Biodiesel is known as one of the best alternative fuels for diesel engines. Low-cost Jatropha oil is considered a potential non-edible feedstock for biodiesel production in India and many other parts of the world. Jatropha oil contains a large amount of free fatty acids (FFA), and soap formation occurs during the alkali catalysed transesterification process, hence decreasing the biodiesel yield. The acid catalyst is less sensitive to FFA, but the reaction rate is extremely slow if the transesterification reaction occurs by conventional heating. In the present investigation, microwave heating was used for biodiesel production by the single-step transesterification reaction of Jatropha oil in the presence of an acidic catalyst (sulphuric acid). The central composite rotatable design (CCRD) matrix of response surface methodology (RSM) was employed to determine the optimum design conditions for the transesterification reaction under microwave irradiation. The effects of three selected variables, namely reaction time, catalyst concentration, and methanol, on the oil molar ratio, were assessed. The maximum yield of biodiesel produced in the selected design space by microwave heating was found to be 61.10 under the 11:7 M ratio of the methanol to oil, 2 wt catalyst concentration, and 90 min reaction time, which was much higher than the biodiesel yield by conventional heating method (3.8) for the same reaction time. The modified polynomial model for the microwave heating method was developed with the help of ANOVA, main effect plots, interaction plots, and surface plots. The experimental and predicted yield values for fatty acid methyl ester (FAME) showed a linear relationship. The validation of experiments confirmed the accuracy of the suggested model. The produced biodiesel was of good quality, as all the properties were within the prescribed limits of the ASTM D6751 standard. The results of this study showed that the microwave heating method can be used efficiently to obtain a high biodiesel yield from low-cost, high-FFA feedstock such as Jatropha oil in a sulphuric acid-catalysed single-step transesterification reaction. © 2022 Elsevier Ltd