A die and a shoebox can both look like little boxes, but they are not the same shape. So, what is the difference between a cube and a cuboid?
The easiest way to remember it is this:
Here’s the interesting part: every cube is a cuboid, but not every cuboid is a cube.
Cube vs Cuboid: Quick Comparison
| Feature | Cube | Cuboid |
|---|---|---|
| Face shape | 6 equal squares | 6 rectangles |
| Edge lengths | All 12 are equal | Opposite edges are equal; dimensions may differ |
| Dimensions | Length = width = height | Length, width, and height can differ |
| Faces | 6 | 6 |
| Edges | 12 | 12 |
| Vertices | 8 | 8 |
| Example | Die, ice cube, Rubik’s Cube | Brick, book, shoebox |
| Volume | a³ | l × w × h |
What Is a Cube?
A cube is a three-dimensional solid with six equal square faces.
Every edge of a cube has the same length. That means its length, width, and height are equal.
For example, if a cube has an edge of 4 cm:
A die, an ice cube, and a Rubik’s Cube are familiar examples.
Cube volume
If the edge length is a, its volume is:
For a cube with a 4 cm edge:
What Is a Cuboid?
A cuboid is a three-dimensional solid with six rectangular faces.
Unlike a cube, its three dimensions do not have to be equal.
For example, a box measuring:
is a cuboid because its length, width, and height are different.
Common examples include books, bricks, cereal boxes, and shoeboxes.
Cuboid volume
For a cuboid:
So, for the 8 cm × 5 cm × 3 cm box:
Is a Cube a Cuboid?
Think of a cuboid as the bigger category. A cuboid can have different dimensions, but when all three dimensions become equal, something special happens: the cuboid becomes a cube.
For example:
→ cuboid
→ cuboid
→ cube
It is similar to the relationship between a square and a rectangle: a square has the extra condition that all its sides are equal.
Cube vs Cuboid Formulas
| Measurement | Cube | Cuboid |
|---|---|---|
| Volume | a³ | l × w × h |
| Total surface area | 6a² | 2(lw + wh + hl) |
| Space diagonal | a√3 | √(l² + w² + h²) |
For a cuboid, you generally need three measurements.
A Common Mistake
A student sees a shape with a square face and immediately calls it a cube.
A cuboid can have two square faces when two of its dimensions are equal. For example, a solid measuring 5 × 5 × 8 is still a cuboid—not a cube.
To call it a cube, all three dimensions must be equal.
Quick memory trick
If length = width = height, you have a cube.
If the dimensions can differ, you have a cuboid.
Can You Spot the Shape?
Try these:
Answer: Cube
Answer: Cuboid
Answer: Cuboid
