Cube Root Calculator

The cube root calculator finds the real cube root of any number, whether it is positive, negative, or zero. The cube root of a number x is the value y that satisfies the equation y cubed equals x, which means y multiplied by itself three times gives back the original number. Unlike square roots, cube roots exist for negative numbers in the real number system: the cube root of negative 27 is negative 3, because negative 3 times negative 3 times negative 3 equals negative 27. This property makes cube roots essential in geometry (finding the edge length of a cube from its volume), physics (working with cubic relationships such as the inverse-square law in three dimensions), and engineering. You simply enter the number you want to find the cube root of, which is called the radicand. The calculator returns the cube root rounded to six decimal places, a verification figure (the result cubed, which should equal your input), the exponent notation x^(1/3), and a note on whether the result is a perfect cube. A perfect cube is an integer whose cube root is also a whole number, such as 8, 27, 64, 125, and 216. The tool is suited to students checking homework, teachers preparing examples, and engineers needing a quick volume-to-edge conversion. Results are computed to floating-point precision and rounded for display.

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6
cube root
Verification (result cubed)216
Exponent form216^(1/3)
Perfect cube?Yes

How it works

The cube root is computed using the formula cbrt(x) = sign(x) × |x|^(1/3). For positive numbers, this is simply x raised to the power of one third. For negative numbers, the sign is preserved and the cube root of the absolute value is taken, then negated. The verification step cubes the result to confirm it equals the original input, accounting for tiny floating-point rounding differences. A number is flagged as a perfect cube when the cube root rounds to a whole number and that whole number cubed matches the original input exactly.

Worked example

Using the default value of 216: the cube root is 216^(1/3) = 6. Verification: 6 x 6 x 6 = 216. The result is a whole number, so 216 is a perfect cube. For a negative example, enter -27: the cube root is -27^(1/3) = -3, and (-3) x (-3) x (-3) = -27.

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Frequently asked questions

What is a cube root?

The cube root of a number x is the value y such that y multiplied by itself three times equals x. It is written as the cube root symbol (a radical with a small 3) over x, or equivalently as x raised to the power of one third. For example, the cube root of 27 is 3 because 3 times 3 times 3 equals 27.

Can a negative number have a cube root?

Yes. Unlike square roots, cube roots of negative numbers are real. The cube root of negative 27 is negative 3, because negative 3 multiplied by itself three times gives negative 27. This is because multiplying three negative numbers always yields a negative result.

How do you simplify a cube root?

To simplify a cube root, factorise the radicand and pull out any perfect cube factors. For example, the cube root of 54 can be written as the cube root of 27 times 2, which simplifies to 3 times the cube root of 2. If no perfect cube factor exists other than 1, the surd is already in simplest form.