  In zero forcing, the focus is typically on finding the minimum cardinality of
any zero forcing set in the graph; however, the number of cardinalities between
$0$ and the number of vertices in the graph for which there are both zero
forcing sets and sets that fail to be zero forcing sets is not well known. In
this paper, we introduce the zero forcing span of a graph, which is the number
of distinct cardinalities for which there are sets that are zero forcing sets
and sets that are not. We introduce the span within the context of standard
zero forcing and skew zero forcing as well as for standard zero forcing on
directed graphs. We characterize graphs with high span and low span of each
type, and also investigate graphs with special zero forcing polynomials.
