Roots undo powers: the cube root of 27 is 3 because 3³ = 27.
How to use the Root Calculator
- Number
- Root (n)
- Want to work backwards? Type a value into nth root and Number is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Raise x to the power 1/n. For odd n and negative x the result is negative.
Inputs explained
| Field | What to enter |
|---|---|
| Number | A number |
| Root (n) | A number |
Example values
How the main result changes when Number changes and everything else stays at the example values above:
| Number | nth root |
|---|---|
| 40.5 | 2.5227 |
| 60.75 | 2.7918 |
| 81 | 3 |
| 101.25 | 3.1721 |
| 121.5 | 3.32 |
| 162 | 3.5676 |
Formula
ⁿ√x = x^(1/n)Worked example
Inputs — Number: 81; Root (n): 4.
Results — nth root = 3; Check: result^n = 81.
Frequently asked questions
Why is there no result for even roots of negatives?
No real number raised to an even power is negative.
Can n be a decimal?
Yes; x^(1/n) works for any positive n.
What formula does the Root Calculator use?
ⁿ√x = x^(1/n).
Can I work backwards from the result?
Yes. Type the result you want into nth root and the calculator finds the matching number.