I want to copy my /home partition to another hard disk, but this second has less size. How can I do it?

Many options here, one of them is rsync...

Assuming you have created a partition on second disk, and even if it is smaller; hopefully still big enough for the data you want to migrate?

Take a look at man page for rsync for some examples.

If you need or wish to keep the partition the same then you copy file by file. Rsync and many other ways can copy file by file. We'd have to assume the total size of original files is less than new partition size otherwise you may need extra work.

If its partition to smaller partition and the partitions are not ntfs fsachiver will work.

As long as the new parition is large enough to accommodate the directories and files to be copied, any standard method for copying files should work.

If you really want to preserve metadata details like ctime timestamps, you could shrink the /home filesystem and then use tools like partclone or image copy to transfer the filesystem to the new partition. Note that shrinking has to be done with the filesystem unmounted, and is not possible for XFS.

Ok, thank u all. I will try with some of those tool

You can also do this with LVM, which lets you create "physical storage pools" and assign them to "logical volumes" within those pools. In this way, what appears to the OS to be a single mount-point may actually occupy many drives and/or partitions. If one disk begins to fill up, you can simply add a new disk and add all or part of it to the storage pool. From the OS's point of view, the mount-point just got bigger.

To specifically address your current requirement, you can use the migration feature of LVM to move the data from one physical place to another, without downtime! Very useful when a hard drive starts to make "funny clicking noises."