The standard U.S. carry-on size is 22 x 14 x 9 inches (56 x 36 x 23 cm) including wheels and handles. This fits the overhead bin on most commercial aircraft and is accepted by American, Delta, United, and most other U.S. carriers.
TSA itself does not set a carry-on size limit. That is set by each airline. TSA only screens for prohibited items and liquids rules.
Southwest allows a slightly larger carry-on at 24 x 16 x 10 inches. Budget airlines like Spirit and Frontier measure more strictly and charge gate fees if the bag is even slightly over.
The 22 x 14 x 9 limit includes external pockets, wheels, and handles. A bag labeled 22 inches is often 23 inches measured with the wheels extended.
See: carry-on size limits by airline and the free luggage calculator.