Cube Root Calculator — find ∛x

How it works

The cube root of x is the number that cubes to give x — the reverse of raising to the third power. Written ∛x (or x^(1/3)), it answers "what number, times itself three times, equals this?":

∛x = a where a × a × a = x

A key difference from the square root: because cubing keeps the sign (a negative cubed stays negative), every real number has exactly one real cube root, positive or negative. Perfect cubes — 1, 8, 27, 64, 125, … — have whole-number roots; other numbers give irrational ones.

Worked example

Find ∛27. Ask which number cubed makes 27 — that's 3, since 3 × 3 × 3 = 27. For a negative input, ∛−8 = −2, because (−2) × (−2) × (−2) = −8. And a number that isn't a perfect cube, like ∛100 ≈ 4.6416, gives an irrational root you can check by cubing: 4.6416³ ≈ 100.

Frequently asked questions

How do I find a cube root?

For a perfect cube, find the whole number that cubes to it (∛64 = 4 since 4³ = 64). Otherwise the root is irrational and you estimate or compute it — ∛50 is between ∛27 = 3 and ∛64 = 4, working out to about 3.68. This calculator computes it to several decimals.

Can you take the cube root of a negative number?

Yes — this is the big difference from square roots. Since a negative number cubed is still negative ((−3)³ = −27), the cube root of a negative is a real negative number: ∛−27 = −3. So the calculator accepts negative inputs and returns a real answer.

How many cube roots does a number have?

Exactly **one real** cube root (unlike square roots, which have two). 8 has the single real cube root 2. (In the complex numbers there are three cube roots, but only one is real.) So there's no ± to worry about with cube roots.

What's a perfect cube?

A number that's the cube of a whole number: 1, 8, 27, 64, 125, 216, … Their cube roots are exact integers, and the negatives (−8, −27, …) are perfect cubes too. Any other number has an irrational cube root.

How is the cube root related to exponents?

The cube root is the ⅓ power: ∛x = x^(1/3). Raising to ⅓ undoes cubing (x³), because ⅓ and 3 are reciprocal exponents. More generally, the nth root is the 1/n power.

When do cube roots come up?

Most often with **volume**: if a cube has volume V, its side length is ∛V, so a cube holding 1000 cm³ has 10 cm sides. They also appear when reversing any cubic relationship — scaling, growth, and the solutions of cubic equations.