There are quite a few recovery programs out there. I've had good luck with Prosoft Data Rescue in the past. (
https://www.prosofteng.com)
What they basically do, is scans the hard drive sector by sector... all the "empty space". This is because the way a drive technically works, is that an erase or format doesn't actually erase or overwrite your data. It marks that area of the drive as now available to write onto. So the data that's most definitely gone is the area of the drive that the new OS was overwritten onto. All the "empty space" still has a good chance of having your old data on it. And that's what these recovery programs do - search that space bit by bit.
Also, what that means is anything you add to your drive now is overwriting some of your old data. So it's recommended to boot from a different drive to run this, and then recover to another drive.
Good luck!