I don't know why my apps use so much storage I haven't downloaded anything.
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Your spotlight database (or worse - filesystem) is corrupted.
I'll link to some other situations that cover this.
- About This Mac -> Storage is wrong?
- How can I figure out what's slowly eating my HD space?
- Mac OS is reporting bad free space
- Noticebly larger amount of free space reported compared to the graph in Storage view
The simplest way to resolve this would be to make a backup (if you don't have one), boot to Recovery HD and use Disk Utility to check / repair your disk. Then you can restart the Mac and let it rebuild the spotlight database overnight. Worst case, you can purge the spotlight database if the situation isn't a transient problem with the calculations.

sudo du -sm /Applications/* | sort -nin Terminal and add the last 10 lines of output to your question. – nohillside Aug 27 '16 at 09:17