Square Root Calculator
Find the square root of a number, with a clear error message for negative inputs since real square roots don't exist for them.
Your results
Calculation breakdown
- Square root
- √x
Worked example
The square root of 144 is 12.
Assumptions
- Only the positive (principal) square root is shown.
- Negative inputs return an error rather than an imaginary result.
How this calculator works
This calculator finds the square root of a non-negative number. For negative numbers, real square roots don't exist, so the calculator explains this instead of returning an invalid result.
Frequently asked questions
Why can't I find the square root of a negative number?
Negative numbers don't have a real square root because no real number multiplied by itself gives a negative result; that requires imaginary numbers, which this calculator doesn't cover.
Is the square root always positive?
This calculator shows the principal (positive) square root, which is the conventional result used in most everyday maths.
How is this different from the Nth root calculator?
Square root is a special case of the Nth root calculator where the root is 2; use the Nth root calculator for cube roots and beyond.