Cube with side, face diagonal and cube diagonal marked.
Side (a)
Cube diagonal (d)
Face diagonal (f)
cu in
Surface area

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
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