The paper describes the calculation of a new topological index called Sadhana index, abbreviated as Sd. This index will be very useful for studying problems related to carbon-nanotubes (CNTs). This index is a very simple W-Sz-PI-type topological index obtained by summing the number of edges on both sides of the elementary cuts of benzenoid graphs. However, unlike Wiener index, Sadhana index is applicable to cyclic graphs only. The Sd index has the similar discriminating power as that of Wiener (W), Szeged (Sz) and PI indices.