The use of the Sumproduct function for doing multiple criteria Sum If’s is possibly one of the greatest extensions of an Excel function beyond what it was primarily designed for. Maybe it was actually designed with that in mind ?
However Sumproduct can be extended even further through use 2D Ranges together with carefully constructed queries.
The examples below are included in the Example File, Excel 2003 Example File.
Scenario 1: Lookup a value within a 2D Range matching 2 criteria
You have a table of Dates and Fruit Sold and Number Sold each Day
How many Bananas did I sell on the 4thMay?
In the above I have setup 3 Named Ranges
Named ranges are used as it makes the reading of forthcoming formulas easier.
Fruit: C2:H2
Dates: B3:B12
FruitData: C3:H12
So, How many Bananas did I sell on the 4th May?
Using the equation =SUMPRODUCT((Fruit=D16)*(Date=D15)*FruitData)
Returns the correct answer 31
Related: Doing 2way lookups in Excel
Scenario 2: Sum all values within a 2D Range matching 2 criteria
You have a table of Dates and Cars Sold and Number Sold each Day. There are multiple entries for on various days, possibly from various salesmen.
How many Holden cars did I sell on the 3rd May?
So, How many Holden cars did I sell on the 3rd May?
Using the equation =SUMPRODUCT((Dates=D17)*(Cars=D18)*CarData)
Returns the correct answer 9 = (1 + 5 + 3)
Scenario 3: Sum values within a 2D Range matching multiple unordered criteria
You have a table of Dates and Cars Sold and Number Sold each Day, There are multiple Entries for on various days.
How many Ford and Suzuki cars did I sell on the 10th May?
So, How many Ford and Suzuki cars did I sell on the 10th May?
Using the equation =SUMPRODUCT((Dates=D24)*((Cars=D25)+ (Cars=E25))*CarData)
Returns the correct answer 13 = (4 + 5 + 3 + 1)
Note that this can be extended to add additional queries where the Car Type can be entered in any cell in the Range D25:H25
=SUMPRODUCT((Dates=D24)*((Cars=D25)+ (Cars=E25) + (Cars=F25) + (Cars=G25) + (Cars=H25))*CarData)
Scenario 4: Sum values within a 2D Range matching multiple ordered criteria
You have a table of Dates and Cars Sold and Number Sold each Day, There are multiple Entries for on various days.
How many Toyota and Holden cars did I sell on the 10th May?
How many Toyota and Holden cars did I sell on the 10th May?
Using the equation =SUMPRODUCT((Dates=D30)*(Cars=D31:H31)*CarData)
Returns the correct answer 21 = (3 + 6 + 6 + 6)
Note that this can be extended to allowing additional queries but the Car Type must be entered into the same position as in the Header Row.
How Does This Work?
The above techniques is using matrix arithmetic to setup a conjunctive truth table within the Sumproduct formula.
Using =SUMPRODUCT((B4:B6=D10)*(C3:E3=D9)*(C4:E6))
The conjunctive truth table logic (B4:B6=D10)*(C3:E3=D9) is simply saying make a matix of elements that are true when the conditions are met and false otherwise
Sumproduct then takes this and multiplies and it by the data values and accumulates the values to get the sum of the matching values.
It is important to note that the Width and Height of the Criteria Row and Column must match the Width and Height of the data area or a #Value! error is returnd.
The Maths
To understand and explain how this works I will use a simple model with 3 rows and 3 columns see below
The formula: =SUMPRODUCT((B4:B6=D10)*(C3:E3=D9)*(C4:E6)), shown above consists of 3 areas
(B4:B6=D10) is a 3 Rows x 1 Column range
(C3:E3=D9) is a 1 Row x 3 Columns range
(C4:E6) is a 3 Row x 3 Column range
Breaking the formula into components
=SUMPRODUCT((B4:B6=D10)*(C3:E3=D9)*(C4:E6))
(B4:B6=D10)*(C3:E3=D9) is the same as multiplying 2 arrays, representing the 2 areas as shown below
You can see that where the components are True I have put a 1 and a 0 where they are false
Where the Date was 3-May Excel evaluates this to 1 and similarly where the Fruit was a Banana, Excel evaluates this to 1.
Where the criteria isn’t met Excel evaluates this to a 0
The multiplication of a 3 x 1 and a 1 x 3 array is a 3 x 3 array
Representing the (B4:B6=D10)*(C3:E3=D9) part of the equation
Next this is multiplied by the data area
=SUMPRODUCT((B4:B6=D10)*(C3:E3=D9)*(C4:E6))
This is the same as multiplying two 3×3 arrays which produces a 3 x 3 array, below:
Sumproduct then adds up all the array components to get the final answer of 3.
Modifications
The Data Area can be included in the Truth Table Logic or as a seperate component of Sumproduct.
=SUMPRODUCT((B4:B6=D10)*(C3:E3=D9)*(C4:E6)) and =SUMPRODUCT((B4:B6=D10)*(C3:E3=D9), (C4:E6)) are both equal
Multiple “OR” crietria can be added by use of the+ operator within criteria
In Scenario 3 above, we sum the number of Ford or Suzuki cars sold on the 10th May.
SUMPRODUCT((Dates=D24)*((Cars=D25) + (Cars=E25) + (Cars=F25) + (Cars=G25) + (Cars=H25))*CarData)
The Or logic is added to the criteria by use of the + operator above within the criteria for Cars
the And logic is added by use of the * between the Dates and Cars criteria
Other Logic Elements
You can add Greater Than (>), Less Than (<) etc and other logic elements to the queries to suit your requirements.
Sample File
The examples below are included in the Example File, Excel 2003 Example File.
What do you think of the above technique ?
What do you think of the above technique ?
Let us know in the comments below.
