The objective of this study was to estimate mathematical relationships derived from biodiesel fuels from various vegetable oils by non-catalytic supercritical methanol and ethanol method. The vegetable oils are all extremely viscous with viscosities ranging from 10 to 20 times greater than petroleum diesel fuel. The aim of the transesterification process is to lower the viscosity of the oil. Methyl and ethyl esters as biodiesels were prepared from vegetable oils through transesterification by non-catalytic supercritical fluids. The biodiesels were characterized for their physical and main fuel properties including viscosity, density, flash point and higher heating value (HHV). The viscosities of biodiesels (3 - 5 mm(2)/s at 311 K) were much less than those of pure oils (27 - 54 mm(2)/s at 311 K), and their HHVs of approximately 40.5 MJ/kg were 10% less than those of petrodiesel fules (similar to 45 MJ/kg). The most important variables affecting the ester yield during the transesterification reaction are molar ratio of alcohol to vegetable oil and reaction temperature. The viscosity values of vegetable oil methyl esters highly decreases after transesterification process. Compared to no. 2 diesel fuel, all of the vegetable oil methyl esters were slightly viscous. The flash point values of vegetable oil methyl esters are highly lower than those of vegetable oils. The flash point values of vegetable oil methyl esters are highly lower than those of vegetable oils. There is high regression between density and viscosity values vegetable oil methyl esters. The relationships between viscosity and flash point for vegetable oil methyl esters are considerably regular.