I'm sure you may have heard that when you delete a file from a computer, it is never "truly deleted." That statement, however, is only partly true. The files do not get deleted after, only the space that they occupy on the disk get prepared to be written over. When you reformatted the memory card in your camera, it did exactly that, and only prepared your pictures to be written over.
SO, the first thing you have to do after format is to not save any more pictures onto that memory card or you risk writing over the photo video files that you are trying to recover!
Got that far? Now you need to choose the appropriate camera recovery software. There are a tons of different programs but some are better than others. I actually recommend a program called 001 File Recovery because they have an option that is designed for recovering media files from FORMATTED memory cards, not only deleted or corrupted photo video files. You can download this software here:
Lastly, if the program does not recognize your SD Card as a drive when you are plugging the camera directly into the computer, you may need to directly plug your card into a card reader. Make sure that the card reader has the capabilities to handle your memory card though. Many older card readers can only handle cards up to 2GB, so if your card is bigger than that, you need a newer card reader.
I hope that helps, and that you get your deleted photo video files back like I did!