How to Calculate the Volume of a Cylinder

Co-authored by Grace Imson, MA

Last Updated: October 3, 2024 References

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A cylinder is a simple geometric shape with two equally-sized and parallel circular bases. Calculating the volume of a cylinder is simple once you know the formula.^{[1]
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Method 1

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Calculating the Volume of a Cylinder

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1
Find the radius of the circular base.^{[2]
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Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco

Expert Interview. 1 November 2019.} Either circle will do since they are the same size. If you already know the radius, you can move on. If you don't know the radius, then you can use a ruler to measure the widest part of the circle and then divide it by 2. This will be more accurate than trying to measure half of the diameter. Let's say that the radius of this cylinder is 1 inch (2.5 cm). Write it down.
- If you know the diameter of the circle, just divide it by 2.^{[3]
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- If you know the circumference, then you can divide it by 2π to get the radius.^{[4]
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Calculate the area of the circular base.^{[5]
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Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco

Expert Interview. 1 November 2019.} To do this, just use the formula for finding the area of a circle, A = πr².^{[6]
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Research source} Just plug the radius you found into the equation. Here's how to do it:
- A = π x 1²
- A = π x 1
- A = π
- Since π is normally rounded to 3.14, you can say that the area of the circular base is 3.14 in.²
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Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco

Expert Interview. 1 November 2019.} If you know the height already, move on. If not, use a ruler to measure it. The height is the distance between the edges of the two bases. Let's say the height of the cylinder is 4 inches (10.2 cm). Write it down.
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Multiply the area of the base by the height.^{[8]
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Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco

Expert Interview. 1 November 2019.} You can think of the volume of the cylinder as the area of the base being extended throughout the height of the cylinder. Since you know that the area of the base is 3.14 in.² and that the height is 4 in., you can just multiply the two together to get the volume of the cylinder. 3.14 in.² x 4 in. = 12.56 in.³ This is your final answer.^{[9]
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- Always state your final answer in cubic units because volume is the measure of a three-dimensional space.^{[10]
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How do I calculate the length of the radius?

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The radius is half of the diameter. If you know the diameter, just divide that by two to find the radius.

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How can I find a cylinder's volume when I know height and diameter?

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Calculate the area of the base (which is a circle) by using the equation πr² where r is the radius of the circle. Then, multiply the area of the base by the height of the cylinder to find the volume.

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How do I calculate the volume of a water tank?

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Measure the tank and calculate the volume like a normal cylinder. If it's irregularly shaped, just fill it with water until it's full, and however much water you filled it is its volume.

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Remember the diameter is the biggest chord in a circle or in a circumference, i.e. the biggest measurement you can get between two points in a circumference or in the circle within. The edge of the circle should meet the zero mark in your ruler/flex tape, and the biggest measurement you obtain without losing contact with your zero mark will be the diameter.^{[11]
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Make up a few problems to practice so you know that you will get it right when you try it for real.

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The volume of a cylinder is given by the formula V = πr²h, and π is about the equivalent of 22/7 or 3.14.

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