  The radius of comparison is an invariant for unital C*-algebras which extends
the theory of covering dimension to noncommutative spaces. We extend its
definition to general C*-algebras, and give an algebraic (as opposed to
functional-theoretic) reformulation. This yields new permanence properties for
the radius of comparison which strengthen its analogy with covering dimension
for commutative spaces. We then give several applications of these results. New
examples of C*-algebras with finite radius of comparison are given, and the
question of when the Cuntz classes of finitely generated Hilbert modules form a
hereditary subset of the Cuntz semigroup is addressed. Most interestingly,
perhaps, we treat the question of when a full hereditary subalgebra B of a
stable C*-algebra A is itself stable, giving a characterization in terms of the
radius of comparison. We also use the radius of comparison to quantify the
least n for which a C*-algebra D without bounded 2-quasitraces or unital
quotients has the property that M_n(D) is stable.
