Data on floppy disks can sometimes be recovered by forensic analysis even after the disks have been overwritten once with zeros (or random zeros and ones). This is not the case with modern hard drives. The bits on modern drives are so small that deviation of tracks between writes cannot be discerned by any means[citation needed].
According to the 2006 NIST Special Publication 800-88 (p. 7): "Studies have shown that most of todays media can be effectively cleared by one overwrite" and "for ATA disk drives manufactured after 2001 (over 15 GB) the terms clearing and purging have converged."[6]
According to the Center for Magnetic Recording Research, "Secure erase does a single on-track erasure of the data on the disk drive. The U.S. National Security Agency published an Information Assurance Approval of single pass overwrite, after technical testing at CMRR showed that multiple on-track overwrite passes gave no additional erasure."[7] "Secure erase" is a utility built into modern ATA hard drives that overwrites all data on a disk, including remapped (error) sectors.
Further analysis by Wright et al. seems to also indicate that one overwrite is all that is generally required.[8]