How to calculate a cube root
The cube root of a number x, written ∛x, is the value that gives x when multiplied by itself three times: ∛x = x^(1/3). For example, ∛27 = 3 because 3 × 3 × 3 = 27, and ∛125 = 5 because 5³ = 125.
Cube roots turn up whenever a volume has to be converted back into a length: if a cubic tank holds 27 cubic metres, each side measures ∛27 = 3 metres.
Handy exact cube roots worth memorising: For the second root rather than the third, use the square root calculator.
- ∛8 = 2
- ∛27 = 3
- ∛64 = 4
- ∛125 = 5
Cube roots of negative numbers
Unlike square roots, cube roots are defined for negative numbers. The cube root of −8 is −2, since (−2)³ = −8. This calculator handles negatives automatically. For square roots instead, try the nth root calculator with n = 2.
The reason is the sign rule for multiplication: three negatives multiplied together stay negative, whereas two negatives cancel to a positive. So every real number has exactly one real cube root.
How to use this calculator
Type any number — positive, negative or decimal — into the field. The cube root appears instantly, rounded for readability. Cube roots that aren't whole numbers are shown as decimals.
Most cube roots are irrational, so the displayed value is an approximation. To check any answer, cube it and compare with your original input. Cubing is the operation a cube root undoes, and the exponent calculator will do that step for you.
Frequently asked questions
- What is the cube root of 27?
- The cube root of 27 is 3, because 3 × 3 × 3 = 27.
- Can you take the cube root of a negative number?
- Yes. The cube root of a negative number is negative, for example ∛(−8) = −2.
- What is the difference between a cube root and a square root?
- A square root finds a value squared to give x; a cube root finds a value cubed (multiplied three times) to give x.
- How do I write a cube root as a power?
- The cube root of x equals x raised to the power 1/3, written x^(1/3).
- Why does my phone calculator reject the cube root of a negative number?
- Many calculators compute x^(1/3) as a power, and raising a negative base to a fractional power is undefined in that system. The fix is to take the cube root of the absolute value and put the minus sign back afterwards, which this tool does automatically.