What this calculator does
A perfect cube is a number that comes from cubing a whole number: 1, 8, 27, 64 and 125 are perfect cubes because they equal 1³, 2³, 3³, 4³ and 5³. This calculator checks whether a given number is a perfect cube, shows its cube root, and finds the nearest perfect cubes on either side when it is not.
A perfect cube is the cube analogue of a perfect square, but with one difference worth knowing: negative numbers can be perfect cubes, since a negative number cubed stays negative. −8 is a perfect cube because (−2)³ = −8, whereas negative numbers can never be perfect squares.
The formula
Take the cube root of the number. If that cube root is a whole number (positive, negative or zero), the original number is a perfect cube. When it is not, the calculator rounds down and up to the nearest whole cube roots and cubes each of those to show the nearest perfect cubes below and above the number entered.
| Term | Meaning |
|---|---|
| Perfect cube | A number equal to n³ for some whole number n. |
| Cube root (∛x) | The number that, when cubed, gives x. Written ∛x. |
| n³ | n multiplied by itself three times: n × n × n. |
The inputs explained
| Field | What to enter |
|---|---|
| Number | The number to test. Can be positive, negative or zero, and does not need to be a whole number. |
When to use it
Checking a homework or exam answer
Confirming that a claimed cube root is exact, or finding the closest perfect cube when it is not, is a quick sanity check before moving on to a bigger problem.
Working with cube-based volumes
If a cube-shaped container’s volume is known and the side length needs to come out as a whole number, checking whether that volume is a perfect cube confirms it before cutting material.
Exploring number patterns
Listing the sequence of perfect cubes (1, 8, 27, 64, 125, …) and seeing how the gap between consecutive cubes grows is a common way to build intuition about cubic growth.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Which numbers near 10 to 125 are perfect cubes?
Testing a run of numbers shows how rare exact cubes are compared with the numbers around them.
| Number | Is it a perfect cube? | Cube root |
|---|---|---|
| 10 | No | 2.154 (not a whole number) |
| 20 | No | 2.714 (not a whole number) |
| 27 | Yes | 3 |
| 50 | No | 3.684 (not a whole number) |
| 64 | Yes | 4 |
| 100 | No | 4.642 (not a whole number) |
| 125 | Yes | 5 |
Questions
Can a negative number be a perfect cube?
Yes. Unlike perfect squares, which are always non-negative, a negative number cubed stays negative, so numbers like −8 (= (−2)³) and −64 (= (−4)³) are perfect cubes.
Is 1 a perfect cube?
Yes, since 1³ = 1. Likewise 0 is a perfect cube, since 0³ = 0.
How is a perfect cube different from a perfect square?
A perfect square is n² for a whole number n and is always zero or positive. A perfect cube is n³ and can be positive, negative or zero. See the perfect square calculator for the squared version.
What is the cube root of a number that is not a perfect cube?
It is an irrational number that cannot be written exactly as a simple decimal or fraction, such as the cube root of 100, which is approximately 4.642. The calculator shows this decimal approximation alongside the nearest exact cubes.
For the squared equivalent of this check, see the perfect square calculator. For roots and powers more generally, see the exponents and roots calculator.