Cube Root Calculator
Find the cube root of any number, positive or negative, and see whether it is a perfect cube.
How it works
cube root of n = the value x such that x³ = n · for negatives, ∛n = −∛|n|
The cube root of n is the number that, multiplied by itself three times, gives n. Unlike square roots, cube roots are defined for negative numbers too, because a negative times a negative times a negative is negative — so the cube root of −8 is −2, a real answer. A number is a perfect cube when its cube root is a whole number, as with 1, 8, 27, 64 and 125.
Worked example
The cube root of 27 is 3, because 3 × 3 × 3 = 27 — a perfect cube. For a negative input, the cube root of −27 is −3, since (−3)³ = −27. Cubing the original 27 gives 27³ = 19,683.
Sources: Cube root — Wikipedia
Frequently asked questions
Can you take the cube root of a negative number?
Yes. Every real number has exactly one real cube root, and it keeps the sign of the number: ∛−64 = −4. This is different from square roots, which have no real value for negatives.
What is a perfect cube?
A whole number whose cube root is also a whole number. The first few are 1, 8, 27, 64, 125 and 216 — the cubes of 1 through 6.
How is a cube root different from a square root?
A square root undoes squaring (x²) and needs a non-negative input; a cube root undoes cubing (x³) and accepts any real number. In exponent form, ∛n = n^(1/3).
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This calculator is for educational purposes. Double-check important results before acting on them.