There is a lot of conflicting info on this but I think you would need a support for anything over 12". You also need to take into account if your granite is 2cm or 3cm thick. There is a good post on this subject if you search on "bar overhang".

Follow the "6 & 10" rule...
For 2cm stone, any overhang over 6" needs support
For 3cm stone, any overhang over 10" needs support

So, if you have a 12" overhang...
2cm stone would require a 6" support [Overhang - 6" = Support required]
3cm stone would require a 2" support [Overhang - 10" = Support required]

See the linked thread for more information. (It's also linked in the "Read Me" thread.)

Here is a link that might be useful: Thread: Stone Information and Advice (& Checklists)

thanks for the responses--My granite is 3cm. I have read and read the threads and was still having a hard time understanding. I do have another question though....I don't see it mentioned anywhere how the support--for instance my 16.5" of wall/cabinets impacts the necessary supports for the overhang. It must?? or am I just not getting it?

The distance the stone is cantilevered out from its supports is the criteria.