External Disk Capacity for Time Machine I have a 500 GB hard drive in my iMac, and I am planning to buy a new external hard drive to use for Time Machine. I don't know if Time Machine synchronizes, or something else. 

What size external drive should I get for Time Machine?
The Time Machine drive should be equal to or larger than the drive that it backs up. TM images the drive completely, then saves incremental changes. Time Machine saves the hourly backups for the past 24 hours, daily backups for the past month, and weekly backups for everything older than a month.

If your internal is 500GB with 100GB free (using 400GB), and your TM is 500GB, then you will get a full image, and then some amount of history (filling up the remaining 100GB of the TM disk). The history length depends on your use habits. 


Change a few small files occasionally? Lots of history. 
Change lots of big files a lot? Then the 100GB free will save a few hours or days.


If you have a bigger TM, you will have a longer history to browse.



I personally have a mostly full internal, an equal sized TM, and change files quite often, and find that I usually have a few months of history. Plenty of time to restore a file I accidentally delete.