The synthesis of biodiesel from Jatropha curcas by transesterification is kinetically controlled. It depends on the molar ratio, reaction time, and temperature, as well as the catalyst nature and quantity. The aim of this study was to explore the transesterification of low-cost, inedible J. curcas seed oil utilizing both homogenous (potassium hydroxide; KOH) and heterogenous (calcium oxide; CaO) catalysis. In this effort, two steps were used. First, free fatty acids in J. curcas oil were reduced from 12.4 to less than 1 wt.% with sulfuric acid-catalyzed pretreatment. Transesterification subsequently converted the oil to biodiesel. The yield of fatty acid methyl esters was optimized by varying the reaction time, catalyst load, and methanol-to-oil molar ratio. A maximum yield of 96% was obtained from CaO nanoparticles at a reaction time of 5.5 h with 4 wt.% of the catalyst and an 18:1 methanol-to-oil molar ratio. The optimum conditions for KOH were a molar ratio of methanol to oil of 9:1, 5 wt.% of the catalyst, and a reaction time of 3.5 h, and this returned a yield of 92%. The fuel properties of the optimized biodiesel were within the limits specified in ASTM D6751, the American biodiesel standard. In addition, the 5% blends in petroleum diesel were within the ranges prescribed in ASTM D975, the American diesel fuel standard.