Question

Are any nonmetals denser than metals

Answer 1

no metals are more dense because they have a tightly packed crystal lattice structure.
why dont u use density = mass/vol.

Another factor is that non-metals can't form the big single-element crystals that metals can. In the few cases they do (S8 for instance) they're not packed as dense. When they form crystals its usually as an ionic solid, which means the have a counter-ion, and again, they can't be packed as dense.