United Airlines Carry- on baggage allowance is:
Carry-on bag
The maximum dimensions for a carry-on bag are 9 inches x 14 inches x 22 inches (22 cm x 35 cm x 56 cm), including handles and wheels.
Personal item
The maximum dimensions for your personal item that fits under the seat in front of you, such as a shoulder bag, purse, laptop bag or other small item, are 9 inches x 10 inches x 17 inches (22 cm x 25 cm x 43 cm).
American Airlines Carry-on baggage allowance is:
Shouldn’t exceed 22 x 14 x 9 inches / 56 x 36 x 23 centimeters