Cube Root Calculator
Calculate cube roots of positive and negative numbers and simplify radicals, e.g. ∛54 = 3∛2.
Your inputs
Results
∛54
3.77976314968
- Simplified radical form
- 3∛2
- Perfect cube?
- No
- Check: result^3
- 54
✓Exact calculation — rounded only for display
What this calculator does
Unlike square roots, cube roots of negative numbers are real: ∛(−27) = −3.
Formula and method
∛n = a∛b where n = a³ × b and b has no cube factor.
Worked example
Calculated by this tool with its default inputs:
Inputs
- Number: 54
Results
- ∛54: 3.77976314968
- Simplified radical form: 3∛2
- Perfect cube?: No
- Check: result^3: 54
How to read the results
If b = 1 the number is a perfect cube.
Assumptions and limitations
- Simplified form is shown for integers up to 10^15.
Questions
Is the cube root of a negative number real?
Yes, because a negative number cubed is negative.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 3 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy