Are faucet aerator a standard size?

The most typical size in American market is 15/16" male thread or 55/64" female thread

While the common size in European market is M24 male thread and m22 female thread

There are also other kinds of thread size in the market, like M18,M20, 13/16" and so on

Female thread size aerator is to match male thread spout, usually you may measure the diameter of the spout before buying a new aerator

If you have bought a wrong size aerator, no worry, it's also can be workable if adding a suitable adaptor

Like below adaptor package will be very convenient to matching for different kinds of thread

The adaptor package including below sizes: 

FM22---M20

FM22---M22

FM22---M24

FM22---FM20

FM22---G1/2