According to the Federal Aviation Administration, or FAA, the maximum sized carry on for most flights is 45 linear inches. This number represents the total of number of inches allowed for the height, width and depth of your luggage. This is typically broken down into 22"x14"x9". The Travel Insider reports that some airlines allow people to board with carry on bags that measure 55 linear inches, but this is rare. Contact the airline you're using before your flight to find out their specific requirements. When packing your carry on bag, remember that stuffing outside pockets will increase the overall dimensions. Measure your bag before leaving home to make sure it will be allowed on the plane; most airports also have small bins that represent the size your bag should be. If you can fit your bag in the container, you're fine. If not, you might have to check your bag, or (worst case scenario) toss excess belongings in the trash.
As a safety precaution, store carry on bags with heavy items underneath the seat in front of you. Don't risk heavy items falling out of the overhead bin in case of turbulence or a bumpy landing, and causing a head injury to someone sitting below your luggage. For the same reason, don't stack bags in the overhead bin on top of each other.
Most airlines allow other items to be carried on to the plane, in addition to your small luggage. These typically include purses, briefcases, camera bags, laptop cases, books/magazines, backpacks, umbrellas, outerwear, a small bag of food, a child's safety seat, a pillow or blanket, an umbrella stroller, wheelchairs and walkers.
If you find your carry on luggage exceeds the dimensions allowed by your airline, you can have your baggage checked. It will be stowed underneath the passenger cabin of the plane, and you can retrieve your bags once you arrive at your destination. Some airlines charge for stowing checked baggage; check the price in advance. It might be less expensive to ship your excess items. Note that some airlines flying very small planes might require you to curbside check your bags, even if your carry on bag is less than 45 linear inches.
