What Paper Format do Boarding Passes use?
Standard boarding passes are the size of an IBM punchcard, ​7⅜ by ​3¼ inches (187.325 mm × 82.55 mm) because paper and printers in that size were readily available at the time, and then inertia kept the size the same even when punchcards fell out of use and it became a specialty item.

Many airlines have switched to rolls of 3⅛ inch (79.375 mm) thermal paper, as is now commonly used in cash registers. For a new system, this is probably less expensive and easier to prototype.