Cube Root Calculator

The cube root of a number x is a value a such that a³ = x. For example, the cube root of 64 is 4, because 4 × 4 × 4 = 64. Every real number has exactly one real cube root.

The cube root of x is equivalent to raising x to the power of 1/3. This is written as ∛x = x^(1/3). For example, ∛8 = 8^(1/3) = 2.

Yes! Unlike square roots, cube roots of negative numbers are real numbers. The cube root of a negative number is simply the negative of the cube root of its absolute value. For example, ∛(−64) = −4, because (−4)³ = −64.

On most scientific calculators, you can compute the cube root by raising the number to the power of (1/3). Enter the number, press the exponent key (often labeled ^ or y^x), then enter 0.3333 or (1÷3), and press equals. On some calculators, there is a dedicated ∛ button.

For perfect cubes (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000), you can memorize the results. For other numbers, narrow down the answer by finding two perfect cubes the number falls between, then estimate. For example, ∛20 is between ∛8 = 2 and ∛27 = 3, so it is approximately 2.7.

A perfect cube is an integer that is the cube of another integer. Examples include 1 (1³), 8 (2³), 27 (3³), 64 (4³), 125 (5³), and 216 (6³). The cube root of a perfect cube is always a whole number.

The cube root of a product ∛(a × b) equals ∛a × ∛b. Similarly, the cube root of a fraction ∛(a/b) equals ∛a ÷ ∛b. For example, ∛(−8/27) = ∛(−8) ÷ ∛27 = −2 ÷ 3 = −2/3.

A square root finds a value that multiplied by itself twice equals x (a² = x), while a cube root finds a value multiplied by itself three times (a³ = x). Square roots of negative numbers are not real numbers, but cube roots of negative numbers are. The cube root symbol is ∛, while the square root symbol is √.