Cube Root Calculator
Calculate the cube root of any number, including negative values. Useful for finding the side length of a cube from its volume or solving cubic equations.
About this calculator
The cube root of a number n is the value x such that x³ = n, written as ∛n. Unlike square roots, cube roots exist for negative numbers: since (−3)³ = −27, the cube root of −27 is −3. The formula used here is: if n ≥ 0, result = n^(1/3); if n < 0, result = −(|n|^(1/3)). This sign-handling step is necessary because raising a negative number to a fractional power is undefined in standard floating-point arithmetic. Cube roots appear in geometry when finding the edge length of a cube from its volume (edge = ∛V), in physics for scaling relationships, and in algebraic solutions to cubic equations. Unlike square roots, every real number has exactly one real cube root.
How to use
Say you have a cubic storage box with a volume of 512 cubic inches and want to know the side length. Enter 512 into the Number field. The calculator computes ∛512 = 8, so each side is 8 inches. Now try a negative number: enter −27. The calculator evaluates −(27^(1/3)) = −3. You can verify: (−3)³ = −3 × −3 × −3 = −27. For a non-perfect cube like 100, ∛100 ≈ 4.642.
Frequently asked questions
How do you find the cube root of a negative number?
Because any real number cubed retains its sign, negative numbers have real cube roots — unlike square roots of negatives. To find the cube root of a negative number, take the cube root of its absolute value and then apply a negative sign. For example, ∛(−125) = −(∛125) = −5, since 5³ = 125. This is why the formula checks whether n is negative before computing: it avoids errors in floating-point math and ensures the correct negative result.
What is the cube root used for in real life?
The most common real-life application is finding the edge length of a cube when you know its volume, since Volume = edge³ means edge = ∛Volume. Architects and engineers use this when designing cubic storage tanks, shipping containers, or rooms. Cube roots also appear in physics — for example, the radius of a sphere scales with the cube root of its volume. In finance, the cube root is used to compute the geometric mean return over three periods.
What is the difference between a cube root and a square root?
A square root asks 'what number times itself gives n?' (x² = n), while a cube root asks 'what number times itself three times gives n?' (x³ = n). Square roots only exist for non-negative real numbers (within the real number system), but cube roots exist for all real numbers including negatives. Every positive number has two square roots (positive and negative) but only one real cube root. These differences mean cube roots are more broadly applicable when working with signed quantities or odd-degree equations.