I'm not aware of any freeware data recovery apps. If there are any, they're probably worth what you pay for them, as data recovery is a very complicated operation.
Data Recovery software is probably your best option, and is dirt cheap compared to professional recovery. It all depends how much your data is worth. Most recovery apps will give you a basic free version to show what may be recoverable, but will not let you actually recover the data. That version costs money.
Whatever you do, don't write anything to the disk you formatted, as that may overwrite the files you're trying to recover.
This type of issues happen one or another day but no need to get panic! You can easily recover data from inaccessible and formatted drives by using data recovery tools. I have perfect solution named as Hard Drive Data Recovery which is specially designed and developed by expert professionals to recover data from formatted hard drive within few minutes.
Hope it can help you!