How to Calculate the Volume of a Cylinder

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Easy formulas & practice problems for finding the volume of a cylinder
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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]

Volume of a Cylinder Formula

To find the volume of a cylinder, use the formula Volume = π • r 2 • h , where r is the radius of the base and h is the height of the cylinder. You can also use the formula Volume = A • h if you already know the area of the base.

Help Finding the Volume of a Cylinder

Method 1
Method 1 of 2:

Calculating the Volume of a Cylinder

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  1. Find the radius of the circular base. [2] 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 (the diameter) and then divide it by 2. 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]
    • If you know the circumference, then you can divide it by 2π to get the radius. [4]
  2. Calculate the area of the circular base . [5] To do this, just use the formula for finding the area of a circle, A = πr 2 . [6] Just plug the radius you found into the equation. Here's how to do it:
    • A = π x 1 2
    • 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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  3. [7] 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.
  4. Multiply the area of the base by the height. [8] 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]
    • Always state your final answer in cubic units because volume is the measure of a three-dimensional space. [10]
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Method 2
Method 2 of 2:

Example Practice Problems

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  1. 1
    Example 1: Find the volume of a cylinder with a radius of 3 cm and a height of 20 cm.
    • Identify values to plug into the formula Volume = π • r 2 • h
      • r = 3 and h = 20
    • Solve for volume!
      • V = π • r 2 • h
      • V = π • 3 2 • 20
      • V = 3.14 • 9 • 20
      • V = 565.49 cm 3
  2. 2
    Example 2: Find the volume of a cylinder with an area of 78.5 cm 2 and height of 12 cm.
    • Let's start by identifying values we'll substitute for variables in the volume equation. Since we’re given area, we can use the formula Volume = A • h where A is the area of the base and h is height.
      • A = 78.5 and h = 12
    • Plug your values in and solve:
      • V = A • h
      • V = 78.5 • 12
      • V = 942 cm 3
  3. 3
    Example 3: Find the volume of a cylinder with a diameter of 24cm and height of 30cm.
    • Identify the values to plug into the formula Volume = π • r 2 • h
      • Since we are given diameter and not radius, we can divide the diameter by 2 to get the radius. Because 24 / 2 is 12, r = 12. We are already given height (h = 30).
    • Plug your variables in and solve:
      • V = π • r 2 • h
      • V = π • 12 2 • 30
      • V = 3.14 • 144• 30
      • V = 13564.8 cm 3
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  • Question
    How do I calculate the length of the radius?
    Community Answer
    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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  • Question
    How can I find a cylinder's volume when I know height and diameter?
    Community Answer
    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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  • Question
    How do I calculate the volume of a water tank?
    Community Answer
    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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      Tips

      • 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 = πr 2 h, and π is about the equivalent of 22/7 or 3.14.
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      • To approximate the area of a circle, square its diameter, then multiply that by .7854. It's not precise, but it helps in a pinch.
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      References

      1. ↑ https://www.mathsisfun.com/definitions/cylinder.html
      2. ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
      3. ↑ https://www.mathsisfun.com/definitions/radius.html
      4. ↑ https://www.mathsisfun.com/definitions/pi.html
      5. ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
      6. ↑ https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-circumference-circle/v/area-of-a-circle
      7. ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
      8. ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
      9. ↑ https://www.mathopenref.com/cylindervolume.html
      1. ↑ https://www.mathsisfun.com/definitions/volume.html
      2. ↑ https://www.cut-the-knot.org/pythagoras/Munching/DiameterChord.shtml

      About This Article

      Article Summary X

      1. Measure the circular base to get the diameter.
      2. Divide the diameter by 2 to get the radius.
      3. Calculate the area with the formula: A = πr^2, where r is the radius.
      4. Measure the height of the cylinder.
      5. Multiply the area by the height to get the Volume.

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