Summing Absolute Values

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)