Explanation
In this example, the goal is to get the minimum value for a given group above a specific temperature. In other words, we want the min value after applying multiple criteria. The easiest way to solve this problem is with the MINIFS function. However, if you need more flexibility (for example, you need to work with arrays and not ranges), you can use the MIN function with the FILTER function. In older versions of Excel without MINIFS or FILTER, you can use a traditional array formula based on the MIN function and the IF function. Each method is explained below.
Excel Table
For convenience, all data is in an Excel Table named data in the range B5:D16. Excel Tables are a convenient way to work with data in Excel because they (1) automatically expand to include new data and (2) offer structured references , which allow you to refer to data by name instead of by address. If you are new to Excel Tables, this article provides an overview .
MINIFS function
One way to solve this problem is with the MINIFS function , which can get the minimum value in a range based on one or more criteria. The generic syntax for MINIFS with two conditions looks like this:
=MINIFS(min_range,range1,criteria1,range2,criteria2)
Note that each condition requires two arguments : range1 and criteria1 define the first condition, and range2 and criteria2 define the second condition. All conditions must be true in order for value to be considered. We start off with the min_range , which is the Value column in the table:
=MINIFS(data[Value],
Next, we add criteria to test for the group value entered in cell F5:
=MINIFS(data[Value],data[Group],F5
If we enter the formula above as-is, we will get the minimum value in group “A”. Next, we need to add a second condition to further restrict values to those above the temperature entered in cell G5:
=MINIFS(data[Value],data[Group],F5,data[Temp],"<"&G5)
Notice we need to concatenate the greater than operator ("<") to cell F5. This is a requirement of the MINIFS function, which uses an unusual formula syntax shared by SUMIFS, COUNTIFS, etc. When we enter this formula, it returns the minimum value in group “A” above a temperature of 72. For reference, the same formula with conditions hardcoded looks like this:
=MINIFS(data[Value],data[Group],"A",data[Temp],">72")
Note that MINIFS will automatically ignore empty cells that meet criteria. In other words, MINIFS will not treat empty cells that meet criteria as zero. On the other hand, MINIFS will return zero (0) if no cells match criteria. The MINIFS function works well, but it does have a significant limitation: the range arguments inside MINIFS must be actual ranges , you can’t substitute arrays . If you need to use arrays, see the MIN + FILTER option below.
MIN + FILTER
In the dynamic array version of Excel , another way to solve this problem is with MIN and FILTER like this:
=MIN(FILTER(data[Value],(data[Group]=F5)*(data[Temp]>G5)))
Inside the MIN function, the FILTER function is configured to filter values by group and temperature:
FILTER(data[Value],(data[Group]=F5)*(data[Temp]>G5))
Array is provided as the Value column in the table. The include argument is a simple expression:
(data[Group]=F5)*(data[Temp]>G5)
This is an example of using Boolean logic in Excel. Because there are 12 values in the table, each expression above generates an array of 12 TRUE and FALSE values like this:
{TRUE;FALSE;FALSE;TRUE;FALSE;FALSE;TRUE;FALSE;FALSE;TRUE;FALSE;FALSE}*{FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;TRUE;TRUE;TRUE;TRUE;TRUE;TRUE}
In the first array, the TRUE values indicate values in group “A”. In the second array, TRUE values indicate values above a temperature of 72. The math operation of multiplication (*) converts the TRUE and FALSE values to 1s and 0s:
{1;0;0;1;0;0;1;0;0;1;0;0}*{0;0;0;0;0;0;1;1;1;1;1;1}
And the result is a single array as the include argument like this:
FILTER(data[Value],{0;0;0;0;0;0;1;0;0;1;0;0})
Note the 1s in this array correspond to values that are in group “A” with a temperature above 72. FILTER returns the two values that meet this criteria directly to the MIN function:
=MIN({94;101})
and MIN returns 94 as a final result. The primary advantage of using the MIN function with the FILTER function is that you don’t need to provide a range of values on the worksheet. You can instead provide an array of values created with another operation. This is important when source data needs to be manipulated before a minimum value is calculated.
MIN + IF
In older versions of Excel that do not have the MINIFS function or the FILTER function, you can solve this problem with an array formula based on the MIN function and the IF function like this:
=MIN(IF((data[Group]=F5)*(data[Temp]>G5),data[Value]))
Note: this is an array formula and must be entered with control + shift + enter in Legacy Excel .
Working from the inside out, the IF function is evaluated first. The logical test inside IF is exactly the same as the logic explained above for FILTER:
(data[Group]=F5)*(data[Temp]>G5) // logical test
After the logic is evaluated, we have an array of 1s and 0s like this:
=MIN(IF({0;0;0;0;0;0;1;0;0;1;0;0},data[Value]))
The 1s correspond to rows where the group is “A” and the Temp is greater than 72. The final result from IF is an array like this:
{FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;94;FALSE;FALSE;101;FALSE;FALSE}
Looking at the values in this array, you can see that the IF function acts like a filter. Only values associated with group “A” and a temperature greater than 72 make it through the filter. The other values are replaced with FALSE. The IF function delivers this array directly to the MIN function :
=MIN({FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;94;FALSE;FALSE;101;FALSE;FALSE})
The MIN function automatically ignores FALSE values and returns the minimum number in the array: 94.
Alternative syntax with nested IFs
The array formula above uses Boolean logic to streamline the formula, but another option you might run into is nesting one IF formula inside another like this:
=MIN(IF(data[Group]=F5,IF(data[Temp]>G5,data[Value])))
Note: this is an array formula and must be entered with control + shift + enter in Legacy Excel .
Each IF formula applies a separate condition, so the values are filtered in two steps instead of one. This works fine, but the formula gets more complicated as additional criteria are added, since each condition requires another IF function. The advantage Boolean logic version of the formula is that you can add additional criteria without adding more IF functions.
Explanation
In this example, the goal is to get the minimum quiz score (i.e. the lowest quiz score) for each person listed in column B from the five quiz scores that appear in columns C through G. This is a job for the MIN function or the SMALL function, as explained below.
MIN function
The MIN function accepts one or more arguments , which can be a mix of constants, cell references, and ranges . MIN will return the minimum value in the data provided. Text values and empty cells are ignored.
In this example, each student has five test scores in the same row, and the goal is to get the minimum score for each student. Because the quiz scores are all together, the data is supplied to MIN as a single range. The formula in I5 is:
=MIN(C5:G5)
As the formula is copied down the table, MIN returns the lowest score for each student. MIN is fully automatic. If data changes, MIN will automatically recalculate. Note that the MIN function will ignore empty cells, but it will return an error if the data contains an error. To calculate a minimum value while ignoring errors you can adapt the formula approach explained here .
SMALL function
The SMALL function can also be used to return the minimum value in a set of data. The generic syntax for SMALL looks like this:
=SMALL(range,n)
where n is a number like 1, 2, 3, etc. For example, you can retrieve the first, second, and third smallest values like this:
=SMALL(range,1) // first smallest
=SMALL(range,2) // second smallest
=SMALL(range,3) // third smallest
In this example, you could use SMALL to get the minimum quiz score for each person like this:
=SMALL(C5:G5,1)
The SMALL function is especially useful when you want to get other nth smallest values, as seen in this example .
Notes
- To get a minimum value with one or more criteria, see the MINIFS function . You can also use the FILTER function with the MIN function, as explained here .
- To get the nth smallest value in a set of data (i.e. 1st smallest, 2nd smallest, 3rd smallest, etc.), see the SMALL function .
