Cube Root Calculator
Find the cube root of any number.
Results update as you type.
How it works
The cube root of a number is the value that, when cubed, meaning multiplied by itself three times, gives back the original number. This cube root calculator takes any number, positive or negative, and returns its real cube root. Cube roots are the inverse operation of cubing, just as square roots reverse squaring. If you cube 3 you get 27, so the cube root of 27 is 3. What makes cube roots distinct from square roots is that they work perfectly well for negative numbers. Because multiplying three negatives together gives a negative result, the cube root of a negative number is itself negative: the cube root of negative 8 is negative 2, since negative 2 times negative 2 times negative 2 equals negative 8. Every real number, whether positive, negative, or zero, has exactly one real cube root, unlike square roots where negatives have no real answer and positives have two. Cube roots come up whenever you work with volume, since the volume of a cube is the side length cubed, so recovering the side from a known volume means taking a cube root. They also appear in scaling problems, physics, and engineering. Perfect cubes like 8, 27, 64, and 125 give whole-number roots, while other inputs give irrational decimals that the calculator approximates. Enter any value and this cube root calculator returns the precise real cube root instantly.
cube root of n = n^(1/3), the value x where x³ = n
The cube root of a number is the value that, when multiplied by itself three times, produces the original number. It is the inverse of cubing, so raising a number to the one-third power undoes raising it to the third power. Unlike square roots, cube roots are defined for negative numbers too, because multiplying three negative factors yields a negative result, so every real number, positive, negative, or zero, has exactly one real cube root.
Source:Standard algebra
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Worked example
How to use this calculator
- 1
Enter your values
Enter number.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
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Frequently asked questions
What is a cube root?
A cube root of a number is the value that, when multiplied by itself three times, produces that number. It is the inverse of cubing. For example, the cube root of 64 is 4 because 4 times 4 times 4 equals 64. The symbol for a cube root is a radical sign with a small 3, and it can also be written as raising the number to the power of one-third.
Can you take the cube root of a negative number?
Yes, unlike square roots, cube roots of negative numbers are real and well defined. Because a negative times a negative times a negative gives a negative, the cube root of a negative number is negative. For instance, the cube root of negative 27 is negative 3. This is a key difference from square roots, which have no real value for negative inputs, so cube roots always return one real answer.
How is a cube root different from a square root?
A square root reverses squaring and finds a value multiplied by itself twice, while a cube root reverses cubing and finds a value multiplied by itself three times. Square roots of negatives are not real, and positive numbers have two square roots. Cube roots are simpler in one way: every real number has exactly one real cube root, positive, negative, or zero, with no ambiguity or restriction on sign.
What are perfect cubes?
Perfect cubes are numbers that result from cubing a whole number, so their cube roots are whole numbers with no decimals. The first few are 1, 8, 27, 64, 125, and 216, coming from 1, 2, 3, 4, 5, and 6 cubed. Recognising perfect cubes helps you estimate and simplify cube roots by hand, since roots of nearby numbers will be close to those whole-number values.
Where are cube roots used?
Cube roots appear whenever a quantity depends on the cube of a length, most commonly in volume calculations. If you know the volume of a cube, its side length is the cube root of that volume. They also arise in scaling laws, where doubling a linear dimension multiplies volume eightfold, and in physics and engineering formulas involving three-dimensional growth, density, or the behaviour of certain equations.