Unfortunately there is no generic answer to the question that you are asking.
The reason is that Linux and Unix system allow complete freedom to install parts of the operating system in one or many partitions, local or remote.
In addition to the partitioning freedom, some sysadmins routinely create symbolic links to well-known (i.e. FHS) OS directory names such as
/usr/local accross partitions. So the operating system could in fact be spread over multiple file systems. This means that there isn't in fact any concept of "operating system filesystem" in the general case.
An extreme example of this would be a Ubuntu LiveCD running with a unionfs RAM disk of 60MiB. In this case there is 60MiB of free space that is available in total but only exists as long as the OS is running.