Square Root Calculator
The Inverse of Squaring
Square roots undo squaring — find the number that, multiplied by itself, produces the value entered. Most square roots of whole numbers are irrational, which is exactly why a calculator is more useful here than a memorized table: √2 runs on forever, but this tool returns it to six decimal places instantly, including for negative inputs where the result becomes an imaginary number.
The Formula
√x
For negative x, there is no real square root, since no real number squared produces a negative result. The calculator instead returns the imaginary result using the definition √x = √(−1 × |x|) = √|x| × i.
Where Square Roots Come Up
- Geometry — finding a side length from an area, or a distance from the Pythagorean theorem.
- Physics — root-mean-square calculations, gravitational fall-time equations, and wave formulas all involve square roots.
- Statistics — standard deviation is the square root of variance.
- Finance — annualizing volatility from periodic returns uses a square-root scaling factor.
| Number | Square Root |
|---|---|
| 144 | 12 |
| 2 | 1.414214 |
| −25 | 5i (imaginary) |
How to Use This Calculator
- Enter a number in the Number field.
- Select Calculate to see the square root, rounded to six decimal places (or the imaginary result for negative inputs).
Related Calculations
Need a root other than square? The Cube Root Calculator and the general-purpose Nth Root Calculator extend this same idea to any index.