A Cube Root Calculator
A cube root asks which number, multiplied by itself twice more, produces the value you started with. It is the exact inverse of cubing, and unlike a square root it has a single real answer for every real input, negative numbers included.
Cube root
3
- Nearest whole cube root
- 3
- Cube of the rounded root
- 27
- Gap to the nearest perfect cube
- 0
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
cube root of x = x^(1/3), with the sign of x carried separately
- x
- The number whose cube root you want
- |x|
- The absolute value, which strips the sign
- sign(x)
- Either 1 or -1, restoring the original sign
- x^(1/3)
- The cube root, written with a fractional exponent
How to check the result by hand
- 1
Take the absolute value
Strip the sign so the power function only ever sees a positive number. The cube root of 27 and the cube root of -27 share the same magnitude, which is 27.
- 2
Raise it to the power of one third
An exponent of one third inverts cubing. Applied to 27 this gives approximately 3, and applied to 64 it gives 3.9999999999999996 in double precision floating point.
- 3
Reapply the sign
Multiply by one if the input was positive and by minus one if it was negative. Cubing a negative number stays negative, so the root must too.
- 4
Cube the answer to check it
Multiply your result by itself twice more. You should land back on the original number, or close enough to it that the difference is explained by rounding.
- 5
Round only the final answer
Keep full precision through intermediate steps and round once at the end. Rounding early, then cubing the rounded value, will not return the original number for non-perfect cubes.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate A Cube Root page.