Cube Root Calculator

Cube root calculator at a glance#

A cube root calculator finds the number that, cubed, gives the number you enter. The cube root of x, written ∛x, is the value y where y times y times y equals x. So ∛27 is 3 because 3 times 3 times 3 is 27. Cube roots work for negative numbers too, since a negative cubed stays negative.

Those are perfect cubes, so their roots are whole numbers. For numbers in between, the root is a decimal. The cube root of 50 is about 3.68, because 3.68 times 3.68 times 3.68 is roughly 50. To estimate one by hand, find the two perfect cubes it falls between: 50 sits between 27 (root 3) and 64 (root 4), so ∛50 is between 3 and 4.

Enter any number in the calculator above for the exact cube root to several decimal places. Roots of non-perfect cubes are irrational, so the result is rounded rather than exact.

What a cube root is#

The cube root of a number is the value that gives that number when multiplied by itself three times. It is the inverse of cubing: since 3 × 3 × 3 = 27, the cube root of 27 is 3. It is written with a small 3 over the radical sign, ∛x, and you can type a number straight into the calculator above to get the answer.

Perfect cubes and decimal results#

A perfect cube is a whole number cubed, so its root is also a whole number: 8 = 2³, 27 = 3³ and 125 = 5³. Numbers that are not perfect cubes have irrational roots, which the calculator rounds to a decimal. The cube root of 10 is about 2.154, since 2.154 cubed is close to 10. Cube roots of negative numbers are negative, because a negative cubed stays negative: ∛-27 = -3, as (-3) × (-3) × (-3) = -27.

Estimating a cube root by hand#

Find the two perfect cubes the number sits between, and the root lands between their roots. The number 50 falls between 27 (root 3) and 64 (root 4), so ∛50 is between 3 and 4, closer to 4 because 50 is nearer 64. The calculator returns the exact value to several decimal places.

Where cube roots come up#

If you know a cube's volume, its cube root is the side length: a cubical container holding 512 cubic feet has sides of ∛512 = 8 feet, since 8 × 8 × 8 = 512. The same logic helps size boxes, tanks and any space where volume is fixed but the dimensions are not.

Cube root calculator FAQ#

What is a cube root?#

It is the number that, cubed, returns the original value. The cube root of 27 is 3 because 3 × 3 × 3 = 27. Cube roots work for negative numbers as well as positive ones.

How is a cube root different from a square root?#

A square root multiplies a number by itself twice to reach the target (the square root of 9 is 3, since 3 × 3 = 9). A cube root multiplies three times, so the cube root of 27 is 3.

Can you take the cube root of a negative number?#

Yes. The cube root of a negative number is negative: ∛-27 = -3, because (-3) × (-3) × (-3) = -27. Unlike square roots, cube roots of negatives are real numbers.

What happens with numbers that are not perfect cubes?#

Their cube roots are irrational, so the calculator shows a rounded decimal. The cube root of 10 is about 2.154 and the cube root of 50 is about 3.68.

Does this tool do other roots, like the nth root?#

This calculator is set for cube roots, the case where n is 3. The nth root is the value that gives the original number when raised to the power n, and a general nth-root tool covers those other cases.