Cube Root Calculator

It is negative and perfectly real. The cube root of −27 is −3, because −3 × −3 × −3 = −27. Odd roots preserve the sign; even roots cannot.

Because squaring any real number gives a positive result, so no real number squares to a negative. The square root of −1 is defined as the imaginary unit i, which is a different number system.

Estimate between known cubes and refine. For 100, you know 4³ = 64 and 5³ = 125, so the answer is between 4 and 5 and nearer 5 — about 4.64.

The cube root of x is x to the power of one third. That identity is how calculators handle roots at all, and it extends to any root: the nth root is the power 1/n.

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 and so on. Knowing the first ten makes estimating any cube root much faster.

Cubing multiplies a number by itself three times; the cube root undoes it. They are inverse operations, so the cube root of a cube returns the original number.

Bracket it between known cubes. For 500, you know 7³ = 343 and 8³ = 512, so it is just under 8 — about 7.94.

One, and it is one of three cube roots of 1 if complex numbers are allowed. Over the reals there is exactly one cube root of any number.

Because cubing is strictly increasing — each input gives a distinct output and vice versa. Squaring is not, which is why square roots have two.

Anywhere a volume is scaled to a length: finding the side of a cube from its volume, or scaling a model where the volume ratio is known and the linear ratio is wanted.

A radical sign with a small 3 in the notch: ∛. The index is written for every root except the square root, where it is omitted by convention.

Yes — take the cube root of the numerator and denominator separately. The cube root of 8/27 is 2/3.