Square Root Calculator
Find the square root of any number.
Results update as you type.
How it works
The square root of a number is the value that, multiplied by itself, reproduces that number, so the square root of 144 is 12, because 12 times 12 is 144. It reverses squaring, unwinding an area back to the length of one side, which is exactly how the operation arises in geometry, physics and statistics. The square root calculator finds this value for any number from zero upward and returns it to several decimal places for precision. Every positive number has two roots that square to it, one positive and one negative, but the calculator reports the principal root, the non-negative one, because that is the value meant in almost all practical contexts. Zero has a single root of zero, and negative numbers have no real square root at all, since no real value squared is negative, which is why a square root calculator restricts its input to zero or greater. Roots appear constantly beyond the classroom: they scale distances through the Pythagorean theorem, define standard deviation in statistics, and set the sizing of squares and circles in design and engineering. Whenever squaring needs to be undone, this square root calculator returns the exact underlying value.
√n = the value x such that x × x = n
The square root asks the inverse of squaring: rather than multiplying a number by itself, it searches for the value whose self-product equals your input. Naming it x, the definition that x times x equals n means x is the side length that produces an area of n. That is why the root of 144 is 12, since twelve is precisely the number that, squared, rebuilds 144.
Source:Standard arithmetic
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter number.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Square root updates instantly as you type — no button to press.
Frequently asked questions
What is a square root?
A square root of a number is a value that gives that number when multiplied by itself. Since 12 times 12 is 144, twelve is a square root of 144. The operation undoes squaring, so it turns an area back into the length of the side that produced it. This inverse relationship is why roots appear anywhere a squared quantity, such as a distance, a variance or an area, needs to be reversed.
Can I take the square root of a negative number?
Not within the real numbers. No real value multiplied by itself gives a negative result, because a positive times a positive and a negative times a negative are both positive. The square root of a negative number is therefore called imaginary and lies outside ordinary arithmetic, which is why this calculator accepts only inputs of zero or greater and leaves negative entries without a real answer.
What is a principal square root?
The principal square root is the non-negative one. Every positive number technically has two roots, one positive and one negative, that both square to it, since 12 and minus 12 each give 144. To keep results unambiguous, the calculator returns only the principal, positive value, which is the root intended in nearly every practical calculation involving lengths, distances and measured quantities.
Is a square root always a whole number?
No. Only perfect squares like 144 have whole-number roots; most numbers have irrational roots that run on forever without repeating. The square root of 2, for example, is about 1.414214 and can never be written exactly as a fraction or a terminating decimal. The calculator handles both cases, returning an exact integer where one exists and a rounded decimal otherwise.
How do I calculate a square root by hand?
For perfect squares, ask which number multiplied by itself gives your value: twelve works for 144 because 12 times 12 is 144. For other numbers, estimate between the two nearest perfect squares and refine, so a value between 121 and 144 has a root between 11 and 12. This guess-and-check narrowing is tedious, which is why a calculator is faster and far more precise for non-perfect squares.