You can't convert an area into a volume, because you need another dimension.
In a domestic environment the height of the ceiling is about 7.5 feet. So if that's the case where your storage area is located, we can multiply the area by 7.5 and that will give you the volume in cubic feet: 150*7.5=1,125 cu ft.
That's a floor to ceiling storage space. If the shape of the storage space is not cuboid, like a space which is wholly or partly under a staircase, for instance, the volume will be smaller. Good luck with your moving!