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; and
- 8 vertices.
Are you interested in a rectangular prism calculator? We have just the tool for you.
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
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
a², and our height also equals
a as all edges are the same. So we got the same formula -
a³ - as expected.
Cube diagonals - face and space
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.
How to find the volume of a cube?
Let's calculate the volume of a Rubik's cube:
- 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.
- 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)