Paper sizes are standardized for reading and for some books but not others.
 North America
In North America the standard sizes are based on an "A" size pager that is 8.5" wide and 11" high. Each larger size doubles the smaller number, thus "B" size is 11" x 17" (double 8.5). Half A is also a common paper size at 5.5" x 8.5" for small notebooks.
The aspect ratio of "A" size is 1.294 but the "B" size is 1.54545. These two aspect ratio swap with each increase or decrease is size. The Half A is thus is the same aspect ratio as "B" size.
Books may have any aspect ratio and be of any size. For portable reading a 6" x 9" book is popular with an aspect ratio of 1.5 (3:2) which is very close to Half A. However PDF files are generally targeted at "A" size making them a better fit on electronic book readers with a 1.33 (4:3) aspect ratio. To show a PDF in full size with full margins on this display would require a 13.9" screen.
There is also a "legal size" that is in use in North America. It is 8.5" x 14" making it have an aspect ratio of 1.65. This size is unique and is not part of a set of sizes. However, it works well the newer widescreen displays.
 World Wide
The metric countries use paper based on the A0 paper size of 84.1 cm by 118.9 cm. This particular size has a total page area of about 1 square meter. The aspect ratio is the square root of 2, or 1.414. Each subsequent size from A1 to A6 is accomplished by dividing the longest dimension by 2. Thus A4 is approximately the same size as the North American "A" size but the aspect ratio is different. All metric sizes have the same aspect ratio.
A1 is about 59.4 cm by 84.1 cm (or 23.38" by 33") and A4 paper is about 21 cm by 29.7 cm (about 8.27" by 11.75"). None are a very good fit in the widescreen eBook reading devices due to the more squarish aspect ratio although larger devices work OK in a 2 page layout. If you allow for holes on the edge of the paper then the usable aspect ratio fits well with the current crop of wide screen eBook Readers held in portrait mode. Most books however are not that narrow. An A5 piece of paper at 21 cm by 14.9 cm (8.27" x 5.9") would be the size of a 10.2" screen. (The popular 9.7" screen would be 7.9" x 5.6" which works well with A5 documents.) See Screen sizes for the dimensions of popular screens. A full size A4 page with margins would require a 14.4" screen to show the page at full size using a 4:3 screen.
There is also a B0 size in use in Europe. It is exactly 1 meter wide and 1.414 meters high (about 39.37 inches by 55.75 inches). Like the A series there are paper sizes that are from B0 to B5 where each size is 1/2 the previous size by halving the larger dimension. The B5 is 17.6 × 25.0 cm (about 6.93" × 9.84") while B4 is 25.0 × 35.3 cm (about 9.84" × 13.90"). These two sizes span the A4 size but are a poorer match for the North American "A" size paper.