How do I determine the block size of an ext3 partition on Linux?

# tune2fs -l /dev/sda1 | grep -i 'block size'
Block size:               1024

Replace /dev/sda1 with the partition you want to check.

Without root, without writing, and for any filesystem type, you can do:

stat -fc %s .

This will give block size of the filesystem mounted in current directory (or any other directory specified instead of the dot).

dumpe2fs -h /dev/md2

will output something with:

Block size:               4096
Fragment size:            4096

In the case where you don't have the right to run tune2fs on a device (e.g. in a corporate environment) you can try writing a single byte to a file on the partition in question and check the disk usage:

echo 1 > test
du -h test

On x86, a filesystem block is just about always 4KiB - the default size - and never larger than the size of a memory page (which is 4KiB).