Author: Oscar Cronquist Article last updated on November 26, 2018

The image above shows an array formula in cell B8 that extracts unique distinct values sorted alphabetically from cell range B2:E5.

Array formula in B8:

=INDEX(\$B\$2:\$E\$5, SMALL(IF(SMALL(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0, COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ""), 1)=COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1), 1), MATCH(MIN(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)>0, "", COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1)), INDEX(COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, SMALL(IF(SMALL(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0, COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ""), 1)=COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1), 1), , 1), 0), 1)

Copy cell B8 and paste it to cells below as far as necessary.

To enter an array formula, type the formula in a cell then press and hold CTRL + SHIFT simultaneously, now press Enter once. Release all keys.

The formula bar now shows the formula with a beginning and ending curly bracket telling you that you entered the formula successfully. Don't enter the curly brackets yourself.

### Explaining formula in cell B11

This formula consists of two parts, one extracts the row number and the other the column number needed to return the correct value.

INDEX(reference, row, col)

Step 1 to 6 shows how the row number is calculated, step 7 to 11 demonstrates how to calculate the column number.

#### Step 1 - Prevent duplicates

The COUNTIF function counts values based on a condition or criteria, in this case, we take into account previously displayed values in order to prevent duplicates in our output list.

COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0

becomes

COUNTIF("Unique distinct", {"Banana", "Raspberry", "Banana", "Raspberry";"Grapefruit", "Banana", "Apple", "Grapefruit";"Blueberry", "Kiwifruit", "Raspberry", "Blackberry";"Raspberry", "Blueberry", "Blueberry", "Banana"})

becomes

{0,0,0,0;0,0,0,0;0,0,0,0;0,0,0,0}=0

and returns

{TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE}.

#### Step 2 - Replace TRUE with the corresponding rank order

The following IF function returns the corresponding sort order if the list had been sorted from A to Z based on the logical expression. FALSE returns "" (nothing).

IF(COUNTIF(\$B\$7:B7,\$B\$2:\$E\$5)=0,COUNTIF(\$B\$2:\$E\$5,"<"&\$B\$2:\$E\$5)+1,"")

becomes

IF({TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE}, {1,12,1,12;9,1,0,9;6,11,12,5;12,6,6,1}+1,"")

becomes

IF({TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE}, {1,12,1,12;9,1,0,9;6,11,12,5;12,6,6,1}+1,"")

becomes

IF({TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE;TRUE, TRUE, TRUE, TRUE}, {2,13,2,13;10,2,1,10;7,12,13,6;13,7,7,2},"")

and returns

{2,13,2,13;10,2,1,10;7,12,13,6;13,7,7,2}

#### Step 3 - Extract smallest value in array

The SMALL function extracts the k-th small number in array, in this case the second argument (k) is 1.

SMALL(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0, COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ""), 1)

becomes

SMALL({2,13,2,13;10,2,1,10;7,12,13,6;13,7,7,2}, 1)

and returns 1.

#### Step 4 - Replace TRUE with the corresponding row number

The IF function uses a logical expression to determine which value (argument) to return.

IF(SMALL(IF(COUNTIF(\$B\$7:B7,\$B\$2:\$E\$5)=0,COUNTIF(\$B\$2:\$E\$5,"<"&\$B\$2:\$E\$5)+1,""),1)=COUNTIF(\$B\$2:\$E\$5,"<"&\$B\$2:\$E\$5)+1,ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1)

becomes

IF(1=COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1)

becomes

IF(1={2,13,2,13;10,2,1,10;7,12,13,6;13,7,7,2}, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1)

becomes

IF({FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,TRUE,FALSE;FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE}, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1)

becomes

IF({FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,TRUE,FALSE;FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE}, {1;2;3;4})

and returns

{FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,2,FALSE;FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE}

#### Step 5 - Find smallest value

The SMALL function finds the smallest value in the array ignoring the boolean values

SMALL(IF(SMALL(IF(COUNTIF(\$B\$7:B7,\$B\$2:\$E\$5)=0,COUNTIF(\$B\$2:\$E\$5,"<"&\$B\$2:\$E\$5)+1,""),1)=COUNTIF(\$B\$2:\$E\$5,"<"&\$B\$2:\$E\$5)+1,ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1),1)

becomes

SMALL({FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,2,FALSE;FALSE,FALSE,FALSE,FALSE;FALSE,FALSE,FALSE,FALSE},1)

and returns 2. This is the row number we need to extract the correct value from cell range B2:E5.

#### Step 6 - Return array

This step uses the INDEX function to return an array from a given row in cell range B2:E5.

INDEX(COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, SMALL(IF(SMALL(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0, COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ""), 1)=COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1), 1), , 1)

becomes

INDEX(COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, 2, , 1)

becomes

INDEX({2,13,2,13;10,2,1,10;7,12,13,6;13,7,7,2}, 2, , 1)

and returns

{10,2,1,10}

#### Step 7 - Match value in array

This step uses the MATCH function to return the correct column number needed to extract the value we need from cell range B2:E5.

MATCH(MIN(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)>0, "", COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1)), INDEX(COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, SMALL(IF(SMALL(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0, COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ""), 1)=COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1), 1), , 1), 0)

becomes

MATCH(MIN(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)>0, "", COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1)), {10,2,1,10}, 0)

becomes

MATCH(1, {10,2,1,10}, 0)

and returns 3. This is the column number we need.

#### Step 8 - Return value

INDEX(\$B\$2:\$E\$5, SMALL(IF(SMALL(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0, COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ""), 1)=COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1), 1), MATCH(MIN(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)>0, "", COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1)), INDEX(COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, SMALL(IF(SMALL(IF(COUNTIF(\$B\$7:B7, \$B\$2:\$E\$5)=0, COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ""), 1)=COUNTIF(\$B\$2:\$E\$5, "<"&\$B\$2:\$E\$5)+1, ROW(\$B\$2:\$E\$5)-MIN(ROW(\$B\$2:\$E\$5))+1), 1), , 1), 0), 1)

becomes

=INDEX(\$B\$2:\$E\$5, 3, 2)

and returns "Apple" in cell B8.