Arithmetic
Cube root from a fractional exponent
The absolute value keeps the power function in positive territory, and multiplying by the sign restores direction.
The Formula
cube root of x = sign(x) * |x|^(1/3)
The absolute value keeps the power function in positive territory, and multiplying by the sign restores direction.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| x | Input | any unit | The number whose cube root you want. |
| |x| | Absolute value | same unit | The input with its sign removed. |
| sign(x) | Sign | unitless | One for positive input, minus one for negative input. |
| 1/3 | Fractional exponent | unitless | The exponent that inverts cubing. |
What Each Symbol Means
xany unit
Input
The number whose cube root you want.
|x|same unit
Absolute value
The input with its sign removed.
sign(x)unitless
Sign
One for positive input, minus one for negative input.
1/3unitless
Fractional exponent
The exponent that inverts cubing.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a cube root page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Cube Root, filed under Math. Every number the guide produces comes from substituting into this one line.