Formating a new partition with ext4 requires root permissions. By default, mkfs requires root permissions to create the new filesystem. Also by defualt, mkfs creates root directory ownership on the new filesystem with the same permissions as the user that issued the command. Practically speaking for desktop-linux, this means that the new filesystem will always be owned by the root account. This can lead to unexpected or undesired result of the regular user not being able to write any files to the partition.
This command will allow you to format a partition with the user-level permissions. The command will create a filesystem with ownership to whatever user starts the sudo command. Note that this command is run as the regular user.
sudo mkfs.ext4 -E root_owner=$UID:$GID /dev/sdXY
where /dev/sdXY should be replaced with /dev/designation_of_partition.