Please Note: This article is written for users of the following Microsoft Excel versions: 2007, 2010, and 2013. If you are using an earlier version (Excel 2003 or earlier), this tip may not work for you. For a version of this tip written specifically for earlier versions of Excel, click here: Summing Absolute Values.

Summing Absolute Values

by Allen Wyatt
(last updated May 16, 2017)

5

Joseph has a worksheet that contains a list of values. Some of those values are above zero and others are below. He can use the SUM function to calculate a sum of the values, but he really wants to calculate a sum of the absolute value of each item in the list. So, the sum of the three values -33, 14, -5 would be 52 instead of -24.

There is no intrinsic function you can use to create the desired sum, but you can create a formula to perform the task. One method is to use the SUMIF function, in the following manner:

=SUMIF(A1:A10,">0")-SUMIF(A1:A10,"<0")

The first SUMIF sums all the values that are greater than zero, and the second sums all those less than zero. Thus, with the four values -33, 14, -5, 42, the first SUMIF would result in a sum of 56 (14 + 42) and the second would result in a sum of -38 (-33 + -5). When you subtract the second sum from the first (56 - -38) you get a final answer of 94, which is the sum of all the absolute values.

Another approach is to use the SUMPRODUCT function. The following formula will produce the desired result:

=SUMPRODUCT(ABS(A1:A10))

The function is typically used to multiply different elements of arrays by each other, and then sum those products. Since only one array (A1:A10) is provided, there is no multiplication done, but a sum of the desired absolute values is returned.

You can also get the desired result by using an array formula, a convenient but seldom used feature of Excel. Assuming your values are in the range A1:A10, type this formula:

=SUM(ABS(A1:A10))

Don't press Enter; instead press Ctrl+Shift+Enter, which signifies this is an array formula. If the formula is entered correctly, you'll see braces around the formula in the Formula bar:

{=SUM(ABS(A1:A50))}

What the formula does is internally create the intermediate column (which is an array of values) which are the individual absolute values of A1:A10. It then sums this array and displays the result.

Finally, if you prefer you could create your own user-defined function (a macro) that will return the sum of the absolute values in a range. The following is a macro that will accomplish this task:

Function SumAbs(Rng As Range) As Double
    Result = 0
    On Error GoTo Done
    For Each element In Rng
        Result = Result + Abs(element)
    Next element
Done:
    SumAbs = Result
End Function

You can use the function by entering a simple formula in your worksheet:

=SumAbs(A1:A10)

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (12615) applies to Microsoft Excel 2007, 2010, and 2013. You can find a version of this tip for the older menu interface of Excel here: Summing Absolute Values.

Author Bio

Allen Wyatt

With more than 50 non-fiction books and numerous magazine articles to his credit, Allen Wyatt is an internationally recognized author. He  is president of Sharon Parq Associates, a computer and publishing services company. ...

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Comments

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What is 8 - 2?

2017-05-17 03:38:40

Dave

John

My formula is correct. If you look at the original comment by Steve D, his expected total is 5, which is delivered. If you change the + to -, you get 27.

The only values in the list of seven that are greater than 5 or less than -5 are the last three, namely 9, 7 and -11. Adding them gives 16 minus 11 which is 5. Subtracting them gives 16 minus minus-11, which is 27.


2017-05-16 10:50:16

John

The formula's in Dave's comment should be "-" (subtraction) operations, not "+" (addition), as the 2nd SUMIF will return a negative result.


2017-05-16 06:53:55

Dave

That's a very elegant solution provided by Micky Avidan. If, like me, you haven't got to grips with SUMPRODUCT, you can always use the following longer, but possibly easier to read, formula:

=SUMIF(A1:A7,">5",A1:A7) + SUMIF(A1:A7,"<-5",A1:A7)

As with many formulae, you could put the value 5 into a cell and replace the 5 by the cell reference (e.g. B1) in the formula. Then it's very easy to change the threshhold and see the total change to suit. So my formula would become:

=SUMIF(A1:A7,">"&B1,A1:A7) + SUMIF(A1:A7,"<-"&B1,A1:A7)


2014-11-25 05:28:08

Michael (Micky) Avidan

@Steve D,
Try: =SUMPRODUCT((ABS(A1:A7)>5)*A1:A7)
Michael (Micky) Avidan
“Microsoft® Answers" - Wiki author & Forums Moderator
“Microsoft®” MVP – Excel (2009-2015)
ISRAEL


2014-11-24 18:27:25

Steve D

Hi Allen,

How would I sum values that are positive or negative but ONLY if the absolute value of the entry is larger than another number?

Say I have the numbers 1,5,-4,-5,9,7,-11

I only wish to add those numbers where the absolute value is > 5, say. So I would add 9+7-11 = 5. How to do this automatically?

Many thanks in advance!


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