The size limitation of your checked luggage and carry on is calculated by adding the total outside dimensions of each bag (*linear dimensions), that is, length + width + height.
It is important that you check with your airline for their specific policy, to avoid additional baggage fees.
In general, most airlines have adopted a maximum carry-on size of 45 linear inches, determined by adding up the length, width and depth of a bag (typically 22 x 14 x 9 inches). These dimensions are determined by taking the longest measurement, including handles and wheels.
While most airlines do not weigh carry on items, most have a 40-pound limit per piece. On domestic flights, the typical allowance is one (1) carry on bag, and one (1) personal item such as a purse, briefcase, laptop bag or camera bag. Almost every airline requires that personal item to be smaller that your carry-on. For example, you may not have two 22 x 14 x 9" carry on bags with you and count one as a personal item. In addition, some airlines set size and weight limits for personal items, so it's important to check with your airline first for their specific policy.
For checked luggage, most airlines allow a maximize size of 62", although some allow up to 72". Most airlines allow a maximum weight per checked bag of 70-pounds. and some allow up to 100 lbs. at extra cost.
Baggage limits are determined by individual air carriers, and can vary widely. These standards can change at any moment, so it's always advisable to check with the airlines prior to travel.
Most airlines employ different rules for domestic flights and international travel, with a more generous allotment for flights abroad.
If in doubt, check with your air carrier.