We show, in a certain specific sense, that both the density and the cardinality of a Hausdorff space are related to the “degree” to which the space is nonregular. It was shown by Sapirovskii that for a regular space and the speaker observed this holds if the space is only quasiregular. We generalize this result to the class of all Hausdorff spaces by introducing the nonquasiregularity degree , which is countable when is quasiregular, and showing for any Hausdorff space . This demonstrates that the degree to which a space is nonquasiregular has a fundamental and direct connection to its density and, ultimately, its cardinality. Importantly, if is Hausdorff then is “small” in the sense that . This results in a unified proof of both Sapirovskii’s density bound for regular spaces and Sun’s bound for the cardinality of a Hausdorff space . A consequence is an improved bound for the cardinality of a Hausdorff space. We give an example of a compact, Hausdorff space for which this new bound is a strict improvement over Sun’s bound.