Can you calculate the maximum physical address space given page size and virtual address size

Question

A system has a 64 bit address space and pages with a size of 256KB how do you calculate the maximum physical address space?

Answer 1

You don't. You query the capabilities of the hardware. Either by reading out some hardware information register (preferably using a standard OS function implementing the details of that), or by looking into the used CPU's datasheet.

The size of the physical address space has no relationship at all to the size of the virtual address space, and even less to the page size.

The page size determines the granularity at which physical addresses can be translated into virtual addresses. I.e. the physical address space is sliced up into pages and, and then these pages are "rearranged" into virtual addresses. However a single physical page may be mapped several times into virtual space. But that's about it.