Dimensions. A traveler who brings carry-on luggage onto a United flight must bring a bag that is less than 22 inches tall. The luggage also needs to be less than than 14 inches wide and 9 inches deep.ome items you bring on board do not count against your one bag and one personal item limit. These items include canes and crutches, child safety seats, coats and hats, reading material and umbrellas. Travelers also may bring with them food or beverages that will be consumed on the flight.