Cylinder Calculator

Please enter ANY TWO of the following

Radius $\hspace{0.2em} \hspace{0.15em} (r) \, = \, \hspace{0.2em}$

Height $\hspace{0.2em} \hspace{0.15em} (h) \, = \, \hspace{0.2em}$

Volume $\hspace{0.2em} \hspace{0.15em} (V) \, = \, \hspace{0.2em}$

Cylinder Type☝️

Please provide your input and click the calculate button

About the Cylinder Calculator

This cylinder calculator can calculate the volume or surface area of a solid or hollow cylinder for you. You may choose from different combinations of values to input.

Also, the calculator will tell you not just the volume/surface area, but also how to calculate it.

Usage Guide

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i. Valid Inputs

Each of the inputs provided must be a non-negative real number. In other words, the input must be 0 or greater. Here are a few examples.

Whole numbers or decimals → $\hspace{0.2em} 2 \hspace{0.2em}$ , $\hspace{0.2em} 4.25 \hspace{0.2em}$ , $\hspace{0.2em} 0 \hspace{0.2em}$ , $\hspace{0.2em} 0.33 \hspace{0.2em}$
Fractions → $\hspace{0.2em} 2/3 \hspace{0.2em}$ , $\hspace{0.2em} 1/5 \hspace{0.2em}$
Mixed numbers → $\hspace{0.2em} 5 \hspace{0.4em} 1/4 \hspace{0.2em}$

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of what a cylinder is and a few different concepts related to the shape.

Cylinder — The Basics

A cylinder is one of those solid shapes you see almost everywhere. Still, let me give you an example of what it looks like.

So you have two circular and parallel surfaces (bases) joined by a uniform circular cross-section - all of the same radius.

Volume and Surface Area of a Cylinder — Formulas

A labeled diagrab of a cylinder showing its surfaces — A cylinder

For a cylinder with a radius $\hspace{0.2em} r \hspace{0.2em}$ and height $\hspace{0.2em} h \hspace{0.2em}$ , the volume is given by

V = \pi r^2 h

And its surface area would be

\begin{align*} S \hspace{0.25em} &= \hspace{0.25em} 2 \pi r h + 2 \pi r^2 \\[1em] &= \hspace{0.25em} 2 \pi r (h + r) \end{align*}

Volume and Surface Area of a Hollow Cylinder

From a solid cylinder, if you cut out a cylinder with a smaller radius (but with the same axis), you get a hollow cylinder.

A labeled hollow cylinder — A hollow cylinder

Now, for a hollow cylinder with a height $\hspace{0.2em} h \hspace{0.2em}$ and internal and external radii $\hspace{0.2em} r \hspace{0.2em}$ and $\hspace{0.2em} R \hspace{0.2em}$ , the volume would be,

V = \pi (R^2 - r^2) h

As you can see, the volume of a hollow cylinder is the difference in volumes of the outer and inner cylinders.

When it comes to the surface area of a hollow cylinder, we must add the areas of its four surfaces —

inner and outer curved surfaces, $\hspace{0.2em} 2 \pi r h + 2 \pi R h \hspace{0.2em}$
two flat rings on the two ends, $\hspace{0.2em} 2 \pi (R^2 - r^2) \hspace{0.2em}$

So,

\begin{align*} S \hspace{0.25em} &= \hspace{0.25em} 2 \pi r h + 2 \pi R h \hspace{0.25em} + \hspace{0.25em} 2 \pi (R^2 - r^2) \\[1em] &= \hspace{0.25em} 2 \pi (R + r) (h + R - r) \end{align*}

Examples

Example

Calculate the volume of a cylinder with a radius of $\hspace{0.2em} 2 \text{ cm} \hspace{0.2em}$ and height of $\hspace{0.2em} 5 \text{ cm} \hspace{0.2em}$ .

Solution

The formula for a cylinder's volume is

V \hspace{0.25em} = \hspace{0.25em} \frac{4}{3} \pi r^2 h

Substituting the values of $\hspace{0.2em} r \hspace{0.2em}$ and $\hspace{0.2em} h \hspace{0.2em}$ , we have

\begin{align*} V \hspace{0.25em} &= \hspace{0.25em} \frac{4}{3} \pi \cdot 2^2 \cdot 5 \\[1em] &= \hspace{0.25em} 83.77 \end{align*}

So the volume of the cylinder is $\hspace{0.2em} 83.77 \text{ cm}^3 \hspace{0.2em}$ .

Example

Calculate the curved and total surface areas of a cylinder with a radius of $\hspace{0.2em} 1 \text{ in} \hspace{0.2em}$ and height of a cylinder $\hspace{0.2em} 4 \text{ in} \hspace{0.2em}$ .

Solution

The curved surface area of a cylinder is given by the formula

A_c \hspace{0.25em} = \hspace{0.25em} 2 \pi rh

Substituting the values of $\hspace{0.2em} r \hspace{0.2em}$ and $\hspace{0.2em} h \hspace{0.2em}$ , we have

\begin{align*} A_c \hspace{0.25em} &= \hspace{0.25em} 2 \pi rh \\[1em] &= \hspace{0.25em} 25.13 \end{align*}

Next for the total surface area, we can either add the area of the two flat surfaces to the curved surface area or just use the formula for total surface area. We'll go ahead with the second approach.

\begin{align*} A \hspace{0.25em} &= \hspace{0.25em} 2 \pi r (r + h) \\[1em] &= \hspace{0.25em} 2 \pi \cdot 1 \cdot (1 + 4) \\[1em] &= \hspace{0.25em} 31.4 \end{align*}

So, the curved and total surface areas of the cylinder are $\hspace{0.2em} 25.13 \text{ in}^2 \hspace{0.2em}$ and $\hspace{0.2em} 31.4 \text{ in}^2 \hspace{0.2em}$ respectively.