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This varies substantially, depending on the sort of book, how well the author negotiated (each book involves an individually negotiated contract), the price of the book, etc. Based on one Springer contract I'm familiar with, here's a first approximation. I can't say for sure how representative it is, but it's at least one data point, and I'd guess it's typical for Springer and competing publishers.

For regular sales, the author may get 9-12% of "net cash receipts", defined as what the publisher made on the sale (excluding taxes), with the percentage depending on things like how well the book has sold. Note that "regular sales" excludes some special cases, for which there may be lower royalty rates.

Then the question is how much Springer charged the bookseller for the book. You can download a 6 megabyte zip file of Springer wholesale prices. I glanced at a few math books, and the prices look like they are about 60% of what bookstores are charging. That's certainly the right ballpark, but I haven't computed any real statistics.

So a first approximation is that the author's royalty is probably 5-7% of the price you pay in a bookstore. Considering that academic books are expensive, that's not bad, but nobody's going to grow rich off it. For advanced books, selling 1000 copies in total is very good and selling 10,000 is amazing.

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I would be interested in the hourly pay for writing such a book :) I guess it would be rather sobering. –  xLeitix Apr 15 at 7:35
    
Also, realtime.springer.com shows download statistics for e-books. Do authors get royalties for e-books, too? –  Geremia Apr 15 at 15:18
    
@Geremia in a word, yes. Individual eBook sales count a normal sales from the royalty point of view. Bulk access from bundles works differently but the author still gets something. –  BSteinhurst Apr 15 at 19:31
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Based on my 1 contract with Springer, I would like to add that the way to get rich (presumably) is translations. The author royalty on those is 50%. Other than that there is a 33% discount on Springer titles, though I haven't used it. Oh and you get a few free copies of your book, in my case I got 5. I haven't seen a cent other than that –  Ivar Persson Apr 16 at 15:00
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@IvarPersson: It's 50% of Springer's net proceeds if they license the translation rights to another publisher, right? (At least that's what I've seen.) Basically, Springer collects royalties from licensed translations and then splits them 50-50 with the original author, but this isn't as lucrative as it sounds since these royalties are only a modest fraction of the price of the translated book (most goes to the translation's publisher and the bookseller). Also, net proceeds are after production costs, so any expenses on Springer's part are deducted before the 50-50 split. –  Anonymous Mathematician Apr 16 at 15:48

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