How to find all combinations of numbers that equal given sum in Excel

3 ways to find all combinations from a set of numbers that sum to a specific total.

Finding combinations of values that add up to a given sum is a common problem in data analysis. For example, you may want to know all possible combinations of items that can be purchased with a given budget, or all possible ways to allocate resources to meet certain requirements. In this article, we will explore how to use Excel Solver and VBA to accomplish the task. We will also discuss some potential pitfalls and limitations of each approach that may arise when handling large datasets or complex constraints.

Find a combination of numbers equal to a given sum with Excel Solver

Regrettably, none of inbuilt Excel functions can help you identify the numbers that add up to a given total. Luckily, Excel provides a special add-in for solving linear programming problems. The Solver add-in is included with all versions of Excel but is not enabled by default. If you are not familiar with this tool, here's a great article on how to add and use Solver in Excel.

With the Solver add-in activated in your Excel, proceed with the following steps:

  1. Create the model.

    For this, enter your set of numbers in one column (A3:A12 in our case) and add a blank column to the right of your numbers for the results (B3:B12). In a separate cell (B13), enter a SUMPRODUCT formula similar to this:

    =SUMPRODUCT(A3:A12, B3:B12) Creating a model for Excel Solver

  2. Run the Solver add-in.

    On the Data tab, in the Analysis group, click the Solver button. Run the Excel Solver add-in.

  3. Define the problem for Solver.

    In the Solver Parameters dialog box, configure the objective and variable cells:

    • In the Set Objective box, enter the address of the formula cell (B13).
    • In the To section, select Value Of and type the desired sum value (50 in this example).
    • In the By Changing Variable Cells box, select the range to be populated with the results (B3:B12).
    Define the problem for Solver.
  4. Add the constraints.

    To specify the constraints, i.e. the restrictions or conditions that must be met, click the Add button. In the Add Constraint dialog window, select the resulting range (B3:B12) and pick bin from the drop-down list. The Constraint will be automatically set to binary. When done, click OK. Add the constraints.

  5. Solve the problem.

    When taken back to the Solver Parameter dialog window, review your settings and click the Solve button. Solve the problem.

    A few seconds (or minutes) later, the Solver Results dialog box will appear. If successful, select the Keep Solver Solution option, and click OK to exit the dialog. Keep Solver solution.

As a result, you will have 1 inserted next to the numbers that add up to the specified sum. Not a user-friendly solution, but it's the best that out of the box Excel can do.

For visualization purposes, I've highlighted the cells that give the desired sum in light green: Find a combination of numbers that equals a specified sum.

Limitation: Excel Solver can find, at most, just one combination of numbers that equals a specific sum.

Find all combinations that equal a given sum with custom function

To get all possible combinations from a given set of numbers that add up to a certain value, you can use the custom function below. If you are new to UDFs, you'll find a lot of useful information in this guide: How to create custom user defined functions in Excel.

Custom function to find all combinations that equal a given sum
Option Explicit Public Function FindSumCombinations(rngNumbers As Range, lTargetSum As Long) Dim arNumbers() As Long, part() As Long Dim arRes() As String Dim indI As Long Dim cellCurr As Range ReDim arRes(0) If rngNumbers.Count > 1 Then ReDim arNumbers(rngNumbers.Count - 1) indI = 0 For Each cellCurr In rngNumbers arNumbers(indI) = CLng(cellCurr.Value) indI = indI + 1 Next cellCurr Call SumUpRecursiveCombinations(arNumbers, lTargetSum, part(), arRes()) End If ReDim Preserve arRes(0 To UBound(arRes) - 1) FindSumCombinations = arRes End Function Private Sub SumUpRecursiveCombinations(Numbers() As Long, target As Long, part() As Long, ByRef arRes() As String) Dim s As Long, i As Long, j As Long, num As Long, indRes As Long Dim remaining() As Long, partRec() As Long s = SumArray(part) If s = target Then indRes = UBound(arRes) ReDim Preserve arRes(0 To indRes + 1) arRes(indRes) = ArrayToString(part) End If If s > target Then Exit Sub If (Not Not Numbers) <> 0 Then For i = 0 To UBound(Numbers) Erase remaining() num = Numbers(i) For j = i + 1 To UBound(Numbers) AddToArray remaining, Numbers(j) Next j Erase partRec() CopyArray partRec, part AddToArray partRec, num SumUpRecursiveCombinations remaining, target, partRec, arRes Next i End If End Sub Private Function ArrayToString(x() As Long) As String Dim n As Long, result As String result = x(n) For n = LBound(x) + 1 To UBound(x) result = result & "," & x(n) Next n ArrayToString = result End Function Private Function SumArray(x() As Long) As Long Dim n As Long SumArray = 0 If (Not Not x) <> 0 Then For n = LBound(x) To UBound(x) SumArray = SumArray + x(n) Next n End If End Function Private Sub AddToArray(arr() As Long, x As Long) If (Not Not arr) <> 0 Then ReDim Preserve arr(0 To UBound(arr) + 1) Else ReDim Preserve arr(0 To 0) End If arr(UBound(arr)) = x End Sub Private Sub CopyArray(destination() As Long, source() As Long) Dim n As Long If (Not Not source) <> 0 Then For n = 0 To UBound(source) AddToArray destination, source(n) Next n End If End Sub

How this function works

The main function, FindSumCombinations, calls a few subsidiary functions that implement smaller sub-tasks. The function named SumUpRecursiveCombinations executes the core algorithm that finds all possible sums in the specified range and filters those that reach the target. The ArrayToString function controls the form of output strings. Three more functions (SumArray, AddToArray, and CopyArray) are responsible for processing intermediate arrays: each time we create a temporary array, add one element from the source array to it, and check if the target sum is reached. The core algorithm is taken from this Stackoverflow thread, thank you guys for sharing!

Syntax

From the user's perspective, the syntax of our custom function is as simple as this:

FindSumCombinations(range, sum)

Where:

  • Range is the range of numbers to test.
  • Sum is the target sum.

Note! The custom function only works in Dynamic Array Excel 365 and 2021.

How to use the FindSumCombinations function:

  1. Insert the above code into a Code module of your workbook and save it as a macro-enabled workbook (.xlsm). The step-by-step instructions are here.
  2. In any blank cell, enter a FindSumCombinations formula and press the Enter key. Make sure there are enough empty cells to the right to output all combinations, otherwise the formula will return a #SPILL error.

For example, to find all possible combinations of numbers in the range A6:A15 that equal the sum in A3, the formula is:

=FindSumCombinations(A6:A15, A3)

As with any other dynamic array function, you enter the formula is just one cell (C6 in the image below) and it populates the results into as many cells as necessary. By default, the comma-separated strings are output in a row: Find all combinations of numbers that equal a given sum.

To return the results in a column, wrap the custom function into TRANSPOSE like this:

=TRANSPOSE(FindSumCombinations(A6:A15, A3)) Return combinations of numbers that equal a given sum in a column.

To output the strings in the form of an array enclosed in curly braces, modify the ArrayToString function as follows:

Private Function ArrayToString(x() As Long) As String Dim n As Long, result As String result = "{" & x(n) For n = LBound(x) + 1 To UBound(x) result = result & "," & x(n) Next n result = result & "}" ArrayToString = result End Function

The results will look similar to this: Return combinations that equal a certain sum in the form of an array.

Limitation: This custom function works only in Dynamic Array Excel 365 and Excel 2021.

Get all combinations that equal a given sum with VBA macro

The custom function described above returns the combinations of numbers as strings. If you'd rather have each number in a separate cell, this macro will be helpful. The code is written by another Excel expert Alexander Trifuntov who has been actively helping users to solve various Excel problems on this blog.

Start by adding the following code to your workbook. For the detailed steps, please see How to insert VBA code in Excel.

Macro to find all combinations that add up to a given value
Public RefArray1 As String Public DS As Variant Public TargetSum As Long Public TargetCol As Integer Public TargetRow As Integer Sub Combination() UserForm1.Show End Sub Function GrayCode(Items As Variant) As String Dim CodeVector() As Integer Dim i, kk, rr, col1, row1, n1, e As Integer Dim lower As Integer, upper As Integer Dim SubList As String Dim NewSub As String Dim done As Boolean Dim OddStep As Boolean Dim SSS Dim TargetArray() As String kk = TargetCol rr = TargetRow col1 = TargetCol + 3 row1 = TargetRow OddStep = True lower = LBound(Items) upper = UBound(Items) Cells(rr - 1, kk) = "Result" Cells(rr - 1, kk + 1) = "Sum" Cells(rr, kk + 1) = TargetSum Cells(rr - 1, kk).Font.Bold = True Cells(rr - 1, kk + 1).Font.Bold = True ReDim CodeVector(lower To upper) 'it starts all 0 Do Until done NewSub = "" For i = lower To upper If CodeVector(i) = 1 Then If NewSub = "" Then NewSub = "," & Items(i) SSS = SSS + Items(i) Else NewSub = NewSub & "," & Items(i) SSS = SSS + Items(i) End If End If Next i If NewSub = "" Then NewSub = "{}" 'empty set SubList = SubList & vbCrLf & NewSub If SSS = TargetSum Then Cells(rr, kk).NumberFormat = "@" Cells(rr, kk) = "{ " & Mid(NewSub, 2) & " }" TargetArray() = Split(Mid(NewSub, 2), ",") n1 = UBound(TargetArray) For e = 0 To n1 Cells(row1, col1) = TargetArray(e) row1 = row1 + 1 Next e col1 = col1 + 1 row1 = TargetRow rr = rr + 1 End If SSS = 0 'now update code vector If OddStep Then 'just flip first bit CodeVector(lower) = 1 - CodeVector(lower) Else 'first locate first 1 i = lower Do While CodeVector(i) <> 1 i = i + 1 Loop 'done if i = upper: If i = upper Then done = True Else 'if not done then flip the *next* bit: i = i + 1 CodeVector(i) = 1 - CodeVector(i) End If End If OddStep = Not OddStep 'toggles between even and odd steps Loop GrayCode = SubList End Function

Next, create a UserForm with the following design and properties: Create a UserForm.

After completing the form's design, add the code for the form. For this, right-click on the form in the Project Explorer and select View Code:

Code for the UserForm
Private Sub CommandButton1_Click() Dim B Dim c As Integer Dim d As Integer Dim A() As Variant Dim i As Integer Dim e As Integer DS = Range(RefEdit1) TargetSum = TextBox1.Value Range(RefEdit2).Select TargetCol = Selection.Column TargetRow = Selection.Row c = LBound(DS) d = UBound(DS) ReDim B(d - 1) For i = 1 To d e = i - 1 B(e) = DS(i, 1) Next i Call GrayCode(B) Unload Me End Sub Private Sub Label1_Click() End Sub Private Sub Label3_Click() End Sub

Tip. Instead of re-creating the form from scratch, you can download our sample workbook at the end of this post and copy the Code module and UserForm1 from there (see how to copy a macro to another workbook). To make the macro accessible in all your workbooks, copy it to the Personal Macro Workbook.

With the code and form in place, press Alt + F8 and run the FindAllCombinations macro: Run the FindAllCombinations macro.

On the form that pops up, define the following:

  • The range with the source numbers (A4:A13)
  • The target sum (50)
  • The upper-left cell of the destination range (C4).

When specifying the upper-left cell of the output range, make sure there is at least one blank row above (for headers) and enough blank cells down and to the right. If there are insufficient blank cells, your existing data will be overwritten. Macro to return all combinations that equal a specified sum.

Clicking OK will produce the result like shown in the screenshot below:

  • In C4:C6, you have the combinations of numbers as comma-separated values.
  • Columns F, G and H hold the same combinations of numbers, with each number residing in a separate cell.
  • In D4, you have the target sum.
Result - combinations of numbers with each number residing in a separate cell.

This form of output makes it easier to check the result - just enter the SUM formula in cell F13, drag it to the right across two more cells and you will see that each combination of numbers adds up to the specified value (50). Use the SUM formula to check the result.

Limitation: For a large set of numbers, the macro may take some time to generate all possible combinations.

Advantages: Works in all versions of Excel 2010 - 365; provides two forms of output - strings of comma separated values and numbers in separate cells.

In conclusion, finding all combinations of values that equal a certain value is a powerful tool for solving a wide range of data analysis problems. Hopefully, this article has provided you with a useful starting point for exploring this topic further and handling similar problems in your own work. Thank you for reading!

Practice workbook

Find combinations that equals a given sum - examples (.xlsm file)

Table of contents

108 comments

  1. find all combinations that equal a given sum in excel without round

  2. How to find the largest possible whole value instead of a given value. I'm work with large decimal datasets and would like to solve for the largest possible whole number instead of playing around with given values.

      • Hi! unfortunately I was not able to figure it out with the linked article.

        Please see below example for finding the largest possible integer sum of the dataset

        0.007
        0.0055
        0.0027
        0.0027
        0.0025
        0.0024
        0.0029
        0.0027
        0.0077
        0.0079
        0.115
        0.1426
        0.2245
        0.081
        0.1348
        0.162
        0.7962
        0.2116
        1
        1
        0.532
        0.6756

        From changing the value I enter in the "target sum", I found the max to be 4, however, I was wondering if there is a way to have it solve directly for the combination that will sum to the largest possible integer of the dataset instead of playing around with target sum. This will be really helpful if I have a larger data set with higher values to solve for.

        • Hi! It is not possible for me to set up all the necessary rules for the Solver tool for you in your workbook. In this blog, we give advice to users, but we don't do their work for them.

  3. Hi! I was wondering if there is a way to find combinations containing repetitions, as this formula given does not allow for repeats.
    For example, I want to find possible combinations to achieve sum of 100, and my options are 10, 20, 30, 90. With this formula, the only combination identified is 10, 90.
    Is there a way to show other combinations like 10, 30, 30, 30 or 20, 20, 30, 30, for example? Thank you!

    • Hello Penny!
      Unfortunately these functions and macros only allow you to use each value once. If each value can be used multiple times, the number of possible combinations is huge.

  4. The articlue is excelent !!!! Thanks for sharing !!
    The solution works fine.
    I'm interested in getting the list of combinations in a given range, not only de exact value.
    Is there a way to achive this?
    I read a couple of months ago that the solution wasn´t available but I wonder if it is now,

    Regards,

    Marcelo

    • Hi! To get all combinations in a given range, you need to modify the VBA code of the function presented above. We do not modify VBA code on request, but you can try to do it yourself.

  5. Hi.

    I tried the solver method and I noticed it does not work for over 200 cells. Please what can I do if I'm working with over 1000 cells?

  6. The requirement is to display all the combination from the list of decimal entries for the value of Total sum without repetition of numbers with condition only 6 entries to be consider for SUM.

    For Example: SUM is 50, Table entries are 1- 30 numbers with decimals . Here the condition is for total SUM 50, only any 6 entries should choose without repetition of values from the initial table .
    Output : Display all the combination for the SUM 50 in column

      • Thank you for prompt response!

        The above solution doesn't meet my requirement.

        Wishing you great day ahead.

  7. I actually want something different.
    I want a formula to cut the values from the range whose sum equals to 228 and paste them in separate row.
    then value being cut down it again pick values from the data range and paste them again in different row.
    and this goes so on until no value remain in data range whose sum equal to 228.

    Please reply

  8. How to find all combinations of numbers that equal given sum in Excel?
    This was my question and the solutions you have given is superb and it worked. I'm a regular Excel user hence this information too important to me.
    Thank you so much.

  9. Hi, this is great. thank you.

    If my list does not contain data that add to my specific number (& therefore, solver is unsuccessful), is there a way that excel can output the "closest" value that can be reached using the data?

    For example if I have list of data & I'm trying to find 4000.
    But it is no possible and solver "unsuccessful".
    But, for example, 3999 is possible and close to my value.

    Thanks,

    • Hi! To find the "closest" value to 4000 in the target cell A1 that can be reached using the data, you can write the formula =ABS(A1-4000) in cell B1. You can then use the Excel Solver to find the minimum value in cell B1 by modifying cell A1.
      I hope it’ll be helpful.

  10. Hi, thanks for sharing your knowledge, i have to do the same thing but with 547 variables, where do i modify the VBA to do it?

  11. How to generate/ bring the values of all possible combination formates/ complete possibilities in excel.? Eg Question - from A To Z alphabets going to pick for letter 4 letter combinations like ABCD, ACDE, ADEF, etc., please understand I am not looking for this numerical answer 14,950. Kindly explain. Thanks.

  12. 200 mm
    175 mm
    1907 mm
    201 mm
    164 mm

    HOW TO SUM IN EXCEL WITHOUT REMOVEING mm

  13. I have 6 parameters (let’s call them A,B,C,D,E,&F) and each parameter can have a possible score of 1 thru 95. I am trying to determine all combinations of the 6 parameters that can sum to 100. How do I do this in EXCEL without EXCEL program crashing?

    VR,

    JPC

    • Hi! Such a huge number of variants, Excel will not be able to calculate. This is 869107785 combinations of numbers.
      You won't even be able to write them down on the worksheet.

    • Hello Sir
      Need your help regarding this method: Find all combinations that equal a given sum with custom function.

      In this tutorial, your values can equal the target number but , What If we would like to Find all closest combinations to a given sum without exceeding It (I mean less or equal)? (assuming that the total might not equal to the target value).

      Also would be helpful if the second combination does not integrate any value listed in the first result , the 3rd combination alike , and so on.
      Looking forward to your reply

      B Rgds

  14. I have no background experience with anything like this. I would love to get this macro to work properly. I get to a point of running the findsumcombinations macro, but keep getting "need object" error 424. Then when I go and re type in the formula my entire excel freezes up. Any help would be appreciated.

    Thank you

    • Hi! Regrettably, I was unable to replicate your issue, as I am unaware of the actions you take and the numbers you select. Please read carefully and follow the recommendations in the article above. Or describe the problem in detail.

  15. In addition to my last comment, I am using and trying to find a negative number (I'm trying to see why there's a discrepancy between my internal math and my bank account). In a tiny experiment, it seems that negative numbers throw everything off, no matter how simple the list of numbers (I had a list which included -7 and -3, with a desired number of -10, and I still received a #VALUE! error). What should I do?

    Thanks again!

  16. Hello,

    I followed all the steps correctly, to my knowledge, and received a "#VALUE!" error. The code I input into the cell was "=FindSumCombinations(A5:A194, A2)".

    What should I check to troubleshoot this?

    Thank you!

    • Hi! A #VALUE! error means that no solution was found. Perhaps text values or empty cells were used. Do you really want to find all combinations of 189 numbers?

      • Hi there, I also got the very same issue, but with strong possibility that some of the values are really close (less than 0,99 diff). but it only looks for exact matches as per example :
        -FindSumCombinations(A1-A25,B2) where B2 might be by 0,99 bigger or smaller than B2 value.

        I'll be more than thankful for everything there as I believe it will save me hundreds of hours of work during the year to come.

        • Hi! I recommend using only integer numbers to find combinations, as Excel does not always work correctly with fractional part of a number. If you need to find a combination of numbers with two decimal digits, multiply them by 100 and then divide the numbers in the resulting combination by 100. If the numbers are the result of calculations, be sure to use rounding.

  17. Hi, I've been struggling with this and can't seem to get solution. I'll appreciate your assistance.
    I have a reference cell B1 to f1 with data 37, 65, 20, 8 and 24 in the cells respectively.
    How do I make excel do a two cell combination of all the 5 cells. Eg. B1+E1 which is 37+20 and then compare with the rest of the worksheet to find all two cells on a row with equal sum total of any of the combinations above. If found, set same border color for cells with equal sum total.
    I tried pairing but it only found cells that were close together. Eg. Cells B22 and C22 with sum total of 28.
    If possible, I can share my worksheet with you via email so you can see what I mean.
    Thanks for your effort

      • I have written the vba macro but it's not working as intended.
        Thanks for your time anyway 🙂

  18. This was TREMENDOUSLY helpful and I learned something new today about the Solver add in. Thank you

  19. Hi,
    I've tried the solutions and don't seem to figure out how to make them work. With macro I get debugging popping up.
    I have a number of incoming invoices and data from bank, that has only total sums of those invoices and how many of them were matched to the sum. So I need to figure out what is what, seems that Solver should do the trick.. But it's running literally forever. I've added limitation based on the amount of invoices, didn't help. The amount of initial variables is below 70, it should be ok then..
    I had to restart the pc everytime to exit excel because it's not responsive and just running the solver, doesn't seem right at all :D

  20. How do I sort the list in excel to 0.01 miles - 10 miles, 10.01 miles - 20 miles, 20.01 miles - 30 miles, 100.01 miles - 110 miles, 120.01 miles - 130 miles, 110.01 miles - 120 miles instead of 0.01 miles - 10 miles, 10.01 miles - 20 miles,100.01 miles - 110 miles, 120.01 miles - 130 miles, 110.01 miles - 120 miles, 20.01 miles - 30 miles

    Thank you

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