There isn't a "formula" per se. You will have to treat each reinvestment of dividends and capital gains as a separate purchase for the purpose of cost basis determination.
Often, it can be helpful to gather all of the transaction confirmations of the transactions and build a spreadsheet to help you and then program the spreadsheet to calculate the average cost.
If you use a full-service broker the broker will often do this for you as they have the information most of the time, they just don't print it on the 1099-B.
Your broker should be able to provide you with the confirmations or historical statements that will have this information or, if you have online account access the statements/confirmations should be there.
@carolinejq2
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