How to check the SHA512 hash of a downloaded software?

Open Terminal, located in /Applications/Utilities/, and type the following line:

shasum -a512

Then type a space. Finally, drag the file that you want to check into the Terminal and then press the return key.

Please don't post duplicates. I posted an answer in your original post:

For examples see: Check SHA1 Checksum in Mac OS X - OS X Daily.