Cube Calculator

By Hanna Pamuła, PhD candidate
Last updated: Jan 05, 2021

Our cube calculator can help you find all the cube parameters. Whether you want to determine the volume of a box or check the area of a die, this flexible tool is the thing you're looking for. Type in one parameter out of five - cube volume, cube surface area, face diagonal, cube diagonal or cube side - and, in a blink of an eye, we will show you the rest. Give it a go! If you are still unsure how to find the volume of a cube formula, keep scrolling to the description part where we will explain everything in detail.

Cube and the others

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,
  • 8 vertices.

Cube surface area

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 where a is the length of one edge, so the cube surface area equation is:

surface_area = 6 * a²

Cube volume formula

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 , and our height also equals a as all edges are the same. So we got the same formula - - as expected.

Cube diagonals - face and space

Cube with side, face diagonal and cube diagonal marked.

If you are wondering how to find the cube diagonals, think for a while about diagonal of a square. The formula for square diagonal is the side length multiplied by square root of 2, and it comes from 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 side length times square root of 3.

How to find the volume of a cube?

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!

Hanna Pamuła, PhD candidate
Cube with side, face diagonal and cube diagonal marked.
Side (a)
in
Cube diagonal (d)
in
Face diagonal (f)
in
Volume
cu in
Surface area
in²
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