How to use the DELTA function

What is the DELTA function?

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

1. Introduction

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.

δ_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.

2. Syntax

DELTA(number1, [number2])

3. Arguments

Argument	Text
number1	Required.
[number2]	Optional, default value is 0 (zero).

4. 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 function  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.

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5. 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.

5.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

5.2 The formula returns an unexpected value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference C3 converted to hard-coded value using the F9 key. The DELTA function requires numerical values which is not the case in this example. We have found what is wrong with the formula.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

5.3 Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

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6. 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.

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Useful resources

DELTA function - Microsoft
Kronecker Delta - Wolfram
Kronecker Delta - Wikipedia

'DELTA' function examples

The following article has a formula that contains the DELTA function.

Functions in 'Engineering' category

The DELTA function function is one of 42 functions in the 'Engineering' category.

Excel function categories

Excel categories

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