British Airways allows its travelers to take one piece of hand baggage, and a briefcase, handbag or laptopcase on board its airplanes. They have predefined maximum measurements: your cabin baggage can be 56cmx45cmx25cm at maximum. Your laptop bag or briefcase can be a maximum of 45cmx36cmx20cm. You can find more information about British Airways' cabin luggage restrictions here.
Budget airlines company Ryanair allows one item of cabin luggage per passenger. Your cabin baggage can be maximum 55cmx40cmx20cm. Other carry-on luggage such as laptop bags, handbags, briefcases,… can be carried in the piece of hand baggage that you take with you. Extra or oversized cabin luggage may be refused at the gate, or you can be charged an extra fee before you can take it with you. You can find more information about Ryanair's cabin luggage restrictions here.
EasyJet allows one piece of hand luggage per passenger. Their maximum dimensions for cabin baggage are 56cmx45cmx25cm. Laptop bags, briefcases and hand baggage are all considered as cabin luggage. It's not permitted to take, for example, a laptop bag and a hand bag with you on the plane; only one bag per person is allowed. You can find more information about Easy Jet's cabin luggage restrictions here.
Australian airline Qantas requires that your carry-on hand baggage fits under the seat in front of you in the plane, or in one of the overhead bins. In all classes, you can take two 105cm bags or one 105cm bag and a 185cm non-rigid garment bag with you. Or you may carry one 115cm bag. All bags can weigh a maximum of 7kg. Other bulky items should not weigh over 7kg either, and shouldn't be over 74cmx51cmx53cm. Qantas recommends you to keep your carry-on luggage as light as possible, as there may be long distances between the different locations in the airport. You can find more information about Qantas' cabin luggage allowance here.
Delta allows one bag and one personal item per passenger, but all items must fit into the overhead bin or under the seat in front of you. A purse, briefcase, laptop computer bag or an item similar to one of those are allowed as personal cabin luggage. Additionally, baggage may not be larger than 115cm in total combined length, height and width. The bag must fit easily into the carry-on baggage tester at the check-in zone. You can find more information about Delta Air Lines' cabin luggage regulations here.
Lufthansa allows you to take up to two pieces of cabin luggage on the plane. One hand luggage piece should not exceed 55cmx54cmx15cm and may not weigh more than 8 kg. Foldable garment bags are an exception to the rule; they count as hand luggage of a size that's up to 57cmx54cmx15cm. If your luggage exceeds these measurements, Lufthansa will ask you to place this luggage in the cargo hold. These rules may be different for smaller aircrafts. You can find more information about Lufthansa's cabin luggage rules here.