Re: File recovery after formatting wrong partition
If you have access to an MS Windows PC, and you can attached the formatted drive to that PC ... and ... are willing to spend some money, you may be able to recover that data using MS Window apps.
If interested, read on ...
In my experience, Windows filesystem utilities have been best at recovering data from former Windows partitions; Linux filesystem utilities have been best at recovering data from former Linux partitions.
Since your data was on a Windows partition, based on my experience at doing this successfully, my suggestions are the following:
[NOTE: If your PC has a working copy of MS Windows on it, skip to step 4]
1) Find someone with a working MS Windows PC
2) Remove your drive from this PC.
3) Connect your old drive to the MS Windows PC.
4) Download and install the trial version of GetDataBack for NTFS from Runtime Software in MS Windows.
5) Run GetDataBack and select the option to find Deleted files.
6) When done, browse the filesystem in the app to see if your directories and files were found. If so, view some to confirm the contents are intact.
7) If they are, you will have to purchase GetDataBack to do the actual recovery. You won't have to reinstall it; instead, they will email you an activation code which you can use to turn on the recovery feature.
And, last time I checked, GetDataBack for NTFS was $80, USD.
There's also a FREE MS Windows file system recovery app known as Recuva. You could try that first -- but my experience in MS Windows is you get what you pay for.
Your data ... your money ... your choice.
Ubuntu 14.04, Mint 17; MS Win 8.1.
Will not respond to PM requests for support -- use the forums.