Cylinder Volume Calculator
Calculate the volume of a cylinder by entering its radius and height. A cylinder is a 3D shape with straight parallel sides and circular cross-sections. Get instant results in multiple units with step-by-step calculations.
Enter radius and height
The cylinder volume updates instantly. Change the unit first if your measurements are not in centimeters.
Half the width of the circular base.
The vertical distance between bases.
Calculated volume
Your result and common conversions will appear here.
What is the Formula for Cylinder Volume?
VolumeCalculator.co uses the formula V = πr²h to calculate cylinder volume. Here r is the base radius and h is the height. This formula calculates the area of the circular base (πr²) and multiplies it by the height to determine the total volume.
The cylinder volume formula is one of the most widely used geometric equations — it applies to everything from soda cans to industrial storage tanks. Since the base is a circle, its area is πr², and multiplying by the height gives the three-dimensional space contained within. For a detailed comparison between cylinders and cones, see our Cylinder vs Cone Volume Comparison Guide.
| Variable | Meaning | Example Value |
|---|---|---|
| V | Volume of the cylinder | 141.4 cm³ |
| π | Pi (mathematical constant) | 3.14159 |
| r | Radius of circular base | 3 cm |
| h | Height of the cylinder | 5 cm |
Cylinder Volume Worked Example
Let VolumeCalculator.co walk you through a practical example. You have a water tank that is cylindrical with a radius of 50 cm and height of 2 meters. Using the formula V = πr²h:
How to Calculate Cylinder Volume — Step-by-Step
Step 1: Measure the Radius
Measure from the center of the circular base to its edge. If you have the diameter (width of the circle), divide by 2 to get the radius. For precise results, measure in multiple directions and average.
Step 2: Measure the Height
Measure the perpendicular distance between the two circular bases. For vertical cylinders (like tanks), this is the height. For horizontal cylinders (like pipes), it is the length.
Step 3: Apply V = πr²h
Square the radius, multiply by π (3.14159), then multiply by the height. VolumeCalculator.co handles the math instantly — enter your measurements and see the result in multiple units.
Real-World Uses of Cylinder Volume
Industrial Storage
Chemical plants size storage tanks using cylinder volume. A tank with 2m radius and 5m height holds approximately 62.8 m³ of liquid — enough to fill 25 hot tubs. VolumeCalculator.co helps engineers verify tank capacities.
Plumbing & Pipe Systems
Plumbers calculate pipe volume to determine water capacity. A 10-meter PVC pipe with 5cm internal radius contains 78.5 liters of water when full. VolumeCalculator.co helps contractors size pipes for projects.
Food & Beverage
A standard soda can (3.25cm radius, 12.2cm height) holds approximately 405 ml. Beer kegs, aerosol cans, and food tins all rely on V = πr²h for capacity specification and quality control.
Architecture
Architects calculate cylindrical column volumes for material estimation. The Roman Pantheon's concrete dome required precise cylinder calculations that still stand after 1,900 years as a testament to Roman engineering.
Tips and Common Mistakes
- •Diameter vs. Radius: Always use the radius in your calculations, not the diameter. Radius = Diameter ÷ 2. Using the diameter directly will make your result 4 times larger than correct.
- •Square the Radius, Not the Height: Remember to square the radius (r²) in the formula, not the height. The formula is V = π × r² × h, not V = π × r × h².
- •Unit Consistency: Ensure all measurements use the same unit before calculating. The volume will be in cubic units of whatever unit you choose.
- •Hollow Cylinders: For hollow cylinders (like pipes), calculate the volume difference between outer and inner radii: V = π × h × (R² - r²), where R is outer radius and r is inner radius.
Frequently Asked Questions
The formula for cylinder volume is V = πr²h, where V is volume, π (pi) is approximately 3.14159, r is the radius of the circular base, and h is the height of the cylinder. This formula works by calculating the area of the circular base (πr²) and multiplying it by the height.
Divide the diameter by 2 to get the radius, then use V = πr²h. For example, a cylinder with a 10 cm diameter has a 5 cm radius. If the height is 20 cm, the volume would be π × 5² × 20 = 1,570.8 cm³. Never use the diameter directly in the formula — always convert to radius first.
If the result is in cubic centimeters (cm³), divide by 1,000 to get liters. If the result is in cubic meters (m³), multiply by 1,000 to get liters. For US gallons, divide cubic inches by 231. Our calculator provides automatic conversions for all common units.
The diameter is the length of a straight line passing through the center of the circular base and touching two points on its edge. The radius is half the diameter, measuring from the center point to any point on the edge of the circle. When calculating cylinder volume, you must use the radius, not the diameter.
For a partially filled cylinder where the liquid level is parallel to the base, simply replace the full height with the height of the liquid: V = π × r² × h_liquid. If the cylinder is on its side (horizontal), the calculation becomes more complex and involves trigonometric functions to determine the segment area.
No, this calculator specifically calculates the volume of a cylinder. For the surface area, use SA = 2πr² + 2πrh, where r is the radius and h is the height. The first term (2πr²) represents the area of the two circular bases, while the second term (2πrh) represents the curved lateral surface area.
Need Help?
Check out our detailed guide to understand how to use this calculator and the concepts behind it.
Learn how to calculate cylinder volume