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Multiple Condition Tests

One of the most basic functions in any spreadsheet is to return an answer based upon some

condition. This becomes especially useful when counting or summing based upon that condition.

One condition is useful, and is easily achieved using COUNTIF or SUMIF. These are incredibly

useful and flexible functions, but limited as they are to single conditions, they can be lacking.

Multiple conditions, such as counting the number of items sold by part number AND by month,

greatly extends the functionality of our solution. There are a number of ways that this can be

achieved within Excel, but this paper is focusing on one particular function, the SUMPRODUCT

function, which by creative use has evolved to a flexibility undreamt of by its originators in

Microsoft. Because this usage has been driven outside of Microsoft, by real-world Excel users,

you will not see it documented within Excel help, or in MSDN.

SUMPRODUCT is one of the most versatile functions provided in Excel. In its most basic form,

SUMPRODUCT multiplies corresponding members in given arrays, and returns the sum of

those products. This page discusses the classic use of SUMPRODUCT, how creativity and

inbuilt flexibility has enabled it to evolve into a far more useful function, and explains some of the

techniques being deployed.

This article comes in two parts. This first part discusses SUMPRODUCT, how it has evolved,

how it works, whilst Part 2 provides a number of real world problems and the solutions,

Buy me a

beer

Standard Use of SUMPRODUCT

Evolving Use of SUMPRODUCT

Advantages of SUMPRODUCT

SUMPRODUCT Explained

Format of SUMPRODUCT

Conditional Counting and Summing in VBA

SUMPRODUCT and Excel 2007

Performance Considerations

Notes

References

Acknowledgments

Examples

If this page,

or this site,

has been

helpful, feel

free to

show your

appreciation

by buying

me a beer.

Standard Use of SUMPRODUCT

In it's classic form, SUMPRODUCT multiplies each value in one array by the corresponding

value in another array, and returns the summed result. As an example, if cells A9:A11 contain the

values 1,2,3 and B9:B11 contain 10,20,30, then

=SUMPRODUCT(A9:A11,B9:B11)

returns 140, or (1*10)+(2*20)+(3*30)=10+40+90=140.

This is a useful function, but nothing more than that. A further, more 'creative' use of

SUMPRODUCT has evolved, and is still evolving, driven as far as I can see mainly by the

regular contributors of the Microsoft Excel newsgroups. This has been a creative and productive

process that has significantly increased the useability of SUMPRODUCT, but in a way that you

will not find documented in Excel's Help.


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Evolving Use of SUMPRODUCT

Within Excel, there are two very useful functions that support conditional counting and summing,

namely COUNTIF and SUMIF. Very useful functions, but limited in that they can only evaluate

a single test range.

In certain instances, a very simple double conditional test between two values can be emulated

by testing for the lower condition and subtracting anything that is beyond the upper condition.

For instance, the formula =COUNTIF(A1:A10,>=10) COUNTIF(A1:A10,>20)

calculates how many items in A1:A10 that fall between 10 and 20, by counting all items greater

than 10, which also includes those items greater than 20, and then subtracting the count of those

items in A1:A10 that are greater than 20. Whilst this emulates a double conditional test, it is very

limited, it cannot work on different ranges, or more conditions.

Multiple conditions are so useful to test ranges (say between two dates), and double tests (one

array = A and another = B), and whilst this can be managed using array functions

=SUM(IF(test_A,IF(test_B, etc. ,

this is somewhat unwieldy, and is an array formula. And there is a better way, using

SUMPRODUCT.

Note that in this section, all formulae given are using the '*' (multiply) operator format, but this in

itself is one of the biggest discussion points around the SUMPRODUCT function, one which is

discussed below.

To understand how SUMPRODUCT can be used, first consider the following data.

A B C

1 Make Month Price

2 Ford June 7,500

3 Ford June 8,300

4 Ford May 6,873

5 Ford June 11,200

6 Renault June 13,200

7 Renault June 14,999

8 BMW June 17,500

9 BMW May 23,500

10 BMW June 18,000

Table 1.

We can easily count the number of Fords with

=COUNTIF(A1:A10,"Ford")

which returns 4.

Similalrly, it is straight-forward to get the value of Fords sold, using

=SUMIF(A1:A10,"Ford",C1:C10)

which gives 33,873.

But supposing that we want a count of how many Fords are sold in June, or the value of them?

The number can be calculated with

=SUM(IF(A1:A10="Ford",IF(B1:B10="June",1,0),0))

which is an array formula so is committed with Ctrl-Shift-Enter, not just Enter. Similarly, the value

is obtained with


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=SUM(IF(A1:A10="Ford",IF(B1:B10="June",C1:C10,0),0))

which is also an array formula.

But as this page is about SUMPRODUCT, you would expect that we could use that function in

this case, and we can. The solution for the number of Fords sold in June using this function is

=SUMPRODUCT((A1:A10="Ford")*(B1:B10="June")) .

The value is obtained with

=SUMPRODUCT((A1:A10="Ford")*(B1:B10="June")*(C1:C10))

The * is being used as the AND operator, the formula is saying, where A1:A10 = Ford AND

B1:B10 = June, and where A1:A10 = Ford AND B1:B10= June, multiplied by C1:C10.

In my view, this formula more readily shows what the author's objective is, and of course, as it is

not an array formula it is simply committed with Enter.

We can see that the * is equivalent to AND in the formula, how this works is explained later, but

supposing we want an OR condition. As a further extension of its use, we use the '+' (plus)

operator to count OR conditions, such as how many cars sold were either Fords or Renaults.

The formula for this is

=SUMPRODUCT((A1:A10="Ford")+(A1:A10="Renault"))

which returns the result 6 as expected[1]

.

So far, so good, in that we have a versatile function that can do any number of conditional tests,

and has an inbuilt flexibility that provides extensibility. Its power is augmented when combined

with other functions, such as can be found in the examples page[2]

.

Advantages of SUMPRODUCT

Multiple conditional tests are a major advantage of the SUMPRODUCT function as descibed

above, but it has two other considerable advantages. The first is that it can function with closed

workbooks, and the second is that the handling of text values can be tailored to the requirement.

In the case of another workbook, the SUMIF function can be used to calculate a value, such as

in

=SUMIF('[Nowfal Rates.xls]RATES'!$K$11:$K$13,"gt;1")

This is fine in itself, and the value remains if the other workbook is closed, but as soon as the

sheet is re-calculated, the formula returns #VALUE. Similarly, if the formula is entered with the

other workbook already closed, a #VALUE is immediately returned.

SUMPRODUCT, however, overcomes this problem. The formula

=SUMPRODUCT(--('[Nowfal Rates.xls]RATES'!$K$11:$K$13>1),--('[Nowfal

Rates.xls]RATES'!$K$11:$K$13))

returns the same result, but it will still work when the other workbook is closed and the sheet is

re-calculated, and can be initially entered referencing the closed workbook, without a #VALUE

error.

The second major advantage is being able to handle text in numeric columns differently.

Consider the follwoing dataset, as shown in Table 2.

A B

1 Item Number


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2 x 1

3 y 2

4 x 3

Table 2.

If we are looking at rows 1:4. we can see that we have a text value in B1 In this case it is simply

a heading row, but the principle applies to a text value in any row.

Using SUMPRODUCT, we can either return an error, or ignore the text. This can be useful if

we want to ignore errors, or if we want to trap the error (and presumably correct it later).

Errors will be returned if we use this version

=SUMPRODUCT((A1:A4="x")*(B1:B4))

To ignore errors, use this amended version which uses the double unary operator (see

SUMPRODUCT Explained below for details)

=SUMPRODUCT(--(A1:A4="x"),(B1:B4))

And a third, most significant advantage, is that the conditional test range or the condition can be

constructed in a huge number of ways to facilitate the requirement, such as

LEFT(A1:A10),

ISNUMBER(MATCH(A1:A10,{"apples","pears"},0), or

ISNUMBER(MATCH(K2:K30,ROW(INDIRECT(TODAY()&":"&TODAY()+10)),0))

But how does it work?

SUMPRODUCT Explained

Understanding how SUMPRODUCT works helps to determine where to use it, how to can

construct thus formula, and thus how it can be extended.

Table 3. below shows an example data set that we will use.

A B C

9 Ford B 3

10 Vauxhall C 4

11 Ford A 2

12 Ford A 1

13 Ford D 4

14 Ford A 3

`5 Ford A 2

16 Renault A 8

17 Ford A 6

18 Ford A 8

19 Ford A 7

20 Ford A 6

Table 3.

In this example, the problem is to find how many Fords with a category of "A" were sold.

A9:A20 holds the make, B9:B20 has the category, and C9:C20 has the number sold. The

formula to get this result is

=SUMPRODUCT((A9:A20="Ford")*(B9:B20="A")*(C9:C20)) .


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The first part of the formula (A9:A20="Ford") checks the array of makes for a value of

Ford. This returns an array of TRUE/FALSE, in this case it is

{TRUE,FALSE,TRUE,TRUE,TRUE,TRUE,TRUE,FALSE,TRUE,TRUE,TRUE,TRUE}

Similarly, the categories are checked for the vale A with (B9:B20="A") . Again, this

returns an array of TRUE/FALSE, or

{FALSE,FALSE,TRUE,TRUE,FALSE,TRUE,TRUE,TRUE,TRUE,TRUE,TRUE,TRUE}

And finally, the numbers are not checked but taken as is, that is (C9:C20) , which returns

an array of numbers

{3,4,2,1,4,3,2,8,6,8,7,6}

So now we have three arrays, two of TRUE/FALSE values, one of numbers. This is showm in

Table 4.

A B C

9 TRUE * FALSE * 3

10 FALSE * FALSE * 4

11 TRUE * TRUE * 2

12 TRUE * TRUE * 1

13 TRUE * FALSE * 4

14 TRUE * TRUE * 3

15 TRUE * TRUE * 2

16 FALSE * TRUE * 8

17 TRUE * TRUE * 6

18 TRUE * TRUE * 8

19 TRUE * TRUE * 7

20 TRUE * TRUE * 6

Table 4.

And this is where it gets interesting.

SUMPRODUCT usually works on arrays of numbers, but we have arrays of TRUE/FALSE

values as well as an array of numbers. By using the '*' (multiply) operator, we can get numeric

values that can be summed. '*' has the effect of coercing these two arrays into a single array of

1/0 values. Multiplying TRUE by TRUE returns 1 (try it, enter =TRUE*TRUE in a cell and see

the result), any other combination returns 0. Therefore, when both conditions are satisfied, we

get a 1, whereas if any or both conditions are not satisfied, we get a 0. Multiplying the first array

of TRUE/FALSE values by the second array of TRUE/FALSE values returns a composite array

of 1/0 values, or

{0,0,1,1,0,1,1,0,1,1,1,1}.

This subsequent array of 1/0 values is then multiplied by the array of numbers sold to give a

further array, an array of numbers sold that satisfy the two test conditions. SUMPRODUCT

then sums the members of this array to give the count.

Table 4. shows the values that the conditional tests break down to before being acted upon by

the '*' operator.

Table 5. shows a virtual representation of those TRUE/FALSE values as their numerical

equivalents of 1/0 and the individual multiplication results. From this, you should be able to see

how SUMPRODUCT arrives at its result, namely 35.

A B C

9 1 * 0 * 3 0


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10 0 * 0 * 4 0

11 1 * 1 * 2 2

12 1 * 1 * 1 1

13 1 * 0 * 4 0

14 1 * 1 * 3 3

15 1 * 1 * 2 2

16 0 * 1 * 8 0

17 1 * 1 * 6 6

18 1 * 1 * 8 8

19 1 * 1 * 7 7

20 1 * 1 * 6 6

35

Table 5.

Table 6. shows you the same virtual representation of 1/0 numerical values without the numbers

sold column, that is using SUMPRODUCT to count the number of rows satisfying the two

conditions, or

=SUMPRODUCT((A9:A20=A1)*(B9:B20="A"))

A B

9 1 * 0 = 0

10 0 * 0 = 0

11 1 * 1 = 1

12 1 * 1 = 1

13 1 * 0 = 0

14 1 * 1 = 1

15 1 * 1 = 1

16 0 * 1 = 0

17 1 * 1 = 1

18 1 * 1 = 1

19 1 * 1 = 1

20 1 * 1 = 1

8

Table 6.

If you have been able to follow this explanation all of the way through, it may have occurred to

you that although we are using the SUMPRODUCT function, the '*' operators have resolved the

multiple arrays into a single composite array, leaving SUMPRODUCT to simply sum the

members of that composite array, that is, there is no product. This is perfectly correct, and

perfectly valid, SUMPRODUCT can work on a single array (put 1,2,3 in cells A1,A2,A3, and

insert =SUMPRODUCT(A1:A3) in a cell, it returns 6 correctly). In reality, we only need the '*'

to coerce the arrays that are being tested for a particular condition, we do not need it for the

array that is not subject to a conditional test. So we could also use

=SUMPRODUCT((A9:A20="Ford")*(B9:B20="A"),(C9:C20)) ,

which does use the product aspect (see more on this in the next section).

When using the SUMPRODUCT function, all arrays must be the same size, as corresponding

members of each array are multiplied by each other.

When using the SUMPRODUCT function, no array can be a whole column (A:A), the array


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must be for a range within a column (although the best part of a column could be defined with

A1:A65535 if so desired). Whole rows (1:1) are acceptable[3]

.

In a SUMPRODUCT function, the arrays being evaluated cannot be a mix of column and row

ranges, they must all be columns, or all rows. However, the row data can be transposed to

present it to SUMPRODUCT as columnar - see the Using TRANSPOSE to test against values in

a column not row example.

Format of SUMPRODUCT

In the examples presented so far, the format has been

=SUMPRODUCT((array1=condition1)*(array2=condition2)*(array3))

As mentioned above, we could also use

=SUMPRODUCT((array1=condition1)*(array2=condition2),(array3))

which works as the '*' operator is only required to coerce the conditional arrays that resolve to

TRUE/FALSE into numeric values.

As it the use of a arithmetic operator that coreces the TRUE/FALSE values to 1/0, we could use

many different operators and achieve the same result. Thus, it is also possible to coerce each of

the conditional arrays individually by multiplying them by 1,

=SUMPRODUCT((array1=condition1)*1,(array2=condition2)*1,(array3))

or

=SUMPRODUCT(1*(array1=condition1),1*(array2=condition2),(array3))

or by raising to the power of 1,

=SUMPRODUCT((array1=condition1)^1,(array2=condition2)^1,(array3))

or by adding 0,

=SUMPRODUCT((array1=condition1)+0,(array2=condition2)+0,(array3))

or

=SUMPRODUCT(0+(array1=condition1),0+(array2=condition2),(array3))

or even by using the N function,

=SUMPRODUCT(N(array1=condition1),N(array2=condition2),(array3))

These methods differ from the '*' operator in that they are applied to individual arrays, '*'

operates on two arrays.

All of these methods work, when there is more than one conditional array, so it is really a matter

of preference as to which to use. If there is a single conditional array, then the '*' operator

cannot be used (there are not two to multiply), so one of the other above methods has to be

used.

Yet another method is to use the double unary operator, --, in this way

=SUMPRODUCT(--(array1=condition1),--(array2=condition2),(array3))

The double unary operator also coerces the indivual array(s), which then acts more akin to

classic SUMPRODUCT.

There has been much discussion that one way is faster than another, or is more of a 'standard'

than another, but in reality there will be few instances where one method will gain a noticeable

performance advantage over another, and as for standards, this is all new territory, and will

mainly be used by people who have never been involved in using these standards, and who care

even less.

For me, I believe it is a matter of preference. Personally, I am being swayed to the double unary

-- notation, because it avoids a function call, it works in all situations (the '*' operator won't work

on a single array), and I don't like the '1*', '*1', '^1', or '+0' variations. So my preference is for


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=SUMPRODUCT(--(array1=condition1),--(array2=condition2),(array3))

which also has more similarity to classic SUMPRODUCT ,

There is one other varitaion which has been promoted recently, which is the single unary

operator, '-', such as

=SUMPRODUCT(-(array1=condition1),-(array2=condition2),(array3))

but I would not encourage this as it has no real merit that I can see, and has to be paired off,

otherwise it will return a negative result.

So, to sum up ...

Tests, like A=10 normally resolve to TRUE or FALSE, and any operator is only needed if you

want to coerce an array of TRUE/FALSE values to 1/0 integers, such as

=SUMPRODUCT(--(B5:B1953=101))

SUMPRODUCT arrays are normally separated by the comma. So, to preserve this format, if

you have multiple conditions, you can use the -- on both conditions like so

=SUMPRODUCT(--(B5:B1953=101),--(C5:C1953=7))

But, if you simply multiply two arrays of TRUE/FALSE, that implicitly resolves to 1/0 values that

are then summed, you don;t need comma, so you could then use

=SUMPRODUCT((B5:B193=101)*(C5:C193=7))

Any further, final, array of values can use the same operator, or could revert to comma. So your

formula can be written as

=SUMPRODUCT(--(B5:B1953=101),--(C5:C1953=7),(D5:D1953))

or

=SUMPRODUCT((B5:B1953=101)*(C5:C1953=7),(D5:D1953))

or

=SUMPRODUCT(--(B5:B1953=101),--(C5:C1953=7),--(D5:D1953))

or

=SUMPRODUCT((B5:B1953=101)*(C5:C1953=7)*(D5:D1953))

or

=SUMPRODUCT(--(B5:B1953=101),--(C5:C1953=7)*(D5:D1953))

If the result is the product of two conditions being multiplied, it is fine to multiply them together

as this will coerce the True/False values to 1/0 values to allow the summing

=SUMPRODUCT((condition1)*(condition2))

However, if there is only one condition, you can coerce to 1/0 with the double unary --

=SUMPRODUCT(--(condition1))

You could achieve this equally as well with

=SUMPRODUCT((1*(condition1)))

and equally the first could be represented as

=SUMPRODUCT(--(condition1),--(condition2))

There is no situation that I know of whereby a solution using -- could not be achieved somehow

with a '*'. Conversely, if using the TRANSPOSE function within SUMPRODUCT, then the '*'

has to be used.

So, as you can see there are a number of possibilities, and you make your own choice. I leave

the final word to Harlan Grove, who once wrote this paragraph on why he prefers the double

unary operator ...

....as I've written before, it's not the speed of double unary minuses I like, it's the fact that due

to Excel's operator precedence it's harder to screw up double unary minuses with typos than it

is to screw up the alternatives ^1, *1, +0. Also, since I read left to right, I prefer my number

type coercions on the left rather than the right of my Boolean expressions, and -- looks nicer

than 1* or 0+. Wrapping Boolean expressions inside N() is another alternative, possibly

clearer, but it eats a nested function call level, so I don't use it.


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Conditional Counting and Summing in VBA

All of the discussion so far has been about conditional formulae, that is directly within Excel

worksheets. It is often necessary to count or sum conditionally some worksheet ranges within a

VBA routine. In these instances, we could code a simple loop to go through all of the data and

check if it matches the condition, summing the matching items as we go.

Excel VBA has a method that allows a call out from VBA routines to a built-in worksheet

function, saving ourselves having to build that functionality, and greatly improving the power of

our VBA code. Whilst there is an overhead to calling an Excel function from within VBA, any

performance impact should be minimal if not over-used, and the usefulness of this facility is

clear. We can utilise this facility to achieve conditional counting and summing in VBA with little

effort, but there are a few things to be aware of.

As an example, consider the data in Table 1. above. If we needed to know how many Fords

were in the range A1:A10from within a VBA procedure, we could simply use the following code

This will load the mCount variable with the number of Fords, 4 in this instance.

Similalry, we can use SUMIF to calculate the value

This will load the mCount variable with the value of the Fords, 33873 in this instance. The natural

next step is to assume that we can extend this technique to our multiple condition test formulae

discussed above. If we are using COUNTIFS and SUMIFS in Excel 2007 (see SUMPRODUCT

and Excel 2007) then this is correct. For example, we can count how many Fords were sold in

June using

We get a result of 3 here in our mCount variable. Unfortunately, this technique cannot be

extended to array formulae, or conditional testing SUMPRODUCT formulae.

For example, a simple formula to count how many Fords were sold in Feb might be

=SUMPRODUCT((A2:A10="Ford")*(B2:B10="Feb"))

(none, as it happens), and you might think that we could use the following VBA to get the same

result


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This fails to compile, never mind getting the correct result. In this case, VBA is trying to make a

simple call to the worksheet function, but when array and these type of SUMPRODUCT

formulae are resolved in Excel each item is within the array is resolved and then passed to the

main function for SUMming, AVERAGEing, or whatever is being actioned. As VBA doesnt

evaluate the ranges, it is not passing correct information to the worksheet function, so we get

the error[4]

.

There is a solution to this problem, and that is to evaluate the function call within VBA, using the

VBA Evaluate method, which converts a Microsoft Excel name to an a value. The code here is

Although there is more effort required to ensure that the syntax of the function call is properly

constructed, and that strings tested against are properly formed with quotes around them[5]

, it

is still a useful technique to have, and provides the capability to use SUMPRODUCT (and by

association, array formulae) within VBA.

SUMPRODUCT and Excel 2007

When Microsoft introduced Excel 2007, the main focus was on ease of use, and improved

business analysis functionality. Unfortunately, the worksheet functions did not get much attention,

but there were a few new functions. Two of the new functions, COUNTIFS and

SUMIFS, support multiple conditional tests. For instance, in our previous examples ,

=SUMPRODUCT((A1:A10="Ford")*(B1:B10="June"))

=SUMPRODUCT((A1:A10="Ford")*(B1:B10="June")*(C1:C10))

where we count those items where A1:A10 is = Ford AND B1:B10 = June, and where A1:A10 =

Ford AND B1: B10 = June multiplied by C1:C10. In Excel 2007, COUNTIFS and SUMIFS can

be used in place of SUMPRODUCT. The Excel 2007 formulae would be

=COUNTIFS(A1:A10,"Ford",B1:B10,"June")

=SUMIFS(C1:C10,A1:A10,"Ford",B1:B10,"June")

A further improvement is that in Excel 2007, SUMPRODUCT can address a whole column,

which is a helpful change.

So, with Excel 2007 supporting multiple conditional tests, does this mean that the special use of

SUMPRODUCT is now redundant, and that it is relegated to its original, simple array


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multiplication role?

Whilst this may seem to be the case at first sight, a little thought shows that SUMPRODUCT

retains its unique position in the Excel developers toolkit. Why? Because COUNTIFS and

SUMIFS are still unable to calculate values in closed workbooks just as their predecessors

could not; and the Excel 2007 functions are still not able to accommodate the complex extra

functions that can be added to the conditional ranges in SUMPRODUCT.

Performance Considerations

Double Unary v * Operator

In most circumstances, either the '*' or -- versions of SUMPRODUCT can be used, and both

will function correctly. There are some exceptions to this. Consider a table of names and

amounts in A1:B10, where row 1 is a text heading of 'Name' and 'Amount'. The formula

=SUMPRODUCT(--(A1:A10="Bob"),--(B1:B10>0),B1:B10)

will correctly sum the positive values in column B where the value in column is 'Bob'. However,

this formula

=SUMPRODUCT((A1:A10="Bob")*(B1:B10>0)*(B1:B10))

returns a #VALUE! Error. The reason for the error is due to the text in B1, multiplying a text

value creates an error. To overcome it with the latter form, the ranges need to start beyond the

heading, in A2 and B2[6]

.

Similalrly, if one or more of the ranges within the formula is multi-column, then the '*' operator

again has to be used. Whilst this formula fails

=SUMPRODUCT(--(A1:A10="Bob"),--(B1:C10>0),--(B1:C10))

this formula works perfectly well

=SUMPRODUCT((A1:A10="Bob")*(B1:C10>0)*(B1:C10))

as indeed does this

=SUMPRODUCT((A1:A10="Bob")*(B1:C10>0),B1:C10)[7]

Using Transpose

If using the TRANSPOSE function within SUMPRODUCT, then the '*' operator has to be used.

Formula Efficiency

Most people will be familiar with the fact that array formulas can be very expensive, and if

over-used can significantly impair the recalculation of a worksheet/workbook.

Whilst SUMPRODUCT is not an array formula per se, it suffers from the same problem.

Although SUMPRODUCT is often faster than an equivalent array formula, it is marginal. And

like array formula, SUMPRODUCT is much slower than COUNTIF/SUMIF,thus it is better to

use these if appropriate.

So, never use SUMPRODUCT in this situation

=SUMPRODUCT((A1:A10="Ford")*(C1:C10))

Use the equivalent SUMIF


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=SUMIF(A1:A10,"Ford",C1:C10)

Even two COUNTIF /SUMIF functions are quicker than one SUMPRODUCT, so this formula

=COUNTIF(A1:A10,>=10)-COUNTIF(A1:A10,>20)

will be more efficient than this one,

=SUMPRODUCT((A1:A10>=10)*(A1:A10<=20))

by a factor of roughly 20%.

Notes

[1] We can also use =SUMPRODUCT(--(A1:A10={"Ford","Renault"})) in this

instance as we have a single range being tested for two (or more) values, the -- is to coerce the

Booleans to numbers that can be counted - see later.

[2] Although array formulae are mentioned here, they are not explained. For a detailed

discussion, see Chip Pearson's Array Formulas web page.

[3] Excel 2007 has now removed this constraint, SUMPRODUCT can now use whole columns,

as can any array formulae - see SUMPRODUCT and Excel 2007

[4] Note that the simple form of SUMPRODUCT, =SUMPRODUCT(rng1,rng2) works

perfectly well in VBA as Application.WorksheetFunction.SUMPRODUCT(rng1,rng2), as VBA is

conforming to the functions call criteria

[5] When embedding quotes within a string, the quotes have to be doubled up, otherwise the

single quote is taken as the start or end of the string. This gets more complex if the quotes are

just after or just before an opening/closing quote, as we then have three quotes, i.e. one to tell

VBA that the next quotes is part of the string, one for the embedded quotes, and one to close

the string

[6] The error is not caused because the text field is being summed, SUM happily ignores text,

but rather because the value in column B is multiplied by the result of the conditional tests, it is

multiplying text by a number that causes the #VALUE!

[7] As can be seen, this restriction applies to SUMPRODUCT formulae with multiple columns,

whether the multiple columns are within a conditional range or a value range

References

As mentioned above, a detailed discussion on arrays and array formulae, by Microsoft Excel

MVP Chip Pearson, can be found here.

Another real-world example of SUMPRODUCT is given in Processing Coloured Cells which, in

conjunction with a custom UDF, shows how to count colour instances.

Felipe Gualberto has translated the majority of this page into Portuguese, at his ambienteoffice

site.

This article also inspired misange to write a French article on SUMPRODUCT (or

SOMMEPROD), which can be found on the excellent excelabo site, with a further page here.


13 of 14 9/5/2011 7:04 PM

Copyright © 2003-2006 xlDynamic.com

Acknowledgements

This method of describing how the SUMPRODUCT formula resolves is originally based upon a

post in the Excel newgroups from Microsoft Excel MVP Ken Wright. It was Ken who initially

explained SUMPRODUCT in this manner, which I found so clear and helpful.

This page was proof-read by the late Frank Kabel, who offered many improvements and some

advanced examples. Frank was one of the most prolific posters in the Excel newsgroups, and

has probably offered more SUMPRODUCT solutions than the other posters together.

Copyright © 2003-2006 xlDynamic.comPage last updated: 2nd Feb 2010

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Multiple Condition Tests

One of the most basic functions in any spreadsheet is to return an answer based upon some condition. This becomes especially useful when counting or summing

based upon that condition. One condition is useful, and is easily achieved using COUNTIF or SUMIF. These are incredibly useful and flexible functions, but limited

as they are to single conditions, they can be lacking.

Multiple conditions, such as counting the number of items sold by part number AND by month, greatly extends the functionality of our solution. There are a number

of ways that this can be achieved within Excel, but this paper is focusing on one particular function, the SUMPRODUCT function, which by creative use has evolved

to a flexibility undreamt of by its originators in Microsoft. Because this usage has been driven outside of Microsoft, by real-world Excel users, you will not see it

documented within Excel help, or in MSDN.

SUMPRODUCT is one of the most versatile functions provided in Excel. In its most basic form, SUMPRODUCT multiplies corresponding members in given

arrays, and returns the sum of those products. This page discusses the classic use of SUMPRODUCT, how creativity and inbuilt flexibility has enabled it to evolve

into a far more useful function, and explains some of the techniques being deployed.

This article comes in two parts. The first part discussed SUMPRODUCT, how it has evolved, how it works, whilst this part provides a number of real world

problems and their solutions.

Examples

Matching against values in another range

Dates for any international setting

Using TRANSPOSE to test against values in a column not row

Testing against multiple non-contiguous ranges

Find instances of a string, ignoring leading or trailing spaces

Count the number of unique values in a range

Avoid double-counting in multiple conditions

Count items matching a list

Count partial matching in a range

Count beteween two dates, excluding holidays

Sum visible cells

References

Acknowledgments

Buy me a beer

If this page, or this site,

has been helpful, feel free

to show your appreciation

by buying me a beer.

Examples

Example 1: Count the number of items where the date, in A42:A407 is earlier than today, and J42:J407 is equal to a variable array of values

Solution: The date test is handled with ($A$42:$A$407<TODAY()). The variable array of values is setup in a range, and this is used in conjunction with the MATCH andISNUMBER functions.

=SUMPRODUCT((ISNUMBER(MATCH(J42:J407,Fred,0)))*($A$42:$A$407<TODAY()))

Example 2: To count the number of sales in 3 locations of service since a given time period.

Solution: In it's basic elements, this is a simple test. If the date to be tested against is in a cell it would be a simple=SUMPRODUCT((C5:C309>$A$1))*(H5:H309="A"))

But this formula shows a technique to use embedded date strings that works, as far as I am aware, in all international versions of Excel.=SUMPRODUCT((C5:C309>(--("2004/05/31")))*(H5:H309="A"))

Example 3: Instead of typing the multiple criteria into the formula, can I have them typed into cells, and just reference the cells?

Solution: This seeemd a simple request to which a solution of=SUMPRODUCT((B5:B63=L1:N1)*(C5:C63))

was suggested.

This failed because the requester wanted the criteria in a column, not a row, so this required the TRANSPOSE function to incorporate in SUMPRODUCT. This wasresult

=SUMPRODUCT((B5:B63=TRANSPOSE(P46:P48))*(C5:C63))

which, because it uses the TRANSPOSE function, has to be entered as an array formula.

Example 4: I originally had this,=SUMIF(J2:J196,J209,L2:L196)

but I need to have these extra ranges aggregated.R2:R196,U2:U196,V2:V196,Z2:Z196

Solution: This could easily be solved by having separate SUMPRODUCT functions for each of the separate test ranges, but with a bit of ingenuity, it can be resolved in one, busing the '+' operator.

=SUMPRODUCT(--(J2:J196=J209),L2:L196+R2:R196+U2:U196+V2:V196+Z2:Z196)

Example 5: Find the occurrences of a string, value of 'good', in a range A1:A100. Some of the cells could include leading and/or trailing spaces, or even HTML non -breaking spac

Solution: The basic count of the string is very simple. Allowing for leading and trailing spaces is also handled by including TRIM in the foirmula. However, TRIM doesn't handHTML non-breaking spaces, these have to be extracted from the range being tested with the SUBSTITUTE function.good

=SUMPRODUCT(--(TRIM(SUBSTITUTE(A1:A100,CHAR(160),""))="good"))

Main Worksheet Formulae SUMPRODUCT

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1 of 3 9/5/2011 7:06 PM

Example 6: Count the number of unique values in a range.

Solution: The first version works if the whole range, A1:A20, is occupied=SUMPRODUCT(1/COUNTIF(A1:A20,A1:A20))

However, this returns #DIV/0 if any of the range is blank. This can be corrected with=SUMPRODUCT((A1:A20<>"")/COUNTIF(A1:A20,A1:A20&""))

And finally, to overcome a bug in the implicit intersection of COUNTIF/SUMIF 1st argument with that argument's parent worksheet's used range., which can also retu#DIV/0, we can use

=SUMPRODUCT((A1:A20<>"")/(COUNTIF(A1:A20,A1:A20)+(A1:A20="")))

Example 7: Count the instances of either of two conditions being met in two different ranges.For this example, consider the range A1:A10 with countries, and B1:B10 with continC1:C10 with a flag saying whether they are G7 countries or not. We want to count the number of countries that are in Europe, or are G7 countries.

Solution: To count the number of countries that are eoither in Europe, or G7 countries, we could use=SUMPRODUCT((B1:B10="Europe")+(C1:C10="Y"))

The problem with this is that it will double-count the countries tin Europe that are also G7 countries. This can be overcome with

=SUMPRODUCT((B1:B10="Europe")+(C1:C10="Y"))-SUMPRODUCT(--(B1:B10="Europe"),--(C1:C10="Y"))

which uses a SUMPRODUCT to calculate the number of countries that are both in Europe and G7 countries, and is then subtracted from the double-counting formu

Example 8: Count the instances of more than one value in a given range. This example is counting how many Fords and Chryslers are in the range A1:A10.

Solution: This can be solved by using OR as described in the prevuious example, but on a single range, that is=SUMPRODUCT((A1:A10="Ford")+(A1:A10="Chrysler"))

But in this in stance, as we are looking for two values in a single range, it is better to test against an array of values, or=SUMPRODUCT(--(A1:A10={"Ford","Chrysler"}))

Example 9: Having a range of stock numbers, A1:A10, corresponding sites in B1:B10, and stock numbers in C1:C10, we need to count how many items of a particular part at aparticular site. This would be a straight-forward SUMPRODUCT normally, but in this case, the stock number contains a number of components, so the part id isembedded within this. SUMIF can use wildcards, but only for one test, but SUMPRODUCT doesn't support wildcards directly.

Solution: To solve this problem, we can use the FIND function to test whetehr our part number if embebbed within the stock number. The ISNUMBER function is used to teswhether it is found or not (avoiding the dreaded #VALUE error)

=SUMPRODUCT(--(ISNUMBER(FIND("ATN",A1:A10))),--(B1:B10="Birmingham"),--(C1:C10))

FIND is case sensitive, if case sensitivity is not required, use SEARCH instead.=SUMPRODUCT(--(ISNUMBER(SEARCH("ATN",A1:A10))),--(B1:B10="Birmingham"),--(C1:C10))

Example 10: Count the number of a certain day between two dates, excluding any holidays that may fall on those days.

Solution: SUMPRODUCT can be used to calculate the number of a particular day between two dates. For example, assuming that the two dates are in cells A1 and A2, thisformula returns the number of Wednesdays bewteen those two dates.

=SUMPRODUCT(--(WEEKDAY(ROW(INDIRECT(A1&":"&A2)))=4))

This solution utilises the fact that as Excel stores dates as serial numbers from 1st Jan 1900, the two dates can be used in an INDIRECT function to 'virtually' load the dates into rows, which can then be tested using the WEEKDAYand the ROW function to determine whether any of those row dates are the day in question. Thof course place a limit on the later date, which is 06-Jun-2079, as Excel is restricted to 65336 rows.

The NETWORKDAYS function provides a facility to exclude holidays in the count. Again, we can achieve this with our function by adding a test against the holdaysAssuming that the holidays are in a named range, holidays, we would use

=SUMPRODUCT(--(WEEKDAY(ROW(INDIRECT(A1&":"&A2)))=4),--(COUNTIF(holidays,ROW(INDIRECT($A$1&":"&A2)))=0))

We could also simulate the NETWORKDAYS function to count the number of days between two dates, excluding Saturdays and Sundays amd holidays using

=SUMPRODUCT(--(WEEKDAY(ROW(INDIRECT(A1&":"&A2)))<>1),(--(WEEKDAY(ROW(INDIRECT(A1&":"&

A2)))<>7)),--(COUNTIF(holidays,ROW(INDIRECT($A$1&":"&A2)))=0))

This might seem unnecessary, as we could more easily use the NETWORKDAYS function, but it does offer one small advantage over that function, it doesn't mattorder the dates are in. It could also be used to exclude any 1,2, 3 or whatever days, not just the Saturdays and Sundays, by changing the weekday value.

Example11:

Sum only the visible cells that match a certain criteria. For instance, in a range A1:A100, sum all cells that have a value of "North" in B1:B100, where some rows are not visdue to a Data Filter having been applied on the data.

Solution: This solution takes advantage of the function which ignores non-visible cells.

The first part is a straight-forward conditional test on range B1:B100 for a value of 'North, and the sum of the cells A1:A100--($B$1:$B$100="North"),$A$1:$A$10

The counting of the visible cells is more complicated. As mentioned above, it uses SUBTOTAL, together with ROW, INDEX and OFFSET functions, like so--(SUBTOTAL(3,OFFSET(INDEX($A$1:$A$100,1,1),ROW($A$1:$A$100)-ROW(INDEX($A$1:$A$100,1,1)),0))=1)

The total formula then becomes=SUMPRODUCT(--(SUBTOTAL(3,OFFSET(INDEX($A$1:$A$100,1,1),ROW($A$1:$A$100)-ROW(INDEX($A$1:$A$100,1,1)),0))=1),--($B$1:$B$100="North"),$A$1:$A

References

As mentioned above, a detailed discussion on arrays and array formulae, written by Microsoft Excel MVP Chip Pearson, can be found here.


2 of 3 9/5/2011 7:06 PM


Another real-world example of SUMPRODUCT is given in Processing Coloured Cells which, in conjunction with a custom UDF, shows how to count colour

instances.

Acknowledgements

This method of describing how the SUMPRODUCT formula resolves is originally based upon a post in the Excel newgroups from Microsoft Excel MVP Ken

Wright. It was Ken who initially explained SUMPRODUCT in this manner, which I found so clear and helpful.

This page was proof-read by the late Frank Kabel, who offered many improvements and some advanced examples. Frank was one of the most prolific posters in

the Excel newsgroups, and has probably offered more SUMPRODUCT solutions than the other posters together.

Copyright © 2003-2006 xlDynamic.comPage last updated: 6th May 2005

Found an error, a bug or just want tocomment on this page, please tell us

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Excel & VBA Tips

Ordinal and Cardinal listing

Ranking a column of values is commonly used in Excel spreadsheets. Surprisingly, people oftendon't know how to do it, or even that it can be done in Excel. In itself, it is very simple to producean cardinal list of ranked values. In essence, it is a simple formula such as

=RANK(A1,$A$1:$A$100)

But better, it is relatively straight-forward to extend it to show the rank as an ordinal list, i.e. witha suffix showing its order, such as 1st, 2nd, 3rd, etc.

This article came about from a discussion in the Excel newsgroups that I participated in,responding to just such a question. The original poster wanted to be able to rank a sequence ofnumbers, preferably with the suffix indicating the ordinality of the rank, but he was willing toforego the latter part. The original response gave the basic ranking formula, and hinted atproviding ordinality. Over the course of the next few days we went through several iterations offormulae, finally arriving at a clean, tight, easy to follow formula. A nice example of co-operationin the newsgroups. Rather than just providing a canned solution, the problem was workedthrough and we all learnt. By the time we had finished, I am sure the original poster had left thethread, he already had the answer that he wanted, but that was almost immaterial.

To demonstrate ranking, both as a cardinal and as an ordinal list, start with the column of valuesshown in column A of Figure 1.

NB.As a slight aside, the row striping that can be seen in the pictures below is achieved by using'Conditional Formatting'.

Main Worksheet Formulae RANK

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1 of 7 9/5/2011 7:09 PM

Figure 1.

First, to determine the Rank for those 21 items, this formula is input to cell B2=RANK(A2,$A$2:$A$22)

and copied down each row. The result of this initial ranking is shown in column B of Figure 2.


2 of 7 9/5/2011 7:09 PM

Figure 2.

To get an ordinal ranking takes a bit more work. As well as determining the cardinal rank, it isnecessary to determine whether the ranking would get a suffix of 'st', 'nd', rd' or 'th'. This can bedetermined using the VLOOKUP function, with an inline array. Although the cardinal ranking canbe any value between 1 and n, for the purposes of the suffix it can be broken down to 4 uniquevalue sets

1, 21, 31, etc., which have a suffix of 'st'2, 22, 32, etc., which have a suffix of 'nd'3, 23, 33, etc., which have a suffix of 'rd'all others, which have a suffix of 'th'

All numbers, except 11, 12, 13 can be resolved to an index by usingMOD(rank_value, 10)

where in this instance 'rank_value' would be the result of the original ranking.

The anomalies of 11,12 and 13 can be managed with an IF function, forcing these numbers toeavaluate to a 0 index, like so

IF(OR(rank_value=11, rank_value=12, rank_value=13),0,MOD(rank_value,10))

The suffix can de derived with a VLOOKUP function, using an array of 5 index/value pairsVLOOKUP(lookup_value,{0,"th";1,"st";2,"nd";3,"rd";4,"th"},2,TRUE)

Embedding the calculated index into the VLOOKUP function, we getVLOOKUP(IF(OR(rank_value=11, rank_value=12,

rank_value=13),0,MOD(rank_value,10)),{0,"th";1,"st";2,"nd";3,"rd";4,"th"},2,TRUE)

Even with the 'rank_value' included, this still only provides the ordinal suffix, so the ranking needsto precede it to give a full ordinal value. The final formula would then look like

=RANK(A2,$A$2:$A$22) & VLOOKUP(IF(OR(RANK(A2,$A$2:$A$22)=11,


3 of 7 9/5/2011 7:09 PM

RANK(A2,$A$2:$A$22)=12,

RANK(A2,$A$2:$A$22)=13),0,MOD(RANK(A2,$A$2:$A$22),10)),{0,"th";1,"st";2,"nd";

3,"rd";4,"th"},2,TRUE)

This formula produces a ranked list as shown in Figure 3.

Figure 3.

Using the interim ranked values in column B this formula can be simplified by replacing multiplereferences to RANK(A2,$A$2:$A$22) by B2 etc. This formula would then be

=B2&VLOOKUP(IF(OR(B2=11,B2=12,B2=13),0,MOD(B2,10)),{0,"th";1,"st";2,"nd";

3,"rd";4,"th"},2,TRUE)

The results of this can be seen in Figure 4., column D.

Finally, we can tidy this formula up a little more by replacing the IF statement that calculates theindex using boolean logic and another inline array (as we did in the VLOOKUP function)

AND(RANK(A2,$A$2:$A$22)<>{11,12,13})*MOD(RANK(A2,$A$2:$A$22),10)

The final, most simplistic, formula is=RANK(A2,$A$2:$A$22)&VLOOKUP(AND(RANK(A2,$A$2:$A$22)

<>{11,12,13})*MOD(RANK(A2,$A$2:$A$22),10),{0,"th";1,"st";2,"nd";3,"rd";

4,"th"},2,TRUE)

This is also shown in Figure 4., column E.


4 of 7 9/5/2011 7:09 PM

Figure 4.

An alternative approach is now presented. Instead of using VLOOKUP we will use the CHOOSEfunction. This part of the formula -

IF(OR(VALUE(RIGHT(RANK(A2,$A$2:$A$22),2))={11,12,13}),"th"

tests for the 3 special cases of 11,12,13 and adds a suffix of 'th'. The failure action invokes thenext part of the formula -

IF(OR(VALUE(RIGHT(RANK(A2,$A$2:$A$22)))=

{1,2,3}),CHOOSE(RIGHT(RANK(A2,$A$2:$A$22)),"st","nd","rd"),"th")

tests the cardinal rank value, and if the rightmost character is 1, 2, or 3 it then uses CHOOSE toselect a suffix from the rightmost character of the ranked value, otherwise it assumes 'th' as thesuffix.

Putting it all together, including the ranked value, we get -=RANK(A2,$A$2:$A$22)&IF(OR(VALUE(RIGHT(RANK(A2,$A$2:$A$22),2))=

{11,12,13}),"th",IF(OR(VALUE(RIGHT(RANK(A2,$A$2:$A$22)))=

{1,2,3}),CHOOSE(RIGHT(RANK(A2,$A$2:$A$22)),"st","nd","rd"),"th"))

Figure 5., column F, shows the results and the formula.


5 of 7 9/5/2011 7:09 PM

Figure 5.

And then we come to the final formula. This again uses CHOOSE, but uses the MOD function asbefore, Boolean evaluation, and a clever use of MIN to get the index to input to a simpleCHOOSE function.

This part of the formula -MIN(4,MOD(RANK(A2,$A$2:$A$22),10))+1

determines the index for the rank value, and by using the MIN function, we restrict it to amaximum value of 4.

To cater for the 3 special cases of 11,12,13 we use a simple Boolean evaluation -AND(RANK(A2,$A$2:$A$22)<>{11,12,13})

which evalates to FALSE for 11,12 or 13, TRUE for all others, and is then used in conjunctionwith the previous part to get an index for all cases.

Combined with the ranked value, and with a simple CHOOSE using the index derived above, wehave the complete solution -

=RANK(A2,$A$2:$A$22)&CHOOSE(AND(RANK(A2,$A$2:$A$22)

<>{11,12,13})*MIN(4,MOD(RANK(A2,$A$2:$A$22),10))+1,"th","st","nd","rd","th")

The final figure, Figure 6., shows this formula in column G.


6 of 7 9/5/2011 7:09 PM


Figure 6.

There you have it. A number of options have been worked through, until the final formula, whichis a good example of how a problem can have many solutions using a variety of techniques.

The formulae that we we worked through, with a couple more variations, are shown below. Allreferences to the ranked value (RANK(A2,$A$2:$A$22)) are shown using the intermediatecolumn, "B", for clarity. The list is presented in my ascending order of preference.

1. =B2&IF(OR(VALUE(RIGHT(B2,2))={11,12,13}),"th",IF(OR(VALUE(B2)=

{1,2,3}),CHOOSE(RIGHT(B2),"st","nd","rd"),"th"))

2. =B2&VLOOKUP(IF(OR(B2=11,B2=12,B2=13),0,MOD(B2,10)),{0,"th";1,"st";2,"nd";

3,"rd";4,"th"},2,TRUE)

3. =B2&VLOOKUP(AND(B2<>{11,12,13})*MOD(B2,10),{0,"th";1,"st";2,"nd";3,"rd";

4,"th"},2,TRUE)

4. =B2&VLOOKUP(AND(B2<>{11,12,13})*MIN(4,MOD(B2,10)),{0,"th";1,"st";2,"nd";

3,"rd";4,"th"},2, TRUE)

5. =B2&VLOOKUP(AND(B2<>{11,12,13})*MIN(4,MOD(B2,10))+1,{1,"th";2,"st";

3,"nd";4,"rd";5,"th"},2,TRUE)

6. =B2&CHOOSE(AND(B2<>

{11,12,13})*MIN(4,MOD(B2,10))+1,"th","st","nd","rd","th")

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