Find the square root of any non-negative number.
How it works
The square root of x is the number that, multiplied by itself, gives x back. This calculator returns the principal (non-negative) square root: √2 ≈ 1.4142, and √81 is exactly 9.
What this does not include
This returns only the principal (positive) root. Every positive number technically has two square roots, one positive and one negative — this calculator reports the positive one, the standard convention. For a different root entirely, see this site’s cube root calculator.
How to use this calculator
- Enter a non-negative number.
A worked example
√2 = 1.414214 — an irrational number, truncated here for display.
√81 = 9, an exact whole-number result.
√0.25 = 0.5 — a fraction less than 1 has a square root larger than itself.
What the variables mean
| Variable | Meaning |
|---|---|
| x | Any non-negative real number |
Edge cases worth knowing
Negative numbers have no real square root — no real number multiplied by itself produces a negative result, so the calculator declines to show one for negative inputs.
A number between 0 and 1 has a square root larger than the original number — a counterintuitive result the third example above demonstrates directly, since √0.25 (0.5) is double the original value.
Why doesn’t a negative number have a real square root?
No real number multiplied by itself produces a negative result, since a negative times a negative is always positive — negative square roots exist only in the complex number system, which this calculator doesn’t cover.
What’s the square root of a perfect square?
An exact whole number — √81 is exactly 9, unlike most square roots, which are irrational and only ever approximated to a chosen number of decimal places.
Is 0’s square root 0?
Yes — 0 × 0 = 0, so the square root of 0 is 0, the one case where the principal and only square root coincide.
