Enter a number to find its cube root instantly. The calculator accepts positive, negative, and decimal values, and you can change the index to calculate another root.
Cube Root Calculator
Cube root and roots of any index
The default index is 3. Use 2 for a square root or another positive integer for an nth root.
How to use the calculator
- Enter the value whose root you want to calculate.
- Keep the index at 3 for a cube root, or enter another positive integer.
- Select Calculate root to see the result.
- Select Clear to start a new calculation.
What is a cube root?
The cube root of a number a is the value x such that x³ = a. In other words, x multiplied by itself three times equals a. It is written as ∛a or a^(1/3).
Unlike a square root, a cube root exists in the real numbers for every negative value: for example, ∛−8 = −2 because (−2)³ = −8.
Cube root formula
A cube root is a fractional power. More generally, an nth root uses the exponent 1/n:
∛a = a1/3 · ⁿ√a = a1/n
Cube root examples
| Number (a) | Cube root (∛a) | Check |
|---|---|---|
| 1 | 1 | 1³ = 1 |
| 8 | 2 | 2³ = 8 |
| 27 | 3 | 3³ = 27 |
| 64 | 4 | 4³ = 64 |
| 125 | 5 | 5³ = 125 |
| −8 | −2 | (−2)³ = −8 |
| −27 | −3 | (−3)³ = −27 |
Frequently asked questions about cube roots
What is the cube root of a number?
It is the value x whose cube equals the original number. For example, ∛27 = 3 because 3 × 3 × 3 = 27.
Does a negative number have a cube root?
Yes. Every negative real number has a negative real cube root, such as ∛−8 = −2.
How can I calculate a cube root by hand?
For a perfect cube, identify the integer whose third power gives the number. For other values, use a^(1/3) or a numerical approximation.
What is the difference between a square root and a cube root?
A square root is a value multiplied by itself twice; a cube root is multiplied by itself three times. Cube roots of negative numbers are real, while square roots of negative numbers are not real.
Can this calculator find roots other than cube roots?
Yes. Change the root index: use 2 for a square root, 4 for a fourth root, and so on.
See also…
