Nth Root Calculator
Find the square, cube or any nth root of a number.
Results update as you type.
About this calculator
An nth root calculator finds the number that, raised to the power n, gives your value. Enter the value and the degree n, and it returns the root along with a check that raises the answer back to the nth power to confirm it lands on your original number.
The root is computed as value^(1/n), the inverse of raising to the power n. The square root uses n = 2 and the cube root n = 3. For example, the cube root of 27 is 27^(1/3) = 3, because 3 × 3 × 3 = 27, and the check shows 3 ^ 3 = 27. Odd roots of negative numbers are real and negative — the cube root of −8 is −2 — but even roots of negatives (like a square root of −4) have no real value, so the tool reports "no real root".
Roots appear in geometry, standard deviation, growth-rate averaging (the geometric mean) and physics. For a plain square root with simplified radical form, use the dedicated square root calculator; this tool handles any degree you enter.
Frequently asked questions
How do you find the nth root of a number?
Raise the number to the power 1/n. The cube root of 27 is 27^(1/3) = 3, because 3 × 3 × 3 = 27.
Can you take an even root of a negative number?
Not within the real numbers — there is no real square root of −4. Odd roots of negatives are fine: the cube root of −8 is −2.
What is the cube root of 27?
It is 27^(1/3) = 3, because 3 raised to the power 3 gives 27.
How does the "Check" line work?
It raises the computed root back to the power n. If it returns your original value, the root is correct — for the cube root of 27 it shows 3 ^ 3 = 27.
How do I find a square root with this tool?
Set the degree n to 2. For a simplified radical form such as 6√2, use the dedicated square root calculator instead.
What is the nth root of 1?
The nth root of 1 is always 1 for any degree, since 1 raised to any power is 1.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/root/curl
curl "https://calculator.free/api/v1/root/?value=27°ree=3"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/root/?" + new URLSearchParams({
"value": "27",
"degree": "3"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.