Cube Root Calculator
The cube root of a number x is the value that, when multiplied by itself three times, equals x. This calculator finds the cube root of any real number, positive or negative. Unlike square roots, cube roots are defined for negative numbers. For example, the cube root of -8 is -2, because (-2)^3 = -8. The calculator displays the result in decimal form and in simplified radical form. For example, the cube root of 54 simplifies to 3 times the cube root of 2 (3∛2). Cube roots are useful in geometry (calculating the side length of a cube from its volume), algebra (solving cubic equations), and physics (understanding scaling relationships in three-dimensional space).
Cube root formula
∛x = number that, when multiplied by itself 3 times, equals x
If a^3 = x, then a = ∛x
∛x = x^(1/3)
Cube roots of negative numbers: ∛(-x) = -∛x
Perfect cubes reference
| Number | Cube | Number | Cube |
|---|---|---|---|
| 1 | 1 | 11 | 1,331 |
| 2 | 8 | 12 | 1,728 |
| 3 | 27 | 13 | 2,197 |
| 4 | 64 | 14 | 2,744 |
| 5 | 125 | 15 | 3,375 |
| 6 | 216 | 20 | 8,000 |
| 7 | 343 | 25 | 15,625 |
| 8 | 512 | 30 | 27,000 |
| 9 | 729 | 50 | 125,000 |
| 10 | 1,000 | 100 | 1,000,000 |
Cube root calculator: frequently asked questions
What is a cube root?
The cube root of a number x is the value that, when multiplied by itself three times, equals x. For example, the cube root of 8 is 2, because 2 × 2 × 2 = 8. The cube root is written as cbrt(x) or as the radical sign: ∛x.
Can you take the cube root of a negative number?
Yes, unlike square roots, cube roots are defined for negative numbers. For example, the cube root of -8 is -2, because (-2) × (-2) × (-2) = -8. Every real number, positive or negative, has exactly one real cube root.
What is the cube root of zero?
The cube root of zero is zero. 0 × 0 × 0 = 0, so cbrt(0) = 0.
What is a perfect cube?
A perfect cube is a number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because 3^3 = 27. The first few perfect cubes are 1, 8, 27, 64, 125, 216, and so on.
How do you simplify a cube root?
To simplify a cube root, factor out perfect cubes. For example, cbrt(54) = cbrt(27 × 2) = 3 × cbrt(2). This works because 27 = 3^3 is a perfect cube, so cbrt(27) = 3.
Official sources
- Cube roots: NIST Special Publication 330.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.