Summary: A binary coupling tree on \(n+1\) leaves is a binary tree in which the leaves have distinct labels. The rotation graph \(G_n\) is defined as the graph of all binary coupling trees on \(n+1\) leaves, with edges connecting trees that can be transformed into each other by a single rotation. In this paper, we study distance properties of the graph \(G_n\). Exact results for the diameter of \(G_n\) for values up to \(n=10\) are obtained. For larger values of \(n\), we prove upper and lower bounds for the diameter, which yield the result that the diameter of \(G_n\) grows like \(n\text{ lg}(n)\).