# How to use the SUMSQ function

**What is the SUMSQ function?**

The SUMSQ function calculates the sum of the squares of the arguments.

**What is the square?**

In mathematics, the square of a number is the result of multiplying the number by itself. Squaring a number is denoted by x^{2}. For example, 5^{2} means 5 * 5 = 25.

Squaring a number results in a positive result as negative signs are removed in multiplication. (-5)^{2} = 25 Squares grow very rapidly. Already x^{2} reaches large values quickly as x increases, higher powers grow even faster.

The square root is the inverse operation of squaring. âˆš25 = 5, since squaring 5 gives 25. Squaring is used in geometry to calculate area of squares, side length squared = area. Squaring is also used when calculating the area of a circle.

For example,Â A = Ï€ rÂ²

A is the area.

r is the radius.

Ï€ is pi.

The graph of y = x2 is a parabola, symmetric about the origin.

Squares appear frequently in equations in physics, math, statistics, and other fields.

**What is the sum?**

Calculating a sum involve adding the numbers together creating a total. Summation combines multiple addends into a total amount. For example, the sum of 2, 3, and 5 is 2 + 3 + 5 = 10.

The numbers added can be positive or negative, resulting in a net sum. For example, the sum of -5, -2, and 5 is -2

Sums can be written using the Greek capital sigma âˆ‘ notation to compactly denote repeated addition. âˆ‘ provides a shorthand for writing out sequences of numbers being added together.

**What is the sum of squares?**

The sum of squares is the result obtained when you take a set of numbers, square each number, and then sum the squares.

If the numbers are x1, x2, ..., xn, the sum of squares is denoted:

âˆ‘(x_{i}^{2}) = x_{1}^{2}Â + x_{2}^{2} + ... + x_{n}^{2}

The sum of square are used in statistics formulas like sample variance, appears in optimization methods like least squares regression and has applications in numerical integration formulas.

Can be computed iteratively or with summation notation.

The sum of square are related to the square of sums, (âˆ‘x_{i})^{2}

### Excel Function Syntax

SUMSQ(*number1*, *[number2]*, ...)

### Arguments

number1 |
Required. The argument for which you want the sum of the squares. |

[number2] |
Optional. Up to 253 additional number arguments. |

### SUMSQ function example

Formula in cell D3:

2^2 = 4, 3^2 = 9, 4^2=16.

4+9+16 = 29

### Functions in 'Math and trigonometry' category

The SUMSQ function function is one of 73 functions in the 'Math and trigonometry' category.

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