  A vertex coloring is called distinguishing if the identity is the only
automorphism that can preserve it. The distinguishing threshold $\theta(G)$ of
a graph $G$ is the minimum number of colors $k$ required that any arbitrary
$k$-coloring of $G$ is distinguishing. In this paper, we calculate the
distinguishing threshold of a Cartesian product graph. Moreover, we calculate
the number of non-equivalent distinguishing colorings of grids.
