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Cube Root Calculator

Calculate the cube root of any number, including negatives and decimals, or switch to a square root, 4th root or any nth root. The calculator tells you whether the number is a perfect cube and simplifies radicals such as ∛54 = 3∛2.

Whole number, decimal or negative (odd roots)

Enter your values to see the result.
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How to use the Cube Root Calculator

  1. Enter a number: whole, decimal or negative.
  2. Choose the root: cube root by default, or square, 4th, 5th, 6th or a custom nth root.
  3. Press Calculate root (results also update as you type).
  4. Read the root, whether it is a perfect cube and the simplified radical form.

Cube root formula

  • Definition: ∛x = r means r³ = x; equivalently ∛x = x1/3.
  • nth root: ⁿ√x = x1/n, the number r with rn = x.
  • Product rule: ∛(a × b) = ∛a × ∛b, which is how radicals are simplified: ∛54 = ∛27 × ∛2 = 3∛2.
  • Negative numbers: ∛(−x) = −∛x for odd roots.
  • Newton's method: rnext = r − (r³ − x) ÷ (3r²) converges quickly to ∛x.

Table of perfect cubes

nn³nn³nn³
118512153,375
289729164,096
327101,000174,913
464111,331185,832
5125121,728196,859
6216132,197208,000
7343142,7442515,625

Cube roots of common non-perfect cubes

x∛x (approx.)Simplified
21.259921∛2
31.442250∛3
102.154435∛10
162.5198422∛2
242.8844992∛3
543.7797633∛2
814.3267493∛3
1004.641589∛100
2506.2996055∛2

Frequently asked questions

What is a cube root?

The cube root of x is the number that, multiplied by itself three times, gives x. ∛27 = 3 because 3 × 3 × 3 = 27. It is the same as raising x to the power 1/3.

Can you take the cube root of a negative number?

Yes. Unlike square roots, odd roots of negative numbers are real: ∛−125 = −5 because (−5)³ = −125. Even roots (square, 4th…) of negative numbers are not real numbers.

How do you simplify a cube root?

Factor the number into primes and pull out every group of three equal factors. 54 = 2 × 3³, so ∛54 = 3∛2. 250 = 2 × 5³, so ∛250 = 5∛2.

How do I know if a number is a perfect cube?

Its cube root is a whole number, or equivalently every exponent in its prime factorization is a multiple of 3. 216 = 2³ × 3³ is a perfect cube (6³); 200 = 2³ × 5² is not.

What is the nth root?

The nth root of x is the number r with rⁿ = x, written ⁿ√x or x^(1/n). The square root is n = 2 and the cube root is n = 3. The 5th root of 3125 is 5 because 5⁵ = 3125.

How do you estimate a cube root by hand?

Find the perfect cubes on either side. 50 lies between 27 (3³) and 64 (4³), so ∛50 is between 3 and 4, closer to 4. A Newton step r − (r³ − x)/(3r²) from r = 4 gives about 3.69; the exact value is 3.684.

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