Is it possible without formatting?
According to
https://www.google.com/search?&q=ubuntu+turn+on+disk+encryption+after+installation
that is possible.
I, personally, would not accept a risk though.
What are the risks? Is there alternatives? Also, is there a software that can save it? Just in case it goes wrong.
You can encrypt your disk with Bitlocker.
The AskUbuntu article explains some of the stuff.
However the risks far outweigh the benefits.
If you want to do a full disk encryption your best practice is going to be to backup your system, confirm that the backup was successful and then to do a new installation with full disk encryption. Then restore your files to your new installation.
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Ok thanks! I appreciate the help. 