Square Root Calculator

What a Square Root Calculator Is For

Every positive number has a square root, meaning a value that multiplied by itself returns the original number. Since 12 x 12 = 144, we say the square root of 144 is 12. This calculator finds that value for any number you type in.

Math students use square roots daily for the Pythagorean theorem and quadratic equations, while builders, designers, and data analysts meet them whenever areas or standard deviations come up. It is one of the most used functions in all of math.

The Math Behind Square Roots

Square roots reverse squaring: if y = sqrt(x), then y x y equals x. Only nonnegative numbers have real square roots, so negative inputs need complex numbers. Most values are irrational; for example sqrt(2) is about 1.414, a nonrepeating decimal that cannot be written as an exact fraction.

Here is a worked example: a 12 by 12 room has area 144 square feet, and sqrt(144) gives 12 feet for each side. Similarly, sqrt(100) equals 10, and sqrt(0.25) is 0.5. Perfect squares like 144 and 100 give whole answers; everything else gives decimals.

How to Use It

Enter a number in the value field and click Calculate Square Root. Your answer shows up under Square Root, rounded to two decimal places. Whole numbers, decimals, and tiny values like 0.01 all work.

Negatives are the main pitfall, since they have no real square root and will trigger an error message; double check your input before retyping. Also note that sqrt(1) is 1 and sqrt(0) is 0, two results people sometimes second guess. Memorizing perfect squares such as 4, 9, 16, 25, and 100 makes it easy to sanity check outputs at a glance.