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How can I estimate how many copies of a book are being sold on Amazon? I presume there is some relationship between the rank of a book and its number of copies sold.

For example, "The C Programming Language", a perennial classic for programmers is listing at #1,506 on Amazon Best Sellers. I estimate this book probably sells at least 10,000 to 20,000 copies per year even though it is 30 years old. By making a number of such estimates and fitting it to a logarithmic curve I could probably figure out the function between Amazon rank and total sales, however, I assume someone else has already done this. Am I right?

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A best selling romance author, Theresa Regan, somehow came up with estimates based on rank:

Amazon Best Seller Rank 50,000 to 100,000 – selling close to 1 book a day.

Amazon Best Seller Rank 10,000 to 50,000 – selling 5 to 15 books a day.

Amazon Best Seller Rank 5,500 to 10,000 – selling 15 to 25 books a day.

Amazon Best Seller Rank 3,000 to 5,500 – selling 25 to 70 books a day.

Amazon Best Seller Rank 1,500 to 3,000 – selling 70 to 100 books a day.

Amazon Best Seller Rank 750 to 1,500 – selling 100 to 120 books a day.

Amazon Best Seller Rank 500 to 750 – selling 120 to 175 books a day.

Amazon Best Seller Rank 350 to 500 – selling 175 to 250 books a day.

Amazon Best Seller Rank 200 to 350 – selling 250 to 500 books a day.

Amazon Best Seller Rank 35 to 200 -selling 500 to 2,000 books a day.

Amazon Best Seller Rank 20 to 35 – selling 2,000 to 3,000 books a day.

Amazon Best Seller Rank of 5 to 20 – selling 3,000 to 4,000 books a day.

Amazon Best Seller Rank of 1 to 5 – selling 4,000+ books a day. 

Note that if we apply this formula to my example, "The C Programming Language" that would 100 books a day, or 36,500 books per year for K&R. My guess is that this is somewhat high, but in the right general ballpark based on my knowledge of that book and its market, so Regan's estimates may be roughly correct.

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