How to Find the Radius of a Cylinder When Given the Volume and Height

By Tim Banas
A cylinder is a rod-shaped object with circular ends.

A cylinder is a three-dimensional object that looks like a rod with circular ends. The radius of a cylinder is the distance from the center of one of the circular faces to its edge. If you know the volume and the height of a cylinder, you can find its radius by using the formula for the volume of a cylinder.

Know the Formula for the Volume of a Cylinder

The formula for the volume of a cylinder contains three elements: the radius of the cylinder (r), the height (h) of the cylinder, and the ratio of the circumference of a circle to its diameter pi. To find the volume of a cylinder, you multiply pi by the cylinder's height and the square of its radius. Here is the formula in mathematical terms:

V = pi x h x r^2

Solve for the Radius (r)

Since you want to find the radius of the cylinder, you need to rearrange the formula to solve for the term r, which is the radius. First, divide both sides by pi and h. These terms will cancel on the right side of the equation, leaving only r^2. Now take the square root of both sides to get rid of the square on the radius. This leaves us with the following:

r = square root of (V / (pi x h))

Plug in the Values for Height (h) and Volume (V) and Calculate

Now just plug your numbers into the equation and compute the radius. For example, if your cylinder has a height of 10 centimeters and a volume of 30 cubic centimeters, the calculation would look like the following:

r = square root of (30 cm^3 / (3.14 x 10 cm)) = 0.98 cm


Remember: pi is always equal to approximately 3.14.

Always remember to include your units in your calculations and especially in your answer.

About the Author

Tim Banas started writing professionally in 2009 after teaching high school science for seven years. He has since written and edited for various online publications including Demand Studios,, and He has a Master of Science in biology from Southern Illinois University.