All airlines have their own rules on carry on allowance and baggage allowance.
It would be nice if they had a standard so it was easy to switch airlines when on multi stop trips, but it isn't the case, so be aware before leaving home.
Here is a quick rough guide on sizes and weights allowed to be carried onboard, but it is just that, a rough guide.
International airlines - all differ somewhat, but most allow 55cm x 40cm x 20cm, which is 21.5” x 16” x 8”. If the bag is less than this you shouldn’t have any problems, providing the weight is ok. Weight allowance varies greatly between airlines, but usually between 8 and 12kg on International.
Domestic airlines often have a size determined by adding the length, width and height together to give a maximum dimension which is usually 115cm or 45”. The weight again varies and is surprisingly generous on some airlines, usually it will be around 7kg but some airlines is as high as 20kg , but best to check with your airline before flying.
Here is a useful website for checking major airlines for both carry on and checked bags:
But be warned, always check with your airline before heading to the airport. I have had several awful occasions of having to reorganise and dump excess weight whilst standing at the airport check-in, and other painful boardings having to pay expensive excess baggage fees.