These following ext3 partitions contain identical data. As we can see, the larger the partition size, the more space is required for the same files:

Filesystem           1K-blocks      Used Available Use% Mounted on
/dev/loop11            3965777    561064   3199964  15% [...]
/dev/loop19             573029    543843     29186  95% [...]

Filesystem            Size  Used Avail Use% Mounted on
/dev/loop11           3.8G  548M  3.1G  15% [...]
/dev/loop19           560M  532M   29M  95% [...]

Filesystem            Inodes   IUsed   IFree IUse% Mounted on
/dev/loop11          1024000    1656 1022344    1% [...]
/dev/loop19          1024000    1656 1022344    1% [...]

I start with a partition of fixed size that possibly wasted a lot of space and I want to create a partition that is able to hold that data but with (almost) minimal size. How can I reliably calculate that minimal partition size needed for storing a certain amount of data? The amount of data changes over time, and I need to automate these calculations.