How do I connect a time machine drive? What drive size do I need?
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If you have not yet started a new time machine backup you’ll need a spare external hard drive equal to or greater than the size of your internal drive. You can temporarily get away with a smaller drive but eventually you’d grow out of that size drive as time machine wouldn’t be able to back up the entire drive if the internal drive contained more data than the external drive was able to hold. So best to do it right the first time. Buy a drive equal to or larger than the internal drive.

Secondly, if the computer doesn’t prompt you to start using the newly connected drive as a TM backup, just go into System Preferences, Time Machine and select the new drive. It may ask you if you’d like to replace an old one. Say yes and let it run. Leave it connected and time machine will periodically backup your internal computer’s hard drive.