The cube root reverses cubing: ∛27 = 3 because 3³ = 27. It turns volumes into lengths – a 1,000 cm³ cube has sides of ∛1000 = 10 cm. Unlike square roots, cube roots of negative numbers are real: ∛−8 = −2.
How to use the Cube Root Calculator
- Number
- Degree of the root
- Every result field is editable: type into Root and Number plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
The calculator uses the real cube root for negative numbers and odd degrees. For even degrees and negative numbers there is no real root.
Inputs explained
| Field | What to enter |
|---|---|
| Number | A number |
| Degree of the root | A number |
Example values
How the main result changes when Number changes and everything else stays at the example values above:
| Number | Root |
|---|---|
| 171.5 | 5.5559 |
| 257.25 | 6.3599 |
| 343 | 7 |
| 428.75 | 7.5405 |
| 514.5 | 8.013 |
| 686 | 8.8194 |
Formula
∛x = x¹/3), y³ = x
n-th root: ⁿ√x = x¹/n)
Worked example
Inputs — Number: 343; Degree of the root: 3.
Results — Root = 7; Check: rootⁿ = 343; Square root (for comparison) = 18.5202591775.
Key terms
- Cube root
- A number that, cubed, gives x.
Frequently asked questions
What is the cube root of 64?
4, because 4 × 4 × 4 = 64.
Can I take the cube root of a negative number?
Yes: ∛−125 = −5.
How do I estimate a cube root?
Find the perfect cubes on either side: ∛50 is between ∛27 = 3 and ∛64 = 4.
How do I simplify ∛54?
54 = 27 × 2, so ∛54 = 3∛2 – see the simplify cube root calculator.