyramid-volume-calculator/) | base length, base width and height | Volume |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive dimensions
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for radius to confirm this.
Frequently asked questions
What is the volume with diameter 6 and height 5?
The same, since radius is 3.
How do I convert to litres?
1,000 cm³ is a litre.
What is a hollow cylinder?
See the Hollow Cylinder Volume calculator.
What if I only know the diameter?
Halve it to get the radius before entering it. A diameter of 6 means a radius of 3.
How do I find the volume of a partly filled cylinder?
Use the depth of the liquid as the height. A cylinder 5 tall filled to 2 holds a volume found with h = 2.
What does the Cylinder Volume Calculator calculate?
Volume of a cylinder. It returns Volume.
What formula does the Cylinder Volume Calculator use?
V = πr²h. Base area times height.
What do I need to enter in the cylinder Volume Calculator?
You enter Radius and Height.
What is an example of a cylinder Volume result?
With radius 3 and height 5, the volume is 141.371669.
Related calculators
- Hollow Cylinder Volume Calculator — Volume of material in a pipe or tube.
- Sphere Volume Calculator — Volume and surface area of a sphere.
- Volume of a Hemisphere Calculator — Volume and surface area of a hemisphere.
- Cone Volume Calculator — Volume, slant height and surface area of a cone.
- Pyramid Volume Calculator — Volume of a pyramid from its base area and height (rectangular base).
- Cube Volume Calculator — Volume, surface area and diagonal of a cube.
- Torus Volume Calculator — Volume and surface area of a torus.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.