It's not possible to know for certain what size data will compress to without actually compressing it. What you can do get an educated guess based on the content you have in your home directory. I'm not aware of any tools to do this automatically, but it's not a difficult process.
Many modern file formats are already compressed, meaning running it through compression again will give you little to no (or negative) gain. This type of data you're better off skipping the compression and simply copying or archiving it as is. Examples of this would be compressed video (mp4, webm, mov, etc), compressed images (jpeg, png, etc), existing archives (zip, rar, gz, bz2, etc), and more.
Text files will generally compress fairly well, especially if there is a lot of repeated data (ie, log files). You could try sampling a subset of files to see how they compress and use that as a guess or use something like 50% as a rough estimate.
Finally, see what portion of your data is made up of each type and multiple that by your estimated percentage to get an estimate of your final size. For example, if 20GB of your data is compressed data and 9GB is text files, your final compressed data size would probably range from 21GB to 25GB.
129GB fits on most USB drives easily, and even on many cloud providers. So, I'd skip the compression but use something like
rsync
instead. (Also, you very likely need a proper backup mechanism any day of the week!) – Arjan – 2019-10-20T08:38:25.813Due to an imminent distro switch, I would like to backup my home directory You should backup you home directory regularly, and not wait for a distro switch. – xenoid – 2019-10-20T12:59:22.277
@Arjan, the problem is that most USB flash drives are formatted as FAT32 or exFAT, which both limit their file sizes at 4GB, I think. – Blue-Maned Hawk – 2019-10-21T05:41:22.197
Good point, so: format an external disk differently ;-) (Agreed, also user/group access right are easily preserved using an archive. Still then, archiving won't make a good way for daily backups. Of course, that's not what you're asking. Still, as for using
– Arjan – 2019-10-21T10:16:55.140rsync
for that, see Time Machine on Ubuntu?.)