is it always all days in the month, or sometimes part month?
and will your dates span years?
and what about leap years?
use the code on this link.
http://www.iaccessworld.com/wp-content/uploads/2016/06/function.png
or
http://www.projectperfect.com.au/microsoft-access-sample-6.htm

The formula has to take into account the number of days per week as well as the hours per day, then divide the whole thing by a regular 8 hour day to get the "work days".

So if Start Date is 10/24/2016, End Date 11/4/2016
Days per Week are 4
Hours per Day are 10

Then the result should be
Oct:
  (8 days/7 days in a week) = work weeks
   Work Weeks * 4 Days per week * 10 hours per day= Total hours worked
  Total hours worked / 8 hour day = Total Work Days (based on an 8 hour day)
= 5.71 days

in response to your question 'Can someone help me choose the right function to count the number of days per month within a given set of dates', the functions provided (above) will do,
24/10/2016 to 4/11/2016 is 9 working days and 11 in total - neither have 4 days/week?
I believe I have answered your original question but do not have time to address the second - hopefully someone else will run with this.

I may not have expressed my question correctly.  It is not necessarily the total days in month I need.  It is the total number of days between two sets of dates subtotaled by month.

For example, if the dates are 10/14/16 through 12/05/16, then I need to know how many of the total days fall in October, how many fall in November and how many fall in December.

There there's the additional calculation of days/week and hours/day, but I think I can add that in easily if I knew how to subtotal my days by month.

I found a custom SQL function by WayneS on the Internet:  http://www.sqlservercentral.com/Forums/Topic1022335-149-1.aspx
But I don't know how to modify this to work in Access.

are Sat and Sun included?

two dates using an Access function

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Upload sample data in an access database.
Add few representative records, and show the required output.

Run a while same-month loop, inside a while not last date loop, incrementing an integer array (of 12 months)  cell at the same time as incrementing the compare date toward the end-of-range date. Each time you reach the end of a month you should increment the array cell index.
The end result will be a number of cells containing the number of days in each month.

This query will return your list of days count:

PARAMETERS 
    DateStart DateTime, 
    DateEnd DateTime;
SELECT DISTINCT 
    10*Abs([Deca].[id] Mod 10)+Abs([Uno].[id] Mod 10) AS Factor, 
    Year(DateAdd("m",[Factor],[DateStart])) AS [Year], 
    Month(DateAdd("m",[Factor],[DateStart])) AS [Month], 
        IIf(DateDiff("m",DateAdd("m",[Factor],[DateStart]),[DateEnd])=0,
            Day([DateEnd]),Day(DateSerial(Year(DateAdd("m",[Factor],[DateStart])),Month(DateAdd("m",[Factor],[DateStart]))+1,0))
                -IIf([Factor]=0,Day([DateStart])-1,0)) AS Days
FROM 
    msysobjects AS Uno, 
    msysobjects AS Deca
WHERE 
    (((10*Abs([Deca].[id] Mod 10)+Abs([Uno].[id] Mod 10))<=DateDiff("m",[DateStart],[DateEnd])));

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Example from 2015-12-15 to 2016-04-17:
/gustav

Gutav, your coding is so far above my skill level that I don't even know how to use it.  Do you happen to have enough patience to walk me through how to implement it in my db?

Gustav your code is flawless.  Now I "think" all I need is to find out how to pass a table field into the parameter.

That is quite simple to do. If your table is named Dates, then:

SELECT DISTINCT 
    Dates.Id, 
    Dates.DateStart, 
    Dates.DateEnd, 
    10*Abs([Deca].[id] Mod 10)+Abs([Uno].[id] Mod 10) AS Factor, 
    Year(DateAdd("m",[Factor],[DateStart])) AS [Year], 
    Month(DateAdd("m",[Factor],[DateStart])) AS [Month], 
        IIf(DateDiff("m",DateAdd("m",[Factor],[DateStart]),[DateEnd])=0,
            DateDiff("d",[DateStart],[DateEnd]),Day(DateSerial(Year(DateAdd("m",[Factor],[DateStart])),Month(DateAdd("m",[Factor],[DateStart]))+1,0))
                -IIf([Factor]=0,Day([DateStart])-1,0)) AS Days
FROM 
    msysobjects AS Uno, 
    msysobjects AS Deca,
    Dates
WHERE 
    (((10*Abs([Deca].[id] Mod 10)+Abs([Uno].[id] Mod 10))<=DateDiff("m",[DateStart],[DateEnd])));

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Note please, that I've corrected an error in the day count of the first month in those cases where both dates fall in the same month, and in the day count of the last month which was off by 1.

Example:
/gustav

I tried so many variations and none of them worked.  Thank you for clarifying that for me.  It works great now except for the last month of the date span.  I seem to be getting strange results.

Sorry, introduced an error.
Here is the corrected query. I've added a field for the total count of days as a control:

SELECT DISTINCT 
    Dates.Id, 
    Dates.DateStart, 
    Dates.DateEnd, 
    10*Abs([Deca].[id] Mod 10)+Abs([Uno].[id] Mod 10) AS Factor, 
    Year(DateAdd("m",[Factor],[DateStart])) AS [Year], 
    Month(DateAdd("m",[Factor],[DateStart])) AS [Month], 
        IIf(DateDiff("m",[DateStart],[DateEnd])=0,
            DateDiff("d",[DateStart],[DateEnd]),
            IIf(DateDiff("m",DateAdd("m",[Factor],[DateStart]),[DateEnd])=0,
                Day([DateEnd])-1,
                Day(DateSerial(Year(DateAdd("m",[Factor],[DateStart])),Month(DateAdd("m",[Factor],[DateStart]))+1,0))
                    -IIf([Factor]=0,Day([DateStart])-1,0))) AS 
    Days, 
    DateDiff("d",[DateStart],[DateEnd]) AS DaysTotal
FROM 
    msysobjects AS Uno, 
    msysobjects AS Deca, 
    Dates
WHERE 
    10*Abs([Deca].[id] Mod 10)+Abs([Uno].[id] Mod 10)<=DateDiff("m",[DateStart],[DateEnd]);

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/gustav

Hi Gustav,

Thank you for sticking with me and helping with this.

It seems that Total Days and the day count of the last month may be off by 1.

I can easily modify the total days formula, ((DateDiff("d",[StartDate],[EndDate]))+1)

But I honestly don't know how to change your other formulas to add a day to the count of the last month.

No, the counts are not off by one. That's why I included the total column as control.
The count is 0 if DateStart equals DateEnd. If you wish to raise the count to include the end date, just add 1, but then you will never be able to have a count of zero.

/gustav

Correct, there should never be a count of zero.  StartDate 11/10/16  to EndDate 11/10/16 should be a count of 1 day.  I don't know how to fix that in your formulas because all but the last month of the count come out correctly.  How do I adjust just the last month of the date range's total?  The total column is off by one but that is an easy fix.

@gus

You should be paid for this help!    ;)

Thanks! That's not the way it goes, but you can start by clicking a thumbs up.

/gustav

I know.

Thank you so very much for all of your help.  You've gone above and beyond with your patience and sharing your knowledge.  It is very much appreciated.

@yo_bee

Thanks man :-(  It wasn't like I wasn't feeling bad enough already.

Thank you. You are welcome!

/gustav