Airlines measure baggage size in linear inches. Linear inches are the length, width and height combined. For American Airlines, Delta and Continental Airlines, the domestic carry-on limit is 45 linear inches and the domestic checked bag limit is 62 linear inches.
Each airline also has the ability to decide weight limits for bags. This is measured in pounds. American and Delta Airlines do not impose weight restrictions on domestic carry-on luggage, but Continental Airlines has a limit of 40 pounds. For domestic checked luggage, American, Continental and Delta each have a limit of 50 pounds.
Airlines each have their own restrictions on the size of luggage for international flights, but for the most part these mirror domestic flights in linear inches. For some regions, airlines have particular policies on what can be used. Check with your individual airline to see what their policy is. In addition, military members often have more liberal restrictions than civilians.
