Operating systems have been used a lot from the past decade or so. Not that what went before, it wasn't unusual for an application program installation to corrupt the OS to the extent that the hard drive or partition would have to be formatted, and the operating system should be reinstalled. Luckily these days, hard drive formatting is done to separate partitions, or re-allocate existing resources. If you realized that you need some data from that recently formatted hard drive, your have less options left for recovering data but still you can restore that data. So unless you have saved or written new data on to the formatted drive, you can use Mac external hard drive recovery to recover data from formatted drive.
Is manual recovery of data possible?
The immediate answer to this query is "no". It is essential to understand that the data you are trying to find is still present on the hard drive, and is undoubtedly recoverable with the help of 3rd party recovery software you will certainly be able to retrieve data from the formatted hard disk drive.
Recover files from formatted drive
Simply lost or deleted files aren't actually gone. They are still present in the same location they were earlier to the formatting of the drive. The only thing that is lost is the drive is their physical address they occupy, and pointer indicating the disk and the operating system that the area is not available to save or write new data. With this knowledge in hand, all you need to do is to search for solid hard drive recovery software.