Softonic

Cube Root Calculator

Step 1 / 3 Cube root
Next

Enter any number, positive, negative or zero, and the calculator returns its cube root (∛x) rounded to the number of decimal places you pick. Unlike a square root, every real number has exactly one real cube root, so negative inputs work too: ∛(−27) = −3. The result also tells you instantly whether your number is a perfect cube, the kind of whole-number answer you can verify by cubing it back.

How the cube root is computed

  1. 1

    Enter the number

    The value whose cube root you want. Any real number is allowed, including negatives and decimals.

  2. 2

    Choose the precision

    Pick how many decimal places to show, from a whole number up to ten digits.

  3. 3

    Read the result

    The cube root appears immediately, with a flag telling you whether the input is a perfect cube.

The formula

The cube root of a number x is the value y that satisfies y³ = x. It is written ∛x or x^(1/3):

∛x = y ⟺ y × y × y = x

Because cubing preserves sign, the cube root of a negative number is negative: ∛(−x) = −∛x. This is the key difference from square roots, which are undefined for negatives in the real numbers.

A worked example

Take x = 343. Try to find a whole number that cubes to it:

  • 6³ = 216, too small
  • 7³ = 343, exact match

So ∛343 = 7, and 343 is a perfect cube. For a non-perfect cube such as 50, the calculator computes ∛50 ≈ 3.684031, because 3.684031³ ≈ 50. You can always check a result by cubing it back and comparing to the original number.

Perfect cubes to know

n n³ ∛(n³)
1 1 1
2 8 2
3 27 3
4 64 4
5 125 5
6 216 6
7 343 7
8 512 8
9 729 9
10 1000 10

Common pitfalls

  • Confusing cube roots with square roots. ∛27 = 3, but √27 ≈ 5.196. They answer different questions.
  • Assuming negatives are invalid. They are perfectly valid for cube roots: ∛(−64) = −4.
  • Reading rounding as exact. ∛2 ≈ 1.259921 is rounded; it is irrational and never terminates. Increase the precision to see more digits.
  • Forgetting the units. If x is a volume in cubic metres, ∛x is a length in metres, useful for sizing the edge of a cube.

Cube root identities

  • ∛(ab) = ∛a × ∛b
  • ∛(a/b) = ∛a / ∛b (for b ≠ 0)
  • (∛a)³ = a for every real a
  • ∛(a³) = a, including negative a

Frequently Asked Questions

Yes. Every real number has exactly one real cube root, and for negatives it is negative. For example, ∛(−125) = −5, because (−5) × (−5) × (−5) = −125.

A number is a perfect cube if its cube root is a whole number. The calculator checks this for you and labels the result as a perfect cube when it is exact, such as 8, 27, 64 or 1000.

A square root asks which number multiplied by itself gives x (y² = x); a cube root asks which number multiplied by itself three times gives x (y³ = x). Square roots are undefined for negatives in the reals, but cube roots are defined for every real number.

The number you enter is sent to the server only to compute the result and is not stored. When you use the step-by-step view, the number also appears in the page link.

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