Calculating your nth root is straightforward once you know the Nth Root formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Nth Root Calculator.
What is Nth Root?
The Nth Root calculation tells you your nth root from a few simple inputs. The figure you are solving for here is the nth root.
The Nth Root formula
The core formula is:
nth root = (Number)^(1 ÷ Root (n))Here is what each input means:
- Number — a number. Example: 32.
- Root (n) — a number. Example: 5.
How to calculate it step by step
- Write down the number (for example, 32).
- Write down the root (n) (for example, 5).
- Apply the formula above to get your nth root.
- Double-check the result with the Nth Root Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Number | 32 |
| Root (n) | 5 |
| nth root | 2.000000 |
With number of 32 and root (n) of 5, the nth root works out to 2.000000.
Example 2
With number of 64 and root (n) of 5, the nth root works out to 2.297397.
| Result | Value |
|---|---|
| nth root | 2.297397 |
Example 3
With number of 16 and root (n) of 5, the nth root works out to 1.741101.
| Result | Value |
|---|---|
| nth root | 1.741101 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Nth Root Calculator does it instantly, for free, with the formula and a worked example built in.
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