How to find surface area of a cube

The only regular hexahedron, a cube is a three-dimensional object with six equal-sized square surfaces or sides, 12 edges, and 8 vertices. Given that its square sides are equal, it follows that a cube’s length, width, and height are equal, too. Examples of cube-shaped objects are dice, jewelry boxes, ice cubes, sugar cubes, and Rubik’s cubes.

Here’s an illustration of a cube. Notice how it forms 6 equal square surfaces or sides when unfolded. The resulting two-dimensional shape when a cube is unfolded is called the cube’s net. 

How to Find the Surface Area of a Cube:

Recall that the surface area of a three-dimensional figure refers to the total area occupied by the figure’s surface. To better understand surface area, look at the net or the flat layout of the cube in the illustration below. 

The surface area of a cube is the sum of all the areas of its 6 square sides. Recall that the area of a square is computed by multiplying the length of each side (a) by itself: a • a  or a². Just multiply the area of a square side by 6 and you’ll have the cube’s surface area.

Use this formula to find the total surface area of a cube: SA = 6a²
where a = length of the cube’s one side and a² = area of one square side of the cube.

Note: Don’t forget that surface areas are measured in square units such as cm2, m2, km2, and in2.

Quick Guide to Finding the Surface Area of a Cube:

Step 1. Write the given figures. You’ll need the length of the cube’s side to find the surface area. Make sure all measurement units are the same. If not, convert either of them to match the other. 

Step 2. Plug the figures into the formula.

Step 3. Perform the operations. Don’t forget to write the square unit for surface area.

Example #1:

Find the surface area of the cube below.

Solution for Example #1:

Step 1. Write the given measurement, a = 8m.
Step 2. Substitute 8m for a in the formula for the surface area.
SA = 6a²
SA = 6(8m)²
Step 3. Simplify & solve the equation.
SA = 6(64m²)
SA = 384m²

Therefore, the surface area is 384m².

Want to learn how to find the volume of this cube?
Related Reading: Volume of a Cube – Formula & Examples

Example #2:

Find the surface area of a cube with a length of 4m.

Step 1. Write the given measurement, a = 4m.
Step 2. Substitute 4m for a in the formula for the surface area.
SA = 6a²
SA = 6(4m)²
Step 3. Simplify & solve the equation.
SA = 6(16m²)
SA = 96m²

Therefore, the surface area is 96m².

Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the surface area of a cube.

Learning how to find the surface area of a cube and how to apply the surface area of a cube formula is a critical and important math/geometry skill that every student should master. Fortunately, calculating the area of a cube is a pretty straightforward task as long as you are able to follow three simple steps for finding the surface area of any cube that are demonstrated in this lesson.

Are you ready to get started?

The following free How to Find the Surface Area of a Cube lesson guide is a step-by-step tutorial that will teach you how to use a simple method for calculating the surface area of a cube using the surface area of a cube formula to solve homework problems, test questions, and more.

This guide also includes a completely free surface area of a cube calculator that can be used to make fast calculations and find the surface area of a cube almost immediately (and while we do not recommend relying on a calculator to solve surface area problems, having access to a calculator can be a very helpful tool when it comes to checking your work—but more on that later!)

Now we are ready to learn how to find the surface area (sometimes referred to as SA) of a cube and we will start with a quick recap of some very important vocabulary and definitions.

In math, what is a cube?

Definition: A cube is a box-shaped three-dimensional figure that has six equal and identical square faces.

The most important word in this definition is equal. A cube is unique in that all of its faces are squares with side lengths, also known as edges, that have the same length (unlike rectangular prisms).

Also make a note that the terms cube and rectangular cube both mean the exact same thing (some questions will refer to a cube as a rectangular cube).

What is the surface area of a cube? What is the SA of a cube?

Definition: The surface area of a cube refers to the total area of all of the faces on the outside of the figure.

The key word in this definition is outside since surface area refers to how many square units it would take to cover the outside of the figure

Surface area is always expressed in square units.

Surface Area of a Cube Formula

Before we get to the practice problems, you need to understand how to use the surface area of a cube formula, which states that the SA of a cube is equal to six times the side length, s, raised to the second power (also known as squared).

If you know the length of one of the edge lengths (or sides), you can simply input the value into the formula and solve to find the surface area.

 Again, remember that SA is measured in square units and that your answers should always include units.

Formula Reference:

Now that you know the surface area of a cube formula, you can use the following 3-step method to solve the practice problems below:

Step 1: Identify the value of s, the edge length of the cube

Step 2: Substitute that value for s into the surface area of a cube formula

Step 3: Solve and express your answer in square units

Example #1: Find the Surface Area of the Cube

Find the surface area of a cube with a side length of 4 cm.

To solve this problem, we will use the previously mentioned 3-step process:

Step 1: Identify the value of s, the edge length of the cube

In this example, the cube has a side length of 4 cm, so S=4

Step 2: Substitute that value for s into the surface area of a cube formula

Next, substitute 4 for s in the SA of a cube formula as follows

SA = 6(s^2) ➝ SA= 6(4^2) ➝ SA = 6(16) ➝ SA = 96

Step 3: Solve and express your answer in square units

Finally, you can conclude that SA equals 96, therefore…

Final Answer: The surface area of the cube is 96 square centimeters.

Remember that surface area is always expressed in square units (square centimeters in this example).

Example #2: Find the SA of the Cube

Find the SA of a cube-shaped box with a height of 9 inches.

In this example, the figure in question is a cube-shaped box or just a cube, so you will be using the process as Example #1 to find the surface area:

Step 1: Identify the value of s, the edge length of the cube

In this example, the cube-shaped box has a side length of 9 inches, so S=9

Step 2: Substitute that value for s into the SA of a cube formula

Next, substitute 9 for s in the SA of a cube formula as follows

SA = 6(s^2) ➝ SA= 6(9^2) ➝ SA = 6(81) ➝ SA = 486

Step 3: Solve and express your answer in square units

Finally, you can conclude that SA equals 486, therefore…

Final Answer: The SA of the cube is 486 square inches

How to Find the Surface Area of a Cube Video

Are you looking for more help with finding the volume and surface area of cubes? Check out our free step-by-step video lesson below:

Surface Area of a Cube Calculator

If you want to use a surface area of a cube calculator to help you when solving SA problems, we recommend Google’s free Surface Area of a Cube Calculator, which allows you to input the edge length (which they refer to as a instead o s) and find the SA with just one click.

Keep in mind that relying on a calculator is never a substitute for learning how to solve problems on your own. However, there are occasions when such a tool can come in handy, like when you want to check your final answers.

(Note: Google’s calculator uses the letter a, not s, to represent the value of the edge length.)

What About the VOLUME of a Cube?

Now that you’ve learned how to find the surface area of a cube, you’re ready to move on to learning how to use a different formula to find the volume of a cube.

How do you find the surface area?

What is the surface area of a 3x3 cube?