Cube Surface Area Calculator

This cube surface area calculator not only gives you the surface area of a cube but also allows you to do further calculations. Just enter one known value - whether it's the edge length, total area, or side area, volume, or space diagonal - and the others will be calculated automatically.

After entering a value and selecting the unit, all other results are shown automatically with the total surface area highlighted as the most important result.

What is the surface area of a cube?

A cube is a three-dimensional shape with six identical square faces, twelve equal-length edges and eight corners. Because all of the interior angles are right angles, cubes are useful for objects like ice cubes, dice or shipping containers where all sides have the same length. The surface area is the total area of all the flat sides of the cube, so it's the sum of the areas that would be covered by paint or wrapping paper. Since it's a two-dimensional measurement, it's expressed in square units such as square centimeters or square inches.

Since all six faces are the same size, the surface area can be calculated directly from the edge length. The area of a single side is the product of the edge length with itself, and when this area is added six times, it results in the total area.

Total area and side surface

There are two types of surface area worth knowing, and this tool calculates both. The total surface area (TSA) counts all six faces. The lateral surface area (LSA) is all the area around the sides, excluding the top and bottom. This is useful for things like wrapping the sides of a box or painting the walls of a cubic room without the floor and ceiling.

As both forms are based on the same square area, the lateral surface is always two thirds of the total surface, while the total surface is one and a half times the lateral surface. Here "a" stands for the length of a side.

How to use this calculator:

Enter the available measurement values i.e. side length, surface area, volume or space diagonal into the corresponding fields and select a unit such as centimeters or inches. Once you have entered one value, the tool will automatically calculate the other values and display the total surface area as the main result. It is not necessary to specify the type of measurement value that has been entered. If you want to start over with another measurement value, simply delete the previously entered fields and enter new values. The graph options allow you to see how the surface area and volume change at different rates when the side length changes.

Formula for surface area of a cube:

All properties of a cube are determined by its side length. The square of the side length gives the area of one face, and all other values are based on this squared value.

The Pythagorean theorem is used to calculate the diagonals. The face diagonals run across one side of the square, while the space diagonal runs from a corner point through the center of the cube to the opposite corner point.

To calculate the side length from the total area, first divide by six and then take the square root.

Example calculation:

Consider a cube with sides of length 6 centimeters. Squaring the side length gives an area of one face as being 36 square centimeters, which is then multiplied by the number of faces.

The area covered by four sides is therefore 144 square centimeters, while the area covered by all six sides is 216 square centimeters. The volume of the same cube is 6 to the third power, or 216 cubic centimeters. The face diagonals measure approximately 8.49 centimeters, and the space diagonals measure approximately 10.39 centimeters. If you use this calculator, all you have to do is enter the value of 6 in the field for side length to get these results directly.

List of all measured values for the cube:

Each measurement of a cube interacts with other measurements through the length of its sides. This table summarizes the relationships used in the calculator so that you can calculate any one value from another.

Surface corresponding to typical edge lengths:

The following table shows some examples of the total area corresponding to different typical side lengths. The results are rounded to two decimal places. Note that as the side length increases, the area grows very quickly since it is squared.

Why surface area becomes less important as a cube gets larger:

Since the surface area depends on the square of the length of an edge and the volume on its cube, as a cube gets larger the volume grows faster than the surface area. If the length of an edge is doubled, then the surface area becomes four times greater while the volume becomes eight times greater.

This surface-area-to-volume ratio can explain many real-world phenomena. A small ice cube melts faster than a larger one because it has more surface area relative to its volume. Cells keep their volume small so that they can efficiently transport nutrients from the outside into the inside of the cell. Engineers use this same principle when designing heat sinks and packaging.

Applications for the surface of a cube.

Cubes and cube-shaped boxes are found everywhere, so this calculation is used in many fields. Packaging designers use it to determine the amount of cardboard and printing materials needed for a package. Painters and interior decorators estimate the amount of paint required to cover rooms or columns with cubic structures. Manufacturers calculate the cost of coating or plating metal blocks. Teachers and students use the cube as a starting point to understand the surface area of all other solids.

Tips for accurate results:

Measure the length of one side carefully. Since a cube has all sides equal, measuring one side will allow you to determine the length of all sides. Be sure to use consistent units of measurement. If you measure the length in centimeters, for example, that means your surface area will be in square centimeters and volume will be in cubic centimeters. Note that small errors in measuring lengths will lead to larger errors in the surface area and volume.