  Let G be a finitely generated group with a given word metric. The asymptotic
density of elements in G that have a particular property P is defined to be the
limit, as r goes to infinity, of the proportion of elements in the ball of
radius r which have the property P. We obtain a formula to compute the
asymptotic density of finite-order elements in any virtually nilpotent group.
Further, we show that the spectrum of numbers that occur as such asymptotic
densities consists of exactly the rational numbers in [0,1).
