SQRT Function

Summary

The Excel SQRT function returns the positive square root of a number. If a value multiplied by itself produces the original number, SQRT returns that value. For example, =SQRT(25) returns 5 because 5 multiplied by 5 equals 25.

SQRT returns only the principal square root, which means the non-negative result. It does not return both algebraic roots. The input must also be non-negative. If the argument is negative, Excel returns #NUM! because standard worksheet SQRT operates in the real-number domain rather than complex numbers.

SQRT is useful when the workbook needs the underlying length or magnitude behind a squared value. It appears in geometry, distance formulas, error measurements, and many models where reversing a square is a natural part of the calculation.

Syntax

=SQRT(number)

SQRT has one required argument: the number whose square root you want. That argument can be a literal, a cell reference, or any formula that evaluates to a non-negative number. When the intent is specifically "take the square root," SQRT is usually clearer than writing the same operation as an exponent.

Arguments

• number - [Required] The non-negative value whose square root should be returned.

SQRT vs Other Functions

SQRT overlaps with exponentiation functions, but it has a narrower and more explicit purpose. When the operation is specifically a square root, SQRT communicates that intent immediately.

SQRT is not broader than exponentiation, but it is more explicit. That matters in shared workbooks because readability is often more valuable than compactness, especially in technical formulas that will be maintained later by another analyst.

Using SQRT

SQRT appears naturally in geometry. If the area of a square is known, the side length is the square root of that area. The function also appears in coordinate geometry, where the Euclidean distance between two points is derived by squaring coordinate differences, summing them, and then taking the square root of the result.

It also surfaces in statistical work because many measures are built from squared deviations. Standard deviation, for example, is conceptually the square root of variance. Excel offers dedicated statistical functions for those tasks, but understanding SQRT helps when you need to build or inspect the underlying calculation structure.

• Use SQRT(area) to derive the side length of a square from its area.
• Use SQRT(POWER(x2-x1,2)+POWER(y2-y1,2)) for straight-line distance in two dimensions.
• Use SQRT on intermediate formula results when the model produces a squared quantity that must be converted back to its original scale.

Example 1 - Find the Square Root of a Number

This example shows the core job of SQRT: taking one value and returning its principal square root. In worksheet terms, that means Excel gives the non-negative square root of a valid input.

This is a useful starting example because it shows the narrow role of the function very clearly. SQRT is not estimating or transforming the number in another way, it is specifically returning the square root.

=SQRT(25)   // 5
=SQRT(2)    // about 1.41421356
=SQRT(B1)   // square root of the value in B1

Example 2 - Find the Side Length from a Known Area

If a square has area 144, its side length is the value that produces 144 when squared. SQRT reverses that relationship directly. This pattern appears in geometry, layout work, and any model where an area must be translated back into a linear dimension.

This makes the example practical because it connects the function to a real measurement question. The formula is taking an area and turning it back into a side length.

=SQRT(B2)
// B2 = 144
// Result = 12

Example 3 - Calculate Distance Between Two Points

This formula applies the Pythagorean theorem. The coordinate differences are squared to remove direction, added together, and then square-rooted to return the straight-line distance. It is a standard pattern in geometric and engineering-style models.

This is helpful because it shows SQRT as the final step of a larger calculation, not only as a standalone function. Many real formulas use it this way after several earlier steps build the value underneath.

=SQRT(POWER(B4-B3,2)+POWER(C4-C3,2))
// (0,0) to (3,4)
// SQRT(3^2 + 4^2) = SQRT(25) = 5

Example 4 - Take the Square Root of a Calculated Value

SQRT does not need a direct cell input. It can be applied to any formula result, which makes it useful in larger expressions. In this example, the sum is evaluated first, and SQRT converts that total into its square root afterward.

That makes the function easier to use in flexible worksheets. The input can come from another formula, not just a typed number or a single cell reference.

=SQRT(B5+C5)
// B5 = 8, C5 = 17
// 8 + 17 = 25
// SQRT returns 5

When negative inputs are possible, decide whether the model should reject them or transform them before calling SQRT. Using SQRT(ABS(A1)) may be appropriate when only magnitude matters, but it also changes the mathematical meaning of the calculation. In models where the sign carries meaning, it is usually better to handle the negative case explicitly instead of masking it.

• SQRT(0) returns 0.
• Negative input returns #NUM!.
• Use a dedicated complex-number function such as IMSQRT when imaginary results are intentional.

Conclusion Recap

SQRT is the direct function for finding a square root, and this lesson showed that it always returns the positive result. That keeps the formula simple for beginners, but it also means negative input gives an error instead of a real-number answer.

The examples showed where SQRT shows up naturally: turning area into side length, finding distance between points, and taking the root of a larger formula result. When the math problem is clearly "find the square root," SQRT is usually the easiest formula to read.

• Summary: SQRT returns the positive square root of a non-negative number.
• Syntax: =SQRT(number) with one required argument.
• Key behavior: The result is always the principal square root, and negative input returns #NUM!.
• Practical usage: Geometry, distance formulas, and calculations derived from squared quantities.