Did you have the quick format option checked when you formatted your drive, or did you do a full format? If you had the quick format option checked there might be a chance you could recover some coins yourself. If you did a full format I would pay a professional data recovery company to try recovering your coins.
Don't boot from that drive. If you continue running the installed operating system it might overwrite your wallet.dat data.
If you know how to use a hex editor you could try scanning your drive for this sequence of bytes: 01 03 6B 65 79 41 04.
That sequence often occurs in a wallet.dat file about 180 bytes before a private key. If you look forward 180 bytes and can find the byte sequence 04 20 then it's likely a private key is the next the thirty-two bytes.
If you find a private key you can change it to a common format by pasting the thirty-two bytes into an offline copy of this webpage.
https://www.bitaddress.org/This is an example of the 32 bytes of a private key in notepad.
This is the private key copied from notepad and pasted into an offline copy of the bitaddress website. Click the view details button to get the private key converted to normal formats.
There's a more detailed explanation of the byte sequences to search for in this quote.
I have been doing some tinkering around, thinking about other people's wallet disasters, and believe I have come to the following conclusion...
If you have lost your wallet.dat for whatever reason (deleted it, formatted your drive, file corruption, etc.) it's possible that it may still be lurking on your computer. If so, recovery is no longer purely theoretical. With a little knowledge of what to search for, you can use a hex editor to potentially find usable remnants of your wallet.dat file and get back your bitcoins, even if the original file isn't fully recoverable.
So here goes...
If you can use a hex-editor to do a sector-by-sector search/edit on your entire hard drive, then search your entire hard drive for occurrences of the following byte sequence:
01 03 6B 65 79 41 04...........
the middle four of these bytes represent the string "keyA" in ASCII.
Each time this byte sequence occurs, a Bitcoin private key is probably stored nearby, about 180 bytes later. The 32-byte private key is the only thing you need to recover your bitcoins!... as long as you find the right one(s).
Approximately 180 bytes after this sequence, you may find the byte sequence 04 20 (hex). These two bytes seem to precede every private key (the 0x20 suggests a length of 32 bytes). If you find this sequence, the thirty-two bytes that come after 04 20 are the private key representing a Bitcoin address and might be the private key that recovers some of your lost bitcoins! Your wallet will have numerous private keys (at least one hundred, due to the pre-allocation of keys)... get as many as you can find. Carefully search the sectors adjacent to any sector containing the "keyA" sequence above. Then yell for help! (But don't share the private keys in public, unless you want to give away your wallet.)
An example of a hex editor that can scan an entire disk volume for specific byte sequences for Windows is WinHex. In WinHex, use Tools, Open Disk (F9), and choose the disk you want to scan. Scanning a full disk can take hours. WinHex must "run as administrator" to be able to scan a physical disk. Someone please recommend a good way to do this in Linux, preferably with a known Live CD, if possible. Also, any time you are scanning a disk for potentially lost data, you should NEVER boot the disk you're searching - always boot from another disk and install the target disk as secondary.
