Dependence of the density of transition metal-metalloid glasses on the nature and concentration of the metalloid element has been examined by comparing published density measurements for glasses with values derived from the lattice parameters of a wide range of crystalline alloys. An appealing similarity is revealed between the effects of concentration and radius ratio on the packing fractions of atoms in each phase. A first-order description of the density of alloy glasses is given in terms of the number of metalloid atoms occupying cavities in the metal sub-lattice and the dilatation which such occupancy entails. A linear relationship allows the density to be predicted with reasonable accuracy from the concentration and metalloid radius ratio. This relationship highlights similarities in structure which appear to exist between crystalline and amorphous phases: in particular, it seems that the metalloid is preferentially situated in trigonal prismatic cavities and there is no evidence for any other occupied polyhedron in these glasses. Packing of metal atoms, and therefore of trigonal prisms, is surprisingly efficient and approaches that of face-centred cubic close-packing. The properties of this model are compared with two earlier descriptions based on dense random packing of hard spheres and both are found to give less satisfactory explanations of experimental measurements.