Cube Root Calculator
Calculate the cube root of a number, including negative values.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
Unlike square roots, cube roots are defined for negative numbers, because multiplying three negatives gives a negative. The cube root of 27 is 3, and of minus 27 is minus 3.
Worked example
calculated with the default values below
Number 27 · Root degree 3 Cube root 3 · Nth root 3 · Number cubed 19,683
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
∛v = sgn(v) × |v|^(1/3)
- v
- Input number
- n
- Degree of the n-th root
Cube roots support negative values. An even-degree real root of a negative value is undefined and is returned as unavailable.
Frequently asked questions
What happens when I take an even root of a negative number?
The cube root supports negative values. An even-degree real root of a negative number is undefined, so the calculator leaves that result unavailable instead of returning zero.