Cube Root Calculator
Undoing a Cube
Where a square root undoes squaring, a cube root undoes raising a number to the third power. The distinction that matters most in practice is that cube roots, unlike square roots, are perfectly well-defined for negative numbers — there's no need for imaginary results, because a negative number cubed stays negative, and the cube root simply reverses that.
The Formula
∛x
For negative inputs, the calculator computes the cube root of the positive equivalent and reapplies the negative sign, since raising a negative base to a fractional exponent directly can produce unreliable results in floating-point arithmetic.
Where Cube Roots Are Used
- Volume-to-length conversion — finding the side length of a cube from its volume, or scaling a 3D object by a target volume ratio.
- Engineering and materials science — certain stress and material property formulas involve cube roots directly.
- Statistics — cube-root transformations are used to normalize skewed data, particularly data that can include negative values.
| Input | Cube Root |
|---|---|
| 27 | 3 |
| 64 | 4 |
| −8 | −2 |
How to Use This Calculator
- Enter a number in the Number field.
- Select Calculate to see the cube root, rounded to six decimal places.
Related Calculations
Need a square root or a root of any other degree? See the Square Root Calculator and the general-purpose Nth Root Calculator.