You can only restore data file or folders from a reformatted hard drive by using a data recovery software. However, it is not guaranteed that you can recover all the files that were previously stored in your reformatted hard drive. You can use Active File Recovery or any other good data recovery software and try to recover your important files.
It is possible to restore deleted files from formatted hard disk drive. You can effectively do this by using a file recovery software like Active File Recovery. However, it is not guaranteed that it could recover all your deleted files from your formatted hard drive because of many factors. You can still use the software and save some of your important files, it is still better to recover some than nothing at all.
To further elaborate on the answers given.
Firstly agree that Active File Recovery is a great piece of software for home data
I would like to expand on the method you should use to optimise the results of the recovery and things high light factors which will reduce the chances of recovering the majority of the data.
To start with, if you imagine the hard disk as big serving plate with lots of little compartments which each hold one item of food (sorry for the food reference but I am hungry! ;)) ). And that every "block" of data that you store is placed by the hard disk into one of these compartments. There is another part of the hard disk which acts like a register, recording the compartment that each block gets put into and the relationships between blocks.
So taking this into consideration, lets have a look at what happens when you format (although this is all an over simplification for the sake of trying to explain the fundementals revelvant to your question). A format of a drive will erase the register that holds the details of each compartment and mark each compartment as "empty". What is does not do is actually wipe / overwrite the data in each compartment. This means therefore that if you ask the hard disk to store some information, it will write to the first "empty" slots and in turn overwrite the data, however if you do not write any data to the formatted drive, the chances are that the data in each compartment remains in tact.
So, taking that very over simplified view on how the data is stored it is important to consider the way in which to get the most data back from a formatted disk.
(1) Do not re-install windows on it if you can help it. Rather attach it as a slave disk (either internally or via an external USB / Esata / Firewire adapter) to a computer that can boot from a partition on another disk. Then run the recovery software from here.
(2) Do not copy any files onto the formatted hard disk prior to trying to recover the data you require. Of course once the recovery is complete you can then use the drive as required.
I hope this is helpful. The only other thing to consider is try to avoid messing around with logical partitions etc.. on the disk prior to the recovery as this will also reduce the success of your recovery.
Good Luck, I hope you are able to recover the data you require, please remember as others have said, to be realistic, it is quite unlikely that all of the data on the disk will be recoverable.