First, a book's size gives an immediate first impression to the reader. If you write a mystery and provide your book in the same small, standard paperback size that most mystery novels come in, it creates the impression that your book is up to those professional standards. Your book will look like all the other books on the shelves. It will be that first step in the reader accepting that your book might be a good quality, worthy book to examine.
If, instead, you wrote a mystery novel but created it in a massive size reserved for coffee-table books, then many mystery readers might not pick it up. They might assume it wasn't what they were looking to read.
In the opposite direction, let's say you wrote a weightier subject like "The Intricacy of Advanced ASP Programming." Those types of books are traditionally large, textbook-sized tomes. If yours was instead a tiny, thin pamphlet, readers might wonder just how much detail you could possibly provide in that space.
Logically, in addition to that first impression, the size of the paper and the font used both impact the number of pages a given book takes up. For example my Believing your Eyes romance novel was 4.25" x 6.88" on Lulu. This was 462 pages. The same book on CafePress was a TINY bit smaller, 4.18" x 6.88", and it was 464 pages. When I moved the book to CreateSpace, which was larger at 5.25" x 8", the book became only 300 pages long. That change "lost" over 150 pages!
On one hand you could say this is good - less pages means less printing cost, so a cheaper price for the buyer and more chance that they will buy. That is definitely true. But on the other hand, the book now looks "thinner." The potential buyer can feel as if they are getting less of a story for their money. Many times readers want that denser experience. If a reader wished to sit down on a rainy afternoon and savor a lengthy book, a thinner book could feel inadequate to them.
In addition, text-per-page does matter. If a book is stuffed so there are "lots of words" on each page, based on the balance of font size, page size, and margin thickness, it's harder for the human eye to traverse the content. One alternative is to increase the font size so that there are fewer words, but that is a balancing act. You don't want the reader to wade through a few gigantic letters per page. Another option is to slightly increase the line spacing to help the book become easier to read.
Research is key here. Go to your library or bookstore and examine a number of books in your topic area. Make a chart as you examine their page size and fonts. See which combinations are easiest to read. You want your book to compete well against same-genre books. Also, see how long the books tend to be. Two random romance novels I picked up in the standard small paperback size were 349 and 394 pages. My Believing your Eyes book in that size, at 462 pages, was a nice hefty length. My Badge of Honor book at 356 pages was just right. However, when I reformatted my books into the larger CreateSpace size, they became:
Badge of Honor - 250 pages
Believing your Eyes - 314 pages
Creating Memories - 248 pages
So these larger format books "look" smaller (less thick) to the end user even though word-count-size they are the normal length in this genre.
The key here is to do your research. Don't just choose a size of your book based on a default setting. Research your genre, examine the font and margin options, and then do what works best in the area you want to shine in.
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