## How to use the DELTA function

The DELTA function evaluates whether two numerical values are equal. This function is also known as the Kronecker Delta function.

##### What is the Kronecker Delta?

The Kronecker Delta is a mathematical function that takes two variables, usually positive whole numbers, and returns 1 if they are equal and 0 if not equal.

Î´_{ij} where i and j are variables. i = j returns 1, i <> j returns 0

The Kronecker delta is often used in mathematics, physics, engineering and computer science.

### Table of Contents

## 1. DELTA Function Syntax

DELTA(*number1, [number2]*)

## 2. DELTA Function Arguments

Argument |
Text |

number1 |
Required. |

[number2] |
Optional, default value is 0 (zero). |

## 3. DELTA Function Example

The image above shows arguments number1 in column B, arguments number2 in column C and the result of the DELTA function in column D.

Formula in cell D3:

Row 3 contains numbers 2 and 3, DELTA functionÂ in cell D3 returns 0 (zero). 2 and 3 are not equal. Row 4 has 7 and 7, the DELTA function returns 1. 7 and 7 are equal.

Row 8 shows that negative numbers, in this case, -3 and -3 returns 1. They are equal.

## 4. DELTA Function not working

The DELTA function returns a #VALUE error value if *number1 or [number2]* is nonnumeric. The image above shows the DELTA function returning a #VALUE error in cell D3, the second argument is "A" and is non numeric which is not allowed.

The DELTA function in cell D4 also returns a #VALUE error, it has a boolean value in the first argument. You can convert boolean values to their numerical equivalents by multiplying the boolean value by 1.

## 5. DELTA function compared to other comparison functions/operators

The **DELTA function** compares only numerical values and the output is 1 or 0 (zero). It can't compare an array of values, not text values or boolean values. It is quite limited if you consider array operations.

The **equal sign =** is a logical operator, it is able to compare numbers, text and boolean values. It also compares a value to an array of values, or an array of values to another array of values. The downside is that it doesn't differentiate between upper and lower letters.

The output from the equal sign is a boolean value TRUE or FALSE, however, it is easy to convert the output to their numerical equivalents TRUE = 1 and FALSE = 0 (zero) by multiplying the output with 1. You can also add a zero if you prefer. It is also possible to use double negations.

The EXACT function is primarily used to compare text strings also considering upper and lower letters. However, it also works with numbers and boolean values as well. It works fine with arrays, the output is either TRUE or FALSE just like the equal sign.

The COUNTIF function is like the equal sign but on steroids. It works fine with arrays and is easy to work with, it can also check if values are smaller/larger than other values. The COUNTIF function returns the actual count meaning a whole number equal or larger than 0 (zero).

The COUNTIFS function is a more advanced than the COUNTIF function.

### Useful resources

DELTA function - Microsoft

Kronecker Delta - Wolfram

Kronecker Delta - Wikipedia

### Functions in 'Engineering' category

The DELTA function function is one of many functions in the 'Engineering' category.

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