There is software available that meets US DOD standards or beyond to completely erase the data on a disk.
re: "completely erase"
There is a reason why governments mandate physical destruction (your "US DOD Standards" probably contains the same requirement) .... and that's complete shredding, not just attacking it with a hammer and nail or drill which is a pointless activity.
What typically happens in business or government is you will secure wipe your drive to the best of your ability and then hand it over to a rigorously vetted contractor for shredding (assuming your data isn't so sensitive that you've got the drive shredding machines in-house !).
If you insist on not destroying, but only erasing, at least do it by triggering the ATA controller ERASE command rather than some wiping software, the fancy sounding "DOD" software you are referring to most likely does not do this.
But generally speaking you should assume any software solution WILL NOT "completely erase", especially if it's some random piece of software you downloaded off the internet (assuming of course we don't start opening up the can of worms of whether you can trust something you downloaded off the internet
)