Free Square Root Calculator

Square Root Calculator

Find the principal square root of a number, check whether it is a perfect square, and optionally calculate the principal complex root of a negative value. Browse more tools in our Math Calculators collection.

Real & complex Perfect-square check Verification No sign-up

Calculator

Find a square root

Enter one finite number and choose whether negative inputs should be handled in the real or complex number system.

x

Examples: 144 → 12, 2 → 1.4142135624, and −9 → 3i in Complex mode.

Advertisement

What is a square root calculator?

A square root calculator finds the value that produces the original number when multiplied by itself. For example, √81 = 9 because 9 × 9 = 81. For more power and root operations, use the Exponent Calculator.

How does the square root calculator work?

For a nonnegative number x, the calculator evaluates √x with the browser's square-root function. If Complex mode is selected and x is negative, it calculates √|x| and appends i to represent the principal complex result.

What formula does a square root use?

√x = x^(1/2), for x ≥ 0 in the real numbers
√(−x) = i√x, for x > 0 in the complex numbers

You can use the Fraction Calculator when a related calculation contains rational values.

Advertisement

How do you use this square root calculator?

  1. Choose Real numbers or Complex numbers allowed.
  2. Enter the number whose square root you want.
  3. Select Calculate Square Root.
  4. Review the root, perfect-square check, and squared verification.

Square root examples

√144 = 12, √2 ≈ 1.4142135624, and in Complex mode √−9 = 3i. For everyday comparisons and proportions, the Ratio Calculator and Percentage Calculator are also available.

What are the limits of this calculator?

The calculator accepts finite browser numbers. Real mode rejects negative inputs because they do not have real square roots. Very large or very small results may be displayed in scientific notation, and irrational roots are rounded for readability.

Frequently asked questions about square roots

The principal square root of a nonnegative number is the nonnegative value that, when multiplied by itself, returns the original number.
The principal square root of 144 is 12 because 12 × 12 = 144.
Yes when Complex mode is selected. A negative number has no real square root, but its principal complex square root can be written using i.
A perfect square is a number whose principal square root is an integer, such as 1, 4, 9, 16, 25 and 144.
Most square roots are irrational numbers with nonterminating decimals, so the display is rounded while the browser keeps greater internal precision.
For nonnegative real x, yes: √x = x^(1/2).

Methodology and calculation scope

Calculations use JavaScript double-precision numbers. Perfect-square detection is only reported when the nonnegative input and resulting integer are within the range where the check is reliable.

Privacy note: Calculations run in your browser. Values entered in this calculator are not sent to a calculation server.
Advertisement