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Quantifying the population density of an urban area is a fraught issue.Measures of density are often defined differently from place to place orapplied inconsistently, and arguments abound over just how much of the landsurrounding a city should and should not be classified as `urban'. The primecandidates for a consistent density measure are overall density OD (also knownas average density) and population-weighted density PWD (as recently adopted bythe US Census Bureau). In this note some less intuitive aspects of PWD areexplored, so that the consequences of adopting PWD as a density measure arebetter understood relative to OD. It will also be seen that one cannot entirelydispense with the need to define urban boundaries, to work preferentially withthe smallest parcels of land for which one has data, and to pay carefulattention to the delineation of boundaries to ensure high-density andlow-density developments are allocated to separate parcels where possible.

Population-Weighted Density, Density-Weighted Population, Granularity, Paradoxes: a Recapitulation