Identify missing numbers in a range

Author: Oscar Cronquist Article last updated on December 03, 2018

Question: How do I find missing numbers between 1-9 in a range?

1 3 4
5 6 7
8 8 3

Array formula in cell B8:

=SMALL(IF(COUNTIF($B$3:$D$5, ROW($1:$9))=0, ROW($1:$9), ""), ROWS(B8:$B$8))

If you have numbers between 5 and 32, change ROW($1:$9) to ROW($5:$32)

The formula won´t work if you have numbers above 1048576 (excel 2007). See this post: Identify missing values in a column using excel formula

How to create an array formula

Copy above array formula
Select cell B8
Press with left mouse button on in formula bar
Paste array formula in formula bar
Press and hold Ctrl + Shift
Press Enter

Explaining formula in cell B8

Step 1 - Check if numbers in range equal numbers in list

The COUNTIF function counts values based on a condition, in this case, multiple conditions. The first argument is the cell range containing the numbers, the second argument is a given list of numbers.

The ROW function returns the row number of a cell, in this case a cell range. The ROW function then returns an array of row numbers of all cells in the cell range.

COUNTIF($B$3:$D$5, ROW($1:$9)

becomes

COUNTIF({1,3,4; 5,6,7; 8,8,3},{1; 2; 3; 4; 5; 6; 7; 8; 9})

and returns

{1;0;2;1;1;1;1;2;0}.

Step 2 - Which numbers are missing?

A 0 (zero) indicates a number is missing, compare the value with 0 (zero) and we get either TRUE or FALSE.

COUNTIF($B$3:$D$5,ROW($1:$9))=0

becomes

{1;0;2;1;1;1;1;2;0}=0

and returns

{FALSE; TRUE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; TRUE}.

Step 3 - Replace TRUE with corresponding number

IF(COUNTIF($B$3:$D$5, ROW($1:$9))=0, ROW($1:$9), "")

becomes

IF({FALSE; TRUE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; TRUE}, ROW($1:$9), "")

becomes

IF({FALSE; TRUE; FALSE; FALSE; FALSE; FALSE; FALSE; FALSE; TRUE}, {1; 2; 3; 4; 5; 6; 7; 8; 9}, "")

and returns

{"";2;"";"";"";"";"";"";9}.

Step 4 - Extract a new number in a cell each

The SMALL function extracts the k-th smallest number from a cell range or array. SMALL( cell_ref, k)

The second argument contains the ROWS function and an expanding cell range. When you copy the cell and paste to cells below the cell reference grows. This makes sure that a new numb er is extracted in each cell.

SMALL(IF(COUNTIF($B$3:$D$5, ROW($1:$9))=0, ROW($1:$9), ""), ROWS(B8:$B$8)

becomes

SMALL({"";2;"";"";"";"";"";"";9}, ROWS(B8:$B$8)

becomes

SMALL({"";2;"";"";"";"";"";"";9}, 1)

and returns 2 in cell B8.

**Get Excel *.xls** file

Missing numbers in a range.xls

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SMALL IF COUNTIF ROW ROWS

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5 Responses to “Identify missing numbers in a range”

Joe says:

April 20, 2012 at 6:06 pm

I have a worksheet that has rows, each containing sequential groupings of values of "1" and "0" These alternate across 1800 colunms of data.

My question: how do I count the number of groupings of each? In other words, across those 1800 columns, how many arrays of value 1 and how many arrays of value 0 do I have?

Thanks.
Joe

Reply
Oscar says:

April 21, 2012 at 12:10 pm

Joe,

see this post:
Count the number of groupings of each value

Reply
manish says:

October 2, 2012 at 5:18 pm

thanks

Reply
Felipe says:

August 15, 2013 at 3:13 pm

Is there any difference to apply this formula in only one column (F2:F1093)? I´m trying to identify missing numbers in a list but I´m making something wrong.

Reply
- Oscar says:
  
  August 30, 2013 at 9:06 am
  
  Felipe,
  
  Did you enter it as an array formula?

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