In this paper, effects of concavity level on performance parameters of a parabolic fin are investigated under the influences of natural convection and radiation. For the prescribed problem, heat is transferred by conduction through the fin along its length and dissipated from the fin surface to the ambient via natural convection and radiation. Total amount of heat dissipated from the fin surface, fin effectiveness and fin efficiency are determined for the concavity levels ranging from 2 to 10. The problem has a special analytical solution for n = 1 which is known as Kummer’s Function but analytical solution is not available for the higher concavity levels. For n = 0, numerical results are compared with the analytical solution and an excellent agreement is observed. Numerical results indicate that the total amount of heat loss from the fin notably decreases with increasing concavity level. Volume of the fin also shows a considerable decrease with increasing concaveness. An increase of about 4% in fin efficiency is observed for the concavity level of 10 compared to the concavity level of 2. On the contrary, fin effectiveness exponentially decreases with increasing concaveness.