Creating a disk backup image

I am trying to create a backup image of my HDD with AOMEI Backupper and save it to an external drive. My HDD is 750GB. Do I need the same size (or larger) external drive to store the image? Only about 40GB of the HDD is actually being used for the OS and other files, but when I try to use a 60GB external SSD for the image, I'm told it's too small.

I've not used that app, but from what you're saying that should work. I use Macrium Reflect and set the compression to maximum for backups. This takes a bit longer but it typically shrinks the backup image by at least 50% of the USED space in the original partition. This allows me to back up a 60GB partition, of which 40GB is used, to a 15GB file.

I thought it should work as well, but so far I haven't been able to make it do so. The program tells me, even before starting the backup, that the selected destination is too small. May just give Macrium a try.