The number of pages in your book divided by your Pages Per Inch. PPI depends upon what kind of paper you're using. If your book has 285 pages, you're printing it paper which has a PPI of 400. Then the width of your book's spine will be 285 ÷ 400 or .713 inches. The best and easiest way to get an accurate calculation is to load your book PDF to the service you are using which then will generate an accurate template or spec numbers by the printer. Here's a quick "guesstimation" calculator for your spine width. Remember, though, this isn't absolutely accurate because the variables mentioned above (font, font size, margins, gutter, and layout choices, etc.) will alter the PPI. Try to always use the template provided by your print service.

Spine Width Calculator