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
- Volume of a hollow cylinder
- Cylinder capacity and packing questions
- Frequently asked questions
How to Use the Cylinder Volume Calculator
Enter the radius and height. This works for soup cans, concrete columns, water tanks, drums, silos, and pipe sections, anything with a circular cross-section and straight sides. The result includes volume, base area, liquid conversions, and the full calculation steps.
If your problem gives diameter instead of radius, divide by 2 before entering. For a real container, measure the inside radius and inside height, outside dimensions include wall thickness and will overestimate the actual capacity.
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 |
Volume of a Hollow Cylinder
A hollow cylinder, like a pipe or a tube, has material between an outer radius R and an inner radius r. To find the volume of the material itself (not the empty space inside), subtract the inner cylinder volume from the outer cylinder volume:
For example, a pipe that is 2 m long with outer radius 0.08 m and inner radius 0.06 m has a material volume of: V = π × 2 × (0.08² − 0.06²) = π × 2 × 0.0028 ≈ 0.0176 m³. To find the capacity of the hollow space, use just the inner radius in V = πr²h.
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 gives the full capacity. For fitting spheres inside a cylinder, calculating void space, or estimating clearance, use the Sphere Packing Calculator. For a rectangular tank instead of a round one, the Tank Volume Calculator covers the box-shaped case with the same litres and gallons output. A full worked walkthrough of converting cylindrical tank capacity to litres and gallons, including a dipstick reference table, is in How Much Water Does a Cylindrical Tank Hold?
References
- Cylinder, Wikipedia: geometric definition, volume and surface area formulas, and oblique cylinder notes.
- Cylinder, Wolfram MathWorld: formal derivation of the cylinder volume formula and related properties.
- Cylinder, Math is Fun: visual explanation of the cylinder formula with worked examples.
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 (3.14159), then multiply by the height. For a cylinder with radius 4 cm and height 11 cm: V = 3.14159 × 16 × 11 ≈ 552.6 cm³.
Can I calculate cylinder volume from diameter?
Yes. Divide the diameter by 2 to get the radius, then use V = πr²h. Alternatively, write it as V = π(d/2)²h. A cylinder with diameter 8 cm and height 12 cm has radius 4 cm and volume ≈ 603.2 cm³.
How do I calculate cylinder volume in gallons?
Find the cubic volume first, then convert. Cubic feet × 7.48052 = US gallons. Cubic inches ÷ 231 = US gallons. The calculator converts automatically for all common units.
How do I calculate the volume of a hollow cylinder (pipe or tube)?
Subtract the inner cylinder volume from the outer cylinder volume: V = πh(R² − r²), where R is the outer radius and r is the inner radius. For the hollow space capacity, use just the inner radius in V = πr²h.
My answer seems way too large, what went wrong?
The most common cause is using diameter instead of radius. The formula squares the radius, so using the diameter makes the result four times too large. Also check that all units match, meters vs centimeters can produce a factor of 1,000,000 difference in cubic volume.
How do I find cylinder height from volume?
Rearrange to h = V ÷ (πr²). If you know the volume must be 395.6 in³ and the radius is 3 in, then h = 395.6 ÷ (3.14159 × 9) ≈ 14 in.
When would I actually need cylinder volume in real life?
Aquariums, well casings, grain silos, above-ground pools, cylindrical fuel tanks, and hot water heaters all use this formula for capacity. Plumbers and HVAC engineers use it to size pipe runs and ductwork. If you need to know how much a round container holds, this is the formula.