df -h - Used space + Avail Free space is less than the Total size of /home

By default, ext2/3/4 filesystems reserve 5% of the space to be useable only by root. This is to avoid a normal user completely filling the disk which would then cause system components to fail whenever they next needed to write to the disk.

You can see the number of reserved blocks (and lots of other information about the filesystem) by doing:

sudo tune2fs -l /dev/sda8

For a /home partition, it is probably safe to set the reserved fraction to zero:

sudo tune2fs -m 0 /dev/sda8

Which should make an additional ~5GB available.

This question is really about interpreting the output of the df command, which is famously confusing and if your Google for it, you'll see many questions about df.

"Size" is df results are INCLUSIVE of the 5% reserved space @chronitis told you about. This is the total ABSOLUTE space. This number will approximate the size shown in the results of fdisk -l for the partition which you're looking at in the df results.

"Used" + "Avail" provides the total EFFECTIVE space and EXCLUDES the 5% reserved space. This is the space you can actually work with.

So nothing is "missing"- the disparity between "Size" and ("Used" + "Avail") totals in df output represents the 5% reserved space

But the confusion about interpreting available space for df doesn't end there! If you delete a large file(s), but the process for it hasn't been terminated, this "free" space will not be reflected in the results of df. You'll be scratching your head thinking "But I deleted that file(s), why can't I see the additional space in df?!?" That's why when you restart, the space from the deleted file "magically" appears now in the df results.

sudo lsof +L1 will identify deleted files still showing a pid.

HTH clears up some confusion about interpreting df output. - Terrence

By default, ext2/3/4 filesystems reserve 5% of the space to be useable only by the superuser, root.

There is also some space reserved for metadata, that is necessary for the file system, for examples inodes and the journal.

You can find some details in the manual

man mkfs.ext4