Backing up Photos library to external hard drive

Solution 1:

If you started a new library from scratch - read: did not convert from a previous iPhoto or Aperture library - then the Your Library Name.photoslibrary bundle contains everything.

Exception: If you are using a referenced library (Photos menu > Preferences > General > Importing: "Copy files" box is not checked) then you need to back up the folder(s) where your actual photos are located as well.

If you did convert from a previous library, and have not removed it, you should back up both to be safe (though theoretically backing up just one should back up everything).