On This Page
- How to use the Cylinder Volume Calculator
- Cylinder volume formula
- How to calculate the volume of a cylinder
- How to find cylinder volume with diameter
- Reverse cylinder volume calculations
- Worked examples
- Cylinder volume units, gallons, and liters
- Cylinder capacity and packing questions
- Frequently asked questions
How to Use the Cylinder Volume Calculator
Use this cylinder volume calculator for cans, pipes, tubes, drums, tanks, columns, and other round containers. Enter the radius and height, choose the unit, and the page shows volume, base area, diameter, liters, gallons, cubic feet, and step-by-step work.
If your problem gives diameter instead of radius, divide the diameter by 2 first. For homework, it helps to solve once by hand and then use the calculator to catch arithmetic or unit mistakes.
Cylinder Volume Formula
The standard formula for calculating cylinder volume is:
- V = volume
- π ≈ 3.14159
- r = radius of the circular base
- h = height of the cylinder
The formula works because a cylinder is like many identical circles stacked on top of each other. The circular base area is πr², and multiplying by height gives the full three-dimensional volume.
How to Calculate the Volume of a Cylinder
To calculate the volume of a cylinder by hand, find the radius of the circular base and the height of the cylinder. Both measurements must use the same unit before you multiply.
Step 1: Find the Radius and Height
The radius is the distance from the center of the circular base to its edge. The height is the straight distance between the two circular bases.
Step 2: Square the Radius
Multiply the radius by itself. For example, if r = 3, then r² = 3 × 3 = 9.
Step 3: Multiply by Pi
Use π ≈ 3.14159 unless your class asks for 3.14. This gives the area of the circular base.
Step 4: Multiply by Height
Multiply the base area by the cylinder height. The final answer is written in cubic units.
- Find the radius: r
- Find the height: h
- Square the radius: r²
- Multiply by π
- Multiply by height
- Write the answer in cubic units, such as cm³, m³, or in³
How to Find Cylinder Volume With Diameter
Many cylinder problems give the diameter instead of the radius. Since diameter is twice the radius, divide diameter by 2 before using the formula.
For example, if a cylinder has a diameter of 8 cm and a height of 12 cm, the radius is 4 cm. The volume is π × 4² × 12 = 192π, or about 603.2 cm³.
Reverse Cylinder Volume Calculations
If you already know the volume and one dimension, rearrange the cylinder formula to solve for the missing height or radius.
Find Height From Volume and Radius
Use this when you know how much a cylinder must hold and you need the required height.
Find Radius From Volume and Height
Use this when you know the capacity and height but need the radius of the circular base.
Worked Cylinder Volume Examples
The examples below follow common classroom and measurement problems. Each one identifies the given dimensions, sets up the formula, and finishes with the correct cubic unit.
Example 1: Soup Can Volume From Radius and Height
Problem: A can of soup is shaped like a cylinder. The inside radius is 4 cm and the inside height is 11 cm. Estimate the volume of soup the can can hold. Use 3.14 for π.
- Radius = 4 cm, height = 11 cm
- Use V = πr²h
- Square the radius: 4² = 16
- Multiply: V = 3.14 × 16 × 11
- V = 552.64 cm³
Answer: The can holds about 552.6 cm³, or about 552.6 mL.
Example 2: Water Tank Capacity in Gallons
Problem: A cylindrical water tank has an inside radius of 1.5 feet and an inside height of 6 feet. Estimate the tank capacity in US gallons. Use 1 ft³ = 7.48052 US gallons.
- Radius = 1.5 ft, height = 6 ft
- Volume = π × 1.5² × 6
- 1.5² = 2.25
- Volume = 3.14159 × 2.25 × 6 ≈ 42.41 ft³
- Gallons = 42.41 × 7.48052 ≈ 317.3 gal
Answer: The tank holds about 317.3 US gallons.
Example 3: Volume From Diameter
Problem: A cylindrical concrete column has a diameter of 18 inches and a height of 8 feet. Estimate its volume in cubic feet. Convert inches to feet before calculating.
- Diameter = 18 in = 1.5 ft
- Radius = 1.5 ÷ 2 = 0.75 ft
- Height = 8 ft
- Volume = π × 0.75² × 8
- Volume ≈ 14.14 ft³
Answer: The column volume is about 14.1 cubic feet.
Example 4: Find Missing Height From Volume
Problem: A cylinder has a volume of 395.64 cubic inches and a radius of 3 inches. Find the height of the cylinder. Use 3.14 for π.
- Known values: V = 395.64 in³, r = 3 in
- Use h = V ÷ (πr²)
- r² = 3² = 9
- πr² = 3.14 × 9 = 28.26
- h = 395.64 ÷ 28.26 = 14
Answer: The cylinder height is 14 inches.
Example 5: Pipe Internal Volume
Problem: A straight pipe is 2 meters long and has an internal diameter of 10 centimeters. Estimate the volume of water inside the pipe in liters.
- Convert diameter: 10 cm = 0.10 m
- Radius = 0.10 ÷ 2 = 0.05 m
- Height/length = 2 m
- Volume = π × 0.05² × 2 ≈ 0.0157 m³
- Convert to liters: 0.0157 × 1,000 = 15.7 L
Answer: The pipe holds about 15.7 liters of water.
Cylinder Volume Units, Gallons, and Liters
Cylinder volume is written in cubic units. Liquid capacity is often converted to liters, milliliters, or gallons depending on the problem.
| Input Unit | Volume Unit | Useful Conversion |
|---|---|---|
| Centimeters | cm³ | 1,000 cm³ = 1 liter |
| Meters | m³ | 1 m³ = 1,000 liters |
| Inches | in³ | 231 in³ = 1 US gallon |
| Feet | ft³ | 1 ft³ ≈ 7.48052 US gallons |
Cylinder Capacity and Related Packing Questions
Volume measures the space inside the cylinder. Surface area measures the outside covering, including the two circular ends and the curved side. A tank or can may need volume for capacity and surface area for material, paint, or label coverage.
Cylinder volume can give a rough capacity check, but fitting spheres inside a container is a packing problem. For sphere diameter, box size, clearance, void space, and simple grid estimates, use the Sphere Packing Calculator.
Cylinder Volume Mistakes to Avoid
- Using diameter as radius: Always divide diameter by 2 before using V = πr²h.
- Mixing units: Convert inches to feet, centimeters to meters, or any mixed units before calculating.
- Forgetting to square the radius: The formula uses r², not just r.
- Using outside dimensions for capacity: For liquid capacity, use inside radius and inside height.
- Confusing volume with surface area: Volume is inside space. Surface area is outside covering.
Frequently Asked Questions
How do you calculate the volume of a cylinder?
Use V = πr²h. Square the radius, multiply by pi, then multiply by the cylinder height.
Can I calculate cylinder volume from diameter?
Yes. Divide diameter by 2 to get radius, then use V = πr²h. You can also write the formula as V = π(d/2)²h.
How do I calculate cylinder volume in gallons?
Calculate cubic volume first, then convert. If the answer is in cubic feet, multiply by 7.48052 to get US gallons. If it is in cubic inches, divide by 231.
How do I find cylinder height from volume?
Rearrange the formula to h = V ÷ (πr²). This is useful when volume and radius are known.
What unit is cylinder volume in?
Cylinder volume is written in cubic units, such as cm³, m³, in³, or ft³. Liquid capacity can also be shown in liters or gallons.
How many spheres fit in a cylinder?
That is a sphere-packing problem, not a cylinder-volume problem. The answer depends on sphere diameter, cylinder radius, cylinder height, layer spacing, and the packing pattern. Use the Sphere Packing Calculator for simple packing and container estimates.