Allowed carry-on baggage dimensions vary between airlines. As of 2015, there are no legal dimension requirements stated by the TSA, but most airlines allow a total of around 45 inches in combined length, width and height.
Most airlines allow one piece of cabin luggage plus one small personal item, such as a laptop, purse or briefcase.
As of 2015, American Airlines specifies carry-on luggage must measure no more than 22" x 14" x 9". Delta and United echo these dimension requirements; however, United allows personal items to include a backpack or other bag that measures no more than 17" x 10" x 9".