Paying for recovery software just to pull data from a formatted drive is the same as burning money.
Formatting doesn't touch your data, it's all there, just not indexed, and there are a dozen free programs that will let you recover all of it without much fuss.
If you actually overwrote it, any overwritten data is just gone. Chances are the NSA would find it a lost cause even if they thought you were the Caliph of the Islamic State and were in the middle of planning a nuclear attack on Christmas spirit and apple pie.
If you have partially overwritten/physically damage data this is where some software suites that cost money can be justified, as they might make putting the pieces that can be recovered back together into something you might be work with a lot easier.
...rightful liberty is unobstructed action according to our will within limits drawn around us by the equal rights of others. I do not add 'within the limits of the law,' because law is often but the tyrant's will, and always so when it violates the right of an individual. -- Thomas Jefferson