*The article shows a few different ways to get the max value in Excel based on one or several conditions that you specify.*

In our previous tutorial, we looked at the common uses of the MAX function which is designed to return the largest number in a dataset. In some situations, however, you may need to drill down into your data further to find the max value based on certain criteria. This can be done by using a few different formulas, and this article explains all possible ways.

Until recently, Microsoft Excel did not have a built-in MAX IF function to get the maximum value based on conditions. A while ago, they introduced MAXIFS, and now the users of Excel 2019 and Excel 2016 included with Office 365 subscriptions can do conditional max an easy way.

In Excel 2013 and earlier versions, you still have to create your own **array formula** by combining the MAX function with an IF statement:

{=MAX(IF(*criteria_range*=*criteria*, *max_range*))}

To see how this generic MAX IF formula works on real data, please consider the following example. Supposing, you have a table with the long jump results of several students. The table includes the data for three rounds, and you are looking for the best result of a particular athlete, say Jacob. With the student names in A2:A10 and distances in C2:C10, the formula takes this shape:

`=MAX(IF(A2:A10="Jacob", C2:C10))`

Please keep in mind that an array formula must always be entered by pressing the Ctrl + Shift + Enter keys simultaneously. As the result, it is automatically surrounded with curly brackets like shown in the screenshot below (typing the braces manually won't work!).

I real-life worksheets, it's more convenient to input the criterion in some cell, so that you can easily change the condition without changing the formula. So, we type the desired name in F1 and get the following result:

`=MAX(IF(A2:A10=F1, C2:C10))`

In the logical test of the IF function, we compare the list of names (A2:A10) with the target name (F1). The result of this operation is an array of TRUE and FALSE, where the TRUE values represent names that match the target name (Jacob):

`{FALSE;FALSE;FALSE;TRUE;TRUE;TRUE;FALSE;FALSE;FALSE}`

For the *value_ if_true* argument, we supply the long jump results (C2:C10), so if the logical test evaluates to TRUE, the corresponding number from column C is returned. The *value_ if_false* argument is omitted, meaning will just have a FALSE value where the condition is not met:

`{FALSE;FALSE;FALSE;5.48;5.42;5.57;FALSE;FALSE;FALSE}`

This array is fed to the MAX function, which returns the maximum number ignoring the FALSE values.

In situation when you need to find the max value based on more than one condition, you can either:

Use nested IF statements to include additional criteria:

{=MAX(IF(*criteria_range1*=*criteria1*, IF(*criteria_range2*=*criteria2*, *max_range*)))}

Or handle multiple criteria by using the multiplication operation:

{=MAX(IF((*criteria_range1*=*criteria1*) * (*criteria_range2*=*criteria2*), *max_range*))}

Let's say you have the results of boys and girls in a single table and you wish to find the longest jump among girls in round 3. To have it done, we enter the first criterion (female) in G1, the second criterion (3) in G2, and use the following formulas to work out the max value:

`=MAX(IF(B2:B16=G1, IF(C2:C16=G2, D2:D16)))`

`=MAX(IF((B2:B16=G1)*(C2:C16=G2), D2:D16))`

Since both are array formulas, please remember to press Ctrl + Shift + Enter to complete them correctly.

As shown in the screenshot below, the formulas produce the same result, so which one to use is a matter of your personal preference. For me, the formula with the Boolean logic is easier to read and build – it allows adding as many conditions as you want without nesting additional IF functions.

The first formula uses two nested IF functions to evaluate two criteria. In the logical test of the first IF statement, we compare the values in the Gender column (B2:B16) with the criterion in G1 ("Female"). The result is an array of TRUE and FALSE values where TRUE represents data that match the criterion:

`{FALSE; FALSE; FALSE; TRUE; TRUE; TRUE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; TRUE; TRUE; TRUE}`

In a similar fashion, the second IF function checks the values in the Round column (C2:C16) against the criterion in G2.

For the *value_if_true* argument in the second IF statement, we supply the long jump results (D2:D16), and this way we get the items that have TRUE in the first two arrays in corresponding positions (i.e. the items where the gender is "female" and round is 3):

`{FALSE; FALSE; FALSE; FALSE; FALSE; 4.63; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; 4.52}`

This final array goes to the MAX function and it returns the largest number.

The second formula evaluates the same conditions within a single logical test and the multiplication operation works like the AND operator:

When the TRUE and FALSE values are used in any arithmetic operation, they are converted into 1's and 0's, respectively. And because multiplying by 0 always gives zero, the resulting array has 1 only when all the conditions are TRUE. This array is evaluated in the logical test of the IF function, which returns the distances corresponding to the 1 (TRUE) elements.

Many Excel users, including me, are prejudiced against array formulas and try to get rid of them wherever possible. Luckily, Microsoft Excel has a few functions that handle array natively, and we can use one of such functions, namely SUMPRODUCT, as kind of "wrapper" around MAX.

The generic MAX IF formula without array is as follows:

=SUMPRODUCT(MAX((*criteria_range1*=*criteria1*) * (*criteria_range2*=*criteria2*) * *max_range*))

Naturally, you can add more range/criteria pairs if needed.

To see the formula in action, we will be using the data from the previous example. The aim is to get the maximum jump of a female athlete in round 3:

`=SUMPRODUCT(MAX(((B2:B16=G1) * (C2:C16=G2) * (D2:D16))))`

This formula is competed with a normal Enter keystroke and returns the same result as the array MAX IF formula:

Casting a closer look at the above screenshot, you can notice that invalid jumps marked with "x" in the previous examples now have 0 values in rows 3, 11 and 15, and the next section explains why.

As with the MAX IF formula, we evaluate two criteria by comparing each value in the Gender (B2:B16) and Round (C2:C16) columns with the criteria in cells G1 and G2. The result are two arrays of TRUE and FALSE values. Multiplying the arrays' elements in the same positions converts TRUE and FALSE into 1 and 0, respectively, where 1 represents the items that meet both criteria. The third multiplied array contains the long jump results (D2:D16). And because multiplying by 0 gives zero, only the items that have 1 (TRUE) in the corresponding positions survive:

`{0; 0; 0; 0; 0; 4.63; 0; 0; 0; 0; 0; 0; 0; 0; 4.52}`

In case *max_range* contains any text value, the multiplication operation returns the #VALUE error because of which the entire formula won't work.

The MAX function takes it from here and returns the largest number that meets the specified conditions. The resulting array consisting of a single element {4.63} goes to the SUMPRODUCT function and it outputs the max number in a cell.

- The range where you search for the highest value must contain only numbers. If there are any text values, a #VALUE! error is returned.
- The formula cannot evaluate the "not equal to zero" condition in a negative data set. To find max value ignoring zeros, use either a MAX IF formula or MAXIFS function.

To find the max value when **any** of the specified conditions is met, use the already familiar array MAX IF formula with the Boolean logic, but add the conditions instead of multiplying them.

{=MAX(IF((*criteria_range1*=*criteria1*) + (*criteria_range2*=*criteria2*), *max_range*))}

Alternatively, you can use the following non-array formula:

=SUMPRODUCT(MAX(((*criteria_range1*=* criteria1*) + ( *criteria_range2*=* criteria2*)) * *max_range*))

As an example, let's work out the best result in rounds 2 and 3. Please pay attention that in the Excel language, the task is formulated differently: return the max value if round is either 2 or 3.

With the rounds listed in B2:B10, the results in C2:C10 and criteria in F1 and H1, the formula goes as follows:

`=MAX(IF((B2:B10=F1) + (B2:B10=H1), C2:C10))`

Enter the formula by pressing the Ctrl + Shift + Enter key combination and you will get this result:

The max value with the same conditions can also be found by using this non-array formula:

`=SUMPRODUCT(MAX(((B2:B10=F1) + (B2:B10=H1)) * C2:C10))`

However, we need to replace all "x" values in column C with zeros in this case because SUMPRODUCT MAX only works with numeric data:

The array formula works exactly the same way as MAX IF with AND logic except that you join the criteria by using the addition operation instead of multiplication. In array formulas, addition works as the OR operator:

Adding up two arrays of TRUE and FALSE (which result from checking the values in B2:B10 against the criteria in F1 and H1) produces an array of 1's and 0's where 1 represents the items for which either condition is TRUE and 0 represents the items for which both conditions are FALSE. As the result, the IF function "keeps" all the items in C2:C10 (*value_if_true*) for which any condition is TRUE (1); the remaining items are replaced with FALSE because the *value_if_false* argument is not specified.

The non-array formula works in a similar manner. The difference is that instead of IF's logical test, you multiply the elements of the 1's and 0's array by the elements of the long jump results array (C2:C10) in the corresponding positions. This nullifies the items that do not meet any condition (have 0 in the first array) and keeps the items that meet one of the conditions (have 1 in the first array).

The users of Excel 2019 and Excel for Office 365 are free from the trouble of taming arrays to build their own MAX IF formula. These versions of Excel provide the long-awaited MAXIFS function that makes finding the largest value with conditions child's play.

In the first argument of MAXIFS, you enter the range in which the maximum value should be found (D2:D16 in our case), and in the subsequent arguments you can enter up to 126 range/criteria pairs. For example:

`=MAXIFS(D2:D16, B2:B16, G1, C2:C16, G2)`

As shown in the screenshot below, this simple formula has no problem with processing the range that contains both numeric and text values:

For the detailed information about this function, please see Excel MAXIFS function with formula examples.

That's how you can find max value with conditions in Excel. I thank you for reading and hope to see you on our blog next week!

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