The maximum dimensions for carry-on luggage on a United Airlines flight are 9 inches by 14 inches by 22 inches. For a personal item such as a laptop bag, handbag or small backpack, the maximum dimensions are 9 inches by 10 inches by 17 inches.
Travelers are allowed to bring one carry-on item in addition to one personal item aboard on all United Airlines flights. This service is free of charge, as of 2015. The following items do not count as a personal item: a jacket, an umbrella, reading material, a diaper bag or food and drink purchased inside the airport.