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There isn't a native formula, but you can get there with a few tools (and a table of holiday dates if you want to exclude those as well). See attached.
1. Generate rows for all dates between your start & end date (add a RecordID before this step if you have more than one date pairing you're wanting to calculate this for)
2. Formula tool to determine the number designation for each date (DateTimeFormat([Date],"%w")
3. Filter for Weekday numbers not equal to 0 (Sunday) or 6 (Saturday) <-- If you have a non-standard workweek, such as Sunday/Monday weekends, you could adjust these #'s
4. Join a list of holiday dates to the True output of your formula, if you would also like to exclude holidays. This has to be a manual input (or pulled from a table somewhere) as the definition of "holiday" varies so widely! :)
5. Summarize tool: Group by RecordID, start date, end date, etc. and then count the number of records (days) remaining
Hope this helps!!
EDIT: ... which appears to be basically the same solution as those from the articles @KaneG included. :)
Just wanted to point out that using this method, you will lose any records that have a negative count or 0 count between days. When you join back the row count to your original row count.. look at what isn't joining.. these are all your 0 or negative day counts. If you need these records, you'll need to use a different method to get a count for them and union them back.
Has this been implemented in Alteryx yet? This seems like a simple ask as all the building blocks are there and a simple loop that shouldn't take more than a few days for a developer to test out. Are there really so few Alteryx users that need to calculate business days that this hasn't been a larger issue over the years?