I'm in the process of installing wainscoting in my dining room and was having the hardest time figuring out the proper spacing of stiles per wall. After several failed attempts, i did some searching and found This Link.
While his explanation of the math was extremely helpful, it was still manually intensive and remembering the formula could be a bit tricky. So I threw it into an excel spreadsheet and has worked great so far and wanted to share. If your smartphone has some flavor of excel (open excel for example) on it, it works GREAT. Here's a small screenshot of what it looks like (not much to it):
I added the imperial and metric counterparts as you sometimes (well every time I've put in values so far) get some odd fractions that don't exactly show up on a tape measure. Metric is easier in those instances.
I've found the Panel + 1 stile spacing is much easier and more accurate than measuring the panel size, placing the stile, rinse and repeat. If you measure from a corner, then you merely need to mark each spot for the start of the next stile.
The only thing I didn't get a chance to play with is modifying the math so you can enter in the number of panels and it will tell you the panel spacing instead, but for a quick and dirty spreadsheet, it does the job!