Cylinder Volume Calculator: Formula, Surface Area and Step-by-Step Answer
Geometry & trigFreeNo sign-up
Enter the radius and height to get the cylinder’s volume and surface area.
A cylinder with radius 5.0000 cm and height 12.0000 cm has a volume of 942.4778 cm³ and a total surface area of 534.0708 cm².
Show the steps
- Base area = π × r² = π × 5.0000² = 78.5398 cm².
- Volume = base area × height = 78.5398 × 12.0000 = 942.4778 cm³.
- Lateral area = 2 π r h = 376.9911 cm²; total surface area = lateral + 2 × base = 534.0708 cm².
Cylinder
V = π r² h
Lateral area = 2 π r h
Surface area = 2 π r h + 2 π r²
- Liquid capacity: 0.9425 liters.
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
A cylinder has two equal circular bases and a curved side. Its volume is the base area times the height: V = π r² h. Use this calculator for cans, pipes, tanks, pillars and any round container.
Enter the radius and height in the same unit. You get the volume, the total surface area, the lateral area and the capacity in liters.
How to use it
- Enter the radius of the circular base and the height.
- Pick the unit, such as cm, m, in or ft.
- Read the volume, surface area and the steps below.
Cylinder formulas
- Volume: V = π r² h
- Lateral (side) area: 2 π r h
- Total surface area: 2 π r h + 2 π r²
Example
A can with radius 5 cm and height 12 cm has a base area of π × 5² = 78.54 cm², so V = 78.54 × 12 = 942.48 cm³, which is about 0.94 liters.
Using the diameter
If you know the diameter, divide it by 2 to get the radius before you enter it.
Sources
Quick check: test yourself
A cylinder has radius 3 cm and height 4 cm. What is its volume to the nearest tenth?
Correct answer: 113.1 cm³. V = π r² h = π × 3² × 4.
If you double the radius of a cylinder and keep the height, the volume is
Correct answer: 4 times as large. Volume depends on r², so doubling r multiplies it by 4.
Which formula gives the volume of a cylinder?
Correct answer: π r² h. Base area π r² times height h.
Pick an answer for each question.
Common questions
How do I find the volume of a cylinder?
Multiply the area of the circular base, π r², by the height.
Do I enter radius or diameter?
Enter the radius. If you have the diameter, divide it by 2.
How do I convert the volume to liters?
1,000 cm³ is 1 liter. The calculator shows the liter capacity in the notes.
What if the units are different?
Convert all lengths to the same unit first.
Does it work for a half-full cylinder?
Use the height of the liquid as the height to get the volume of liquid.
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