The standard European carry-on size is 55 x 40 x 20 cm, which is about 21.7 x 15.7 x 7.9 inches including handles and wheels. That makes European cabin bags slightly narrower and thinner than the U.S. standard of 22 x 14 x 9 inches.
Major European airlines using this size include British Airways, Air France, Lufthansa, KLM, and Iberia.
Budget carriers enforce stricter limits. Ryanair and Wizz Air often charge for any bag larger than their free 40 x 30 x 20 cm personal item. The larger 55 x 40 x 20 cm bag requires priority boarding or an upgrade fee.
Personal items in Europe are usually capped at 40 x 30 x 15 cm and must fit under the seat.
See: carry-on size limits by airline and the luggage calculator.