Cube Calculator

Let's start from the beginning - what's a cube? It's a 3D solid object bounded by six square faces with three faces meeting at each vertex. It's a regular square prism in three orientations. The cube is the only regular hexahedron, and it has

• 6 faces;
• 12 edges; and
• 8 vertices.

Are you interested in a rectangular prism calculator? We have just the tool for you.

The formula for the cube surface area is really easy - it's the area of one face times 6, as every cube has six identical square faces. The area of a square is equal to a² where a is the length of one edge, so the cube surface area equation is:

surface_area = 6 × a²

To calculate the cube volume, raise the edge length to the third power:

volume = a³

You can think about the volume of a cube formula as calculating any other prism volume - simply multiply the base area times height of the solid. Our base is a square, so its area is a², and our height also equals a as all edges are the same. So we got the same formula - a³ - as expected.

If you are wondering how to find the cube diagonals, think about the diagonal of a square for a while. The formula for square diagonal is the side length multiplied by square root of 2, and it comes from the Pythagorean theorem:

face diagonal = √(a² + a²) = √2a² = a√2 - it's our cube × face diagonal*

For cube diagonal, all you need to do is to use the Pythagorean theorem once more:

cube diagonal = √((a√2)² + a²) = √3a² = a√3

So the diagonal of the cube is equal to the length of the side times the square root of 3.

Are you interested in learning more about the Pythagorean theorem? Visit our pythagorean theorem calculator.

Let's calculate the volume of a Rubik's cube:

1. Enter the known value. In our case, we know that a standard Rubik's Cube measures 5.7 centimeters (2 1⁄4 in) on each side.
2. Wow, that was quick! All the other parameters appear. Thanks to the cube calculator, we have just learned that:

• Volume is 11.4 cu in.
• Surface area is 30.4 in².
• Cube diagonal is 3.9 in.
• Face diagonal is 3.18 in.

Now, try a small task to check the flexibility of our tool: imagine you have one gallon of water and you want to pour it into a cubic tank. You can use this cube calculator to check how big it needs to be!

If you are interested in learning more about calculating surface area you should check out our [surface area of a cube calculator].(calc:1934)