Cylinder Calculator
Find the volume, lateral surface area and total surface area of a right circular cylinder from radius and height, with a worked example.
Results
Volume
- Lateral surface
- 125.663706
- Total surface
- 150.796447
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Educational estimates · not financial advice · free, no signup
Formula / how it works
Volume = π r² h. Lateral surface area = 2 π r h. Total surface area = 2 π r h + 2 π r² = 2 π r (h + r).
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
A cylinder is the shape of a can, pipe, tank or pillar: two parallel circular ends joined by a curved side. Its volume is the area of the circular base times the height, and its surface area is the curved side plus the two circular ends. This calculator takes the radius and height and returns the volume, the lateral surface and the total surface. Students use it for geometry, and makers and engineers use it to size tanks, pipes and containers or to estimate paint and material. It assumes a right circular cylinder with a uniform radius. Make sure radius and height use the same unit; volume is then in cubic units of that length.
When to use / who it helps
- You need the capacity of a cylindrical tank, can or pipe.
- You want the amount of material to wrap or paint a cylinder.
- You are checking a geometry homework answer.
- You are comparing containers of different dimensions.
- You need the lateral area of a label or sleeve.
How to use
Steps
- Enter the radius, which is half the diameter.
- Enter the height.
- Use the same length unit for both.
- Read the volume.
- Read the lateral surface and total surface.
- Convert units afterwards, for example cubic centimetres to litres by dividing by 1,000.
How to interpret results
- Volume is in cubic units of the length you used.
- Lateral surface excludes the circular ends; total surface includes them.
- Doubling the radius quadruples the volume, while doubling the height only doubles it.
- Inner dimensions give capacity; outer dimensions give material use.
- Total surface area grows more slowly than volume as the cylinder gets bigger, which is why large tanks hold more per unit of material.
Common mistakes & gotchas
- Entering the diameter as the radius.
- Mixing units, such as centimetres for radius and metres for height.
- Using total surface when only the side is needed.
- Forgetting that capacity uses inner dimensions.
- Rounding π too coarsely.
Worked example
Worked example — radius 2, height 10
- Base area: π × 2² = 12.566.
- Volume: 12.566 × 10 = 125.664.
- Lateral surface: 2 × π × 2 × 10 = 125.664.
- Total surface: 125.664 + 2 × 12.566 = 150.796.
Result: Volume 125.66; lateral surface 125.66; total surface 150.80 (in the units used).
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Volume = π r² h. Lateral surface area = 2 π r h. Total surface area = 2 π r h + 2 π r² = 2 π r (h + r).
Frequently asked questions
What is the volume formula for a cylinder?
π times radius squared times height.
What is lateral surface area?
The area of the curved side only, 2πrh.
How do I convert volume to litres?
If volume is in cubic centimetres, divide by 1,000. If in cubic metres, multiply by 1,000.
What if I know the diameter?
Divide it by 2 to get the radius.
Does this work for oblique cylinders?
The volume is the same if the perpendicular height is used, but surface area differs.
Why are the lateral area and volume the same number in the example?
With radius 2, 2πrh and πr²h are equal, which is a coincidence of those inputs and not a general rule.