Introduced 7 years ago, the concept of relative inverse admittance represents a new fin performance parameter intended to encompass all the requirements needed for fin applications in thermal engineering. A noteworthy characteristic of this concept is that it serves as a vehicle to optimize a wide variety of longitudinal fins of rectangular profile. In this article, the relative inverse admittance is numerically calculated for longitudinal fins of rectangular profile under real two-dimensional (2-D) and quasi one-dimensional (1-D) conditions, with adiabatic and convective tips. In the case of an adiabatic tip, optimum fins are deduced from a double-entry abacus that uses effectiveness as a parameter. The connection between effectiveness and the Biot transversal number is also shown graphically. The independent design variables are the heat transfer coefficient/thermal conductivity ratio and the volume of the fin. The definition of Biot number provides the optimum thickness of the fin. For the convective tip condition, the double-entry abacus directly provides the optimum length for the same independent variables. From this optimum thickness, the Biot number provides the effectiveness through the graph that relates these two parameters.