In the US most airlines allow a carry on bag up to 45 linear inches in size, or measuring 22″x14″x9″.

However, if you are flying Internationally this size carry-on bag may not fit in the overhead compartment.  If you want to make sure your bag will fit, you may want to consider a international size carry on which is only 20″ high.  Many luggage manufacturers are making these bags to be slightly shorter and fatter.