Cylinder Surface Area Calculator

This cylinder surface area calculator can calculate the surface of a cylinder and also supports reverse calculations. It uses four basic measurements: radius, height, volume, and lateral surface area.

If you input any two of these values, this tool will calculate the remaining ones and show the total surface as a result. By entering two values and selecting the unit, other measurements are automatically displayed.

What is the surface area of a cylinder?

A cylinder is a body that consists of two circular end faces of equal size and a curved side face that connects them together. The vertical distance between the two end faces is the height while the distance from the center of the end face to its edge is the radius. Cans, pipes, tanks, and rollers are examples of cylinders. The surface area is the sum of all outer surfaces or the area covered by a label, paint, or metal plate. Since this area is two-dimensional, it is measured in square centimeters or square inches.

The outside of a cylinder is made up of two parts: the curved side that wraps around the sides and the two flat circular ends that close off both ends. When you add these together, you get the total surface area.

The difference between lateral surface area and total surface area

There are two types of surface area that are worth knowing, and this tool will show you both. The lateral surface area (LSA) refers to the curved side wall only, which can be stretched out to form a rectangle. The total surface area (TSA) is the sum of the LSA and the areas of the two circular ends. Since the side wall stretches out to form a rectangle with height equal to that of the cylinder and width equal to its circumference, the area is the product of the circumference and the height.

When labelling a can or calculating the amount of metal needed to make the sides of a tank, you use the lateral surface area. When painting closed rolls including ends, or coating a solid roll, you use total surface area. Where r is the radius and h is the height.

How to use this calculator:

Enter any two of the four available measurements - radius, height, volume or lateral surface area - into their respective fields and select the unit (e.g. centimeters or inches). Once you enter the second value, the tool will automatically calculate the remaining two values and prominently display the "Total Surface Area" result. Additionally, it will show the areas of both end faces, as well as the diameter and circumference of the base. It is not necessary to specify which two values you have entered. If you want to start with a new set of data, simply leave one field blank and enter new values. By opening the visualization option, you can see how the total surface area is distributed between the curved side face and the two end faces.

Cylinders formulas:

All calculations for a right cylinder can be derived from the radius and height. The square of the radius gives the area of one circular end face, and all other values are derived from that.

Each circular end face is a regular circle whose area is equal to pi multiplied by the square of its radius. The two end faces together therefore have an area that is twice as large as this individual surface area.

Backwards calculation

Both the volume and surface area depend on both the radius and height. So any two of the four measurements are sufficient to determine the remaining quantities. The calculator re-arranges the equation algebraically but internally performs the following calculations:

Full example calculation

Let's take a cylinder with a radius of five centimeters and a height of ten centimeters. We'll first calculate the lateral surface area, which is the circumference multiplied by the height.

Then we add the two circular end surfaces to obtain the total surface area.

Thus the area marked with the curved surface covers about 314.16 square centimeters while the total outer area covers about 471.24 square centimeters. The volume of that same cylinder is pi times 25, and then again by 10, which equals approximately 785.40 cubic centimeters. The area of each end face is about 78.54 square centimeters each. With this calculator you can simply type in the values 5 and 10 into the fields for Radius and Height to get those results directly above.

List of measured values for cylinders

Any one measurement of a cylinder depends on the radius and height. This table summarizes the relationships used by the calculation tools so that you can enter any two values to calculate the remaining ones.

Total surface area of a typical cylinder

The following table shows the total surface area for some common combinations of radius and height, rounded to two decimal places. Note that the radius has a large effect on the result since both formulas for end surfaces contain the square of the radius.

Why surface area per unit volume decreases with larger cylinders

Because surface area depends on the square of length and volume depends on the cube of length, the volume of a cylinder always grows faster than its surface area. If each dimension of a cylinder is doubled, its surface area quadruples while its volume increases eightfold.

The difference is the ratio of surface area to volume. This can explain many real world phenomena. Large tanks need relatively less steel to hold a liter of liquid than small tanks do. Thin pipes have large surface area while holding little liquid, so heat escapes quickly. Cylindrical batteries or reactors are determined by this same principle for how fast they can dissipate the heat they generate.

Applications of cylinder surface area calculations

Since cylinders are found everywhere, this calculation is used in many fields. Label and packaging designers use the lateral surface area to determine the dimensions of a package that will enclose a container or bottle. Tank and vessel manufacturers estimate the amount of steel and paint needed for a closed drum using total surface area. Plumbers and HVAC engineers calculate the insulation required and heat loss for a particular piping system. Students studying cube geometry soon learn about cylinders, which is another step toward understanding the surface areas of curved surfaces.

Tips for accurate results

Measure the radius carefully. The formula for area involves squaring the radius, so small errors will be magnified. If you're measuring across a circular space, divide your measurement by two to get the radius. Be consistent with units of measure. If the radius is in centimeters, then the surface area will be in square centimeters and volume will be in cubic centimeters. While calculation tools may perform unit conversions, it's helpful to understand what each result means.