Density is an important, multifaceted concept that occurs at many levels of physics education. Previous research has shown that a primary instantiation of the concept, mass density, is not well understood by high school or university students. This study seeks to determine how students understand the broad concept of density, and whether particular aspects of their understanding are helpful in structuring the concept of charge density. Qualitative data were gathered in the form of questionnaires distributed to 172 freshmen comprising three different academic groups. Broad, open ended questions prompted for responses involving free writing and drawn diagrams. The data were analyzed by an approach suggested by Grounded Theory. Using the theoretical lens of Conceptual Metaphor Theory, six underlying (foothold) concepts were identified in terms of which density was conceptualized: 'filled container'; 'packing'; 'weight/heaviness'; 'intensive property'; 'floating/sinking'; 'impenetrability/solidity'. The foothold concept of 'packing' proved to be the most productive for conceptualizing 'charge density'.