The challenge is that Earth's air isn't dense enough. That said, the math is "easy" density is volume/mass, vacuum adds no mass, so it is just material mass / volume.

A 20cm diameter diamond sphere that was .5mm thick would have a mass of about 41g, a 20cm diameter sphere of air at sea level and "room" temperature is about 50g. So you would get 9g of "lifting force" from such a balloon (assuming I did all the calculations correctly). And experience about 2,900lbs of compression force.

Any air in the sphere would add weight.