Square Root Calculator
Find principal square roots for zero and positive finite numbers, with four-decimal results, worked examples, domain limits, and cited guidance.
Formula: √x = y, where y ≥ 0 and y² = x
Enter 0 or a positive finite number. Decimal values are supported; the principal square root is rounded to four decimal places.
The Square Root Calculator returns the principal real square root of an input. Enter 0 or a positive finite number. Decimal values are supported; the principal square root is rounded to four decimal places. Select Calculate after entering or changing the number.
The default input 144 returns 12.0000 because 12² = 144. An input of 2 returns approximately 1.4142, and 0 returns 0.0000. These examples distinguish the nonnegative principal root from the two signed solutions that an equation such as y² = 144 can have.
How to Use the Square Root Calculator
- Enter zero or a positive finite whole or decimal number.
- Select Calculate.
- Read the principal square root shown to four decimal places.
Changing the input clears the earlier result until you calculate again. Blank, nonnumeric, non-finite and negative entries are rejected with an accessible field error. This real-number widget does not return complex roots and does not impose an arbitrary maximum inside the browser’s finite numeric range.
Square Root Formula and Worked Examples
√x = y, where y ≥ 0 and y² = xThe principal square root is the nonnegative number y whose square equals x. The OpenStax College Algebra 2e section on radicals and rational exponents defines principal roots and explains why an even-index radical requires a nonnegative radicand when working with real numbers.
For 25, the result is 5.0000 because 5² = 25. Although both 5 and −5 solve y² = 25, the radical symbol √25 denotes the principal value 5. For 2, the internal result is approximately 1.4142135624 before the widget displays 1.4142.
Square roots can recover a nonnegative side length from a square area and appear in distance formulas. Use the Distance Calculator for coordinate distance, or the Cube Root Calculator when the radical index is 3 and negative real inputs are allowed.
Input Limits, Rounding and Related Calculators
The widget uses standard browser floating-point numbers. MDN’s Number.MAX_VALUE reference documents JavaScript’s largest positive finite numeric value. Inputs outside the finite range are invalid; Number.MAX_VALUE itself still has a finite principal square root.
Results are displayed to four decimal places. Display formatting does not add precision, and a very small positive square root can appear as 0.0000 after rounding even though the internal result is greater than zero. Use more precision elsewhere when downstream work depends on additional digits.
The Average Calculator finds an arithmetic mean; it does not calculate the square-root step used by separate statistics formulas. Keep units consistent when a square root is part of a larger geometry or statistics calculation.
Frequently asked questions
What is a principal square root?
The principal square root of x is the nonnegative number y for which y² = x. For example, the principal square root of 9 is 3.
What formula does the Square Root Calculator use?
It evaluates √x = y, where y is nonnegative and y² = x. The displayed value is the principal real square root.
Can I enter a negative number?
No. A negative radicand has no real square root, so this real-number calculator rejects negative inputs with a field error rather than returning a complex result.
Can I enter zero or a decimal number?
Yes. Zero and positive finite decimals are supported. For example, √0 = 0 and √2 is approximately 1.4142 in the display.
How can I check a square-root result?
Square the result. Before display rounding, a correct principal square root y satisfies y² = x and y is nonnegative.
How are results rounded?
Results are displayed to four decimal places using standard browser floating-point arithmetic. Display rounding does not add precision to the calculation.
What input limits apply?
The input must be zero or a positive finite browser number. Blank, nonnumeric, non-finite and negative values are rejected; there is no arbitrary maximum below the browser’s finite-number limit.