Cube Root Calculator

What this calculator does

So, you want the cube root of a number. This tool takes a number and returns its cube root, worked out to ten decimal places.

There is one input, the number. The cube root is the degree 3 root, the natural next step up from the square root.

How to use it

1. Enter your number.
2. Press Calculate.

What a cube root is

The cube root of a number is the value that, multiplied by itself three times, gives that number. The cube root of 27 is 3, because 3 times 3 times 3 is 27. The cube root of 8 is 2, because 2 times 2 times 2 is 8. The name comes from volume: if a cube has a volume of 27, then each edge is 3 long, so the cube root turns a volume back into an edge length, just as the square root turns an area back into a side. It is the nth root with degree 3.

How it differs from a square root

The difference is how many times the number is multiplied to get back to the original. A square root undoes two multiplications, a cube root undoes three. This changes their behaviour: a cube root grows more slowly than a square root for large numbers, since you are unwinding an extra factor. It also means cube roots of most numbers are not whole. The cube root of 10, for instance, is about 2.154, sitting between the cube root of 8, which is 2, and the cube root of 27, which is 3.

The input this tool expects

This tool works with any real number, whether positive, negative, or zero. Cube roots of negative numbers exist as real values, since a negative multiplied by itself three times stays negative, so the cube root of minus 8 is minus 2, and the tool returns exactly that. Enter any number and it will give you its cube root directly.

A worked example

Enter 27 and the tool returns 3, since 3 cubed is 27. Enter 8 and it returns 2. Enter 10 and it returns about 2.1544346900, a cube root that falls neatly between the cube roots of 8 and 27.

Cube roots and beyond

The cube root is degree 3, one step past the square root's degree 2. If you want both a number's cube and its cube root at once, the cube and cube root calculator shows the pair together. For roots of any degree, the general root calculator covers them, and the radical calculator writes them in proper radical notation. The cube root is one familiar member of that larger family of roots.

Questions people ask

What is a cube root?

The number that, multiplied by itself three times, gives your number. The cube root of 27 is 3 because 3 times 3 times 3 is 27.

How is it different from a square root?

A square root undoes two multiplications, a cube root undoes three. Cube roots grow more slowly and are whole only for perfect cubes.

Why is it called a cube root?

Because it turns the volume of a cube back into its edge length. A cube of volume 27 has edges of length 3.

Do negative numbers have cube roots?

Yes. The cube root of minus 8 is minus 2, because minus 2 multiplied by itself three times is minus 8, and this tool returns it.

Can I see the cube and cube root together?

Yes, the cube and cube root calculator shows both from a single number. This tool gives just the cube root.

References

On the cube root. The cube root of a number is the value whose cube is that number, the nth root with degree 3.

1. Eric W. Weisstein, "Cube Root," from MathWorld, a Wolfram resource, on the cube root as the number whose cube gives the original.
2. Eric W. Weisstein, "nth Root," from MathWorld, a Wolfram resource, on the cube root as the nth root with degree 3.