Every piece of rack equipment says its height in rack units on the label or the data sheet: 1U is 44.45 mm (sample note).
Add them up, then add 1U for a patch panel and 1U for a switch if you bring your own. Leave a quarter free for the next two years: moving later costs more than the empty units.
Then check the power. A rack full of storage can need more power than the space suggests, and power, not space, is often what decides the size.