Rebecca Lewis gives us a rule of thumb:
How big will my backup file be? Very good question. And of course, it depends… especially if you’re using compression.
I was working something today that required a backup beforehand for safety measures, and the server had limited storage. So, I needed to estimate the backup file size beforehand to confirm whether I had enough space for the bak file.
Click through for the script. It does, of course, include some simplifications and your actual numbers can turn out a bit different, but for a quick and dirty estimate of disk space needed, this isn’t bad at all.