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I think @kboy is mostly right. A clean install would remove all the os caches and virtual memory it used on your drive. That's where the free space comes from. Time machine doesn't back up that "other" portion.
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I think my extra space came from the fact that i partitioned my drive a couple of years ago to add bootcamp. I am rubbish at things like this so when i came to uninstall it i am not sure i did it all correctly. I was reading online that if you format and reinstall, all of the old crud that's not a system file is cleaned up.
We’re talking about different things. What I mean is:
1 - back up to time machine hdd
2 - format computer, do a clean install of OS X
3 - restore from time machine hdd
This way you’ll get a clean install of OS X but with your settings, files and apps.