How many ‘Friday the 13th’s are in this year? [Formula fun + challenge]

Posted on May 13th, 2016 in Excel Howtos , Learn Excel - 12 comments

Today is Friday the 13th. If you are a raging friggatriskaidekaphobiac, I suggest you to stop reading this post. For the rest of you, I have something fun.

Given a year in cell C3, let’s find out all the months with Friday the 13th. Something like this:

friday-13th-in-an-year

[Related: Finding next Friday the 13th using formulas]

Finding all Friday the 13ths in a year

Here is a formula to find the first Friday the 13th in a year.

{=IFERROR(SMALL(IF(WEEKDAY(DATE($C$3,ROW($A$1:$A$12),13))=6,ROW($A$1:$A$12)),1),””)}

Let’s understand how it works, going from inside out:

DATE($C$3,ROW($A$1:$A$12),13) portion: This generates an array of 12 dates, one for each 13th of the month in the year C3.

WEEKDAY(DATE(…))=6 portion: This checks how many of those dates are Fridays. Returns an array of TRUE / FALSE values.

IF(WEEKDAY(DATE(…))=6,ROW($A$1:$A$12)) portion: This returns an array of month numbers where we have Friday the 13th and FALSE values.

SMALL(IF(…),1) portion: This will give us the first month (ie 1st smallest value) with Friday the 13th in the year C3.

IFERROR() to suppress any errors.

To show all the Friday the 13ths in a year, simply replace 1 with an array of numbers (up to 3 should do).

Download Friday the 13th finder workbook

Click here to download Friday the 13th finder workbook. Enter a year in cell C3 and see all the months with Friday the 13th instantly.

A challenge for you…

If you are still reading, I have a challenge for you. Can you write a formula to find the next year with three Friday the 13ths? Assume the year is in C3. Post your formulas / VBA in the comment section.

hint: in the downloadable workbook, you can find an answer for this.

So that’s all for now. Enjoy your Friday the 13th.

Written by Chandoo
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12 Responses to “How many ‘Friday the 13th’s are in this year? [Formula fun + challenge]”

  1. in C3=2016
    in C4=3
    in C5=1 (the first next year with three Friday the 13ths)

    =SMALL(IF(MMULT(--(MOD(DATE(C3+ROW(1:1000),COLUMN(A:L),13),7)=6),ROW(1:12)^0)=C4,C3+ROW(1:1000)),C5)

    formula check in the next 1000 years

  2. Brian says:

    This will generate a table of counts of Friday the 13th's by year. If I didn't screw it up the next year with three is 2026.

    I created a simple parameter table with a start date and end date that I wanted to evaluate. That calculates the number of days and generates a list of those days. Then filter and group. The generation of the list in power query (i.e. without populating a date table in excel) is pretty cool, otherwise this isn't really doing anything than creating a big date and filtering/counting.

    let
    Source = List.Dates(StartDateAsDate, Days2, #duration(1,0,0,0)),
    ConvertDateListToTable = Table.FromList(Source, Splitter.SplitByNothing(), null, null, ExtraValues.Error),
    AddDayOfMonthColumn = Table.AddColumn(ConvertDateListToTable, "DayOfMonth", each Date.Day([Column1])),
    AddYearColumn = Table.AddColumn(AddDayOfMonthColumn, "Year", each Date.Year([Column1])),
    AddDayOfWeekColumn = Table.AddColumn(AddYearColumn, "Day of Week", each Date.DayOfWeek([Column1])),
    FilterFriday13 = Table.SelectRows(AddDayOfWeekColumn, each ([DayOfMonth] = 13) and ([Day of Week] = 5)),
    Friday13thsByYear = Table.Group(FilterFriday13, {"Year"}, {{"Number of Friday the 13ths!", each Table.RowCount(_), type number}})
    in
    Friday13thsByYear

    • Brian says:

      With the parameters replaced by values should you want to play along at home. This runs for 20 years starting on 1/1/2016.

      let
      Source = List.Dates(#date(2016,1,1), 7300, #duration(1,0,0,0)),
      ConvertDateListToTable = Table.FromList(Source, Splitter.SplitByNothing(), null, null, ExtraValues.Error),
      AddDayOfMonthColumn = Table.AddColumn(ConvertDateListToTable, "DayOfMonth", each Date.Day([Column1])),
      AddYearColumn = Table.AddColumn(AddDayOfMonthColumn, "Year", each Date.Year([Column1])),
      AddDayOfWeekColumn = Table.AddColumn(AddYearColumn, "Day of Week", each Date.DayOfWeek([Column1])),
      FilterFriday13 = Table.SelectRows(AddDayOfWeekColumn, each ([DayOfMonth] = 13) and ([Day of Week] = 5)),
      Friday13thsByYear = Table.Group(FilterFriday13, {"Year"}, {{"Number of Friday the 13ths!", each Table.RowCount(_), type number}})
      in
      Friday13thsByYear

  3. Alex Groberman says:

    =MATCH(3,MMULT(N(WEEKDAY(DATE(C3+ROW(1:100)-1,COLUMN(A:L),13))=6),1^ROW(1:12)),)+C3-1

    • David N says:

      It should be pointed out that Alex's solution, unlike some others, has the additional advantage of being non-array. My solution was nearly identical but with -- and SIGN instead of N and 1^.

      =C3-1+MATCH(3,MMULT(--(WEEKDAY(DATE(C3-1+ROW(1:25),COLUMN(A:L),13))=6),SIGN(ROW(1:12))),0)

  4. SunnyKow says:

    Sub Friday13()

    Dim StartDate As Date
    Dim EndDate As Date
    Dim x As Long
    Dim r As Long

    Range("C7:C12").ClearContents
    StartDate = CDate("01/01/" & Range("C3"))
    EndDate = CDate("31/12/" & Range("C3"))
    r = 7
    For x = StartDate To EndDate
    If Day(x) = 13 And Weekday(x, vbMonday) = 5 Then
    Cells(r, 3) = Month(x)
    r = r + 1
    End If
    Next
    End Sub

    • SunnyKow says:

      Calculate next year with 3 Friday 13th. Good for 100 years different from year entered in cell C3

      Sub ThreeFriday13()

      Dim StartDate As Date
      Dim EndDate As Date
      Dim x As Long
      Dim WhatYear As Integer
      Dim Counter As Integer

      Range("E7").ClearContents
      StartDate = CDate("01/01/" & Range("C3") + 1)
      EndDate = CDate("31/12/" & Range("C3") + 100)
      Counter = 0

      For x = StartDate To EndDate
      If WhatYear Year(x) Then
      WhatYear = Year(x)
      'Different year so reset counter
      Counter = 0
      End If
      If Day(x) = 13 And Weekday(x, vbMonday) = 5 Then
      Counter = Counter + 1
      If Counter = 3 Then
      WhatYear = Year(x)
      Exit For
      End If
      End If
      Next
      Range("E7") = WhatYear

      End Sub

      • SunnyKow says:

        *RE-POST as not equal did not show earliuer
        Calculate next year with 3 Friday 13th. Good for 100 years different from year entered in cell C3

        Sub ThreeFriday13()

        Dim StartDate As Date
        Dim EndDate As Date
        Dim x As Long
        Dim WhatYear As Integer
        Dim Counter As Integer

        Range("E7").ClearContents
        StartDate = CDate("01/01/" & Range("C3") + 1)
        EndDate = CDate("31/12/" & Range("C3") + 100)
        Counter = 0

        For x = StartDate To EndDate
        If WhatYear NE Year(x) Then
        WhatYear = Year(x)
        'Different year so reset counter
        Counter = 0
        End If
        If Day(x) = 13 And Weekday(x, vbMonday) = 5 Then
        Counter = Counter + 1
        If Counter = 3 Then
        WhatYear = Year(x)
        Exit For
        End If
        End If
        Next
        Range("E7") = WhatYear

        End Sub

  5. Devesh says:

    I've a doubt with using array formula here.
    In sample workbook, I tried to replicate the formula again.
    =IFERROR(SMALL(IF(WEEKDAY(DATE($C$3,ROW($A$1:$A$12),13))=6,ROW($A$1:$A$12)),$B7),"")
    For this I selected C7 to C12, and typed the same formula and pressed ctrl+alt+Enter. But in all cells it is taking $B7 (and not $B7, $B8, $B9.... etc)
    and since it is array formula I can't edit individual cell.
    Please guide.
    Thanks

  6. Pablo says:

    Hi Chandoo,
    Cool stuff. You need to clarify that the answer of 5 represents the 1st month in the year that has a Friday the 13th, and not the number of Fridays the 13th in the year. Subtle, but important difference.
    Thanks,
    Pablo

  7. Micah Dail says:

    I like the MMULT() function far more, but here's how I would have tackled it. It uses an EDATE() base and MODE() over 100 years. I'm assuming that 100 years is enough time to catch the next year with 3 friday 13th's. Array entered, of course.

    {=MODE(IFERROR(YEAR(IF((WEEKDAY(EDATE(DATE(C3, 1, 13), ROW(INDIRECT("1:1200"))))=6), EDATE(DATE(C3, 1, 13), ROW(INDIRECT("1:1200"))), "")), ""))}

  8. Jason Morin says:

    Finding all the Friday the 13ths in a Year:

    =SUMPRODUCT((DAY(ROW(INDIRECT(DATE(C3,1,1)&":"&DATE(C3,12,31))))=13)*(TEXT(ROW(INDIRECT(DATE(C3,1,1)&":"&DATE(C3,12,31))),"ddd")="Fri"))

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