Catalytic high-yield biodiesel production from fatty acids and non-food oils over a magnetically separable acid nanosphere

•A magnetically reusable acid microsphere was developed for biodiesel synthesis.•97.8 % biodiesel yield was obtained from fatty acids and non-food oils at 65 °C.•Acid catalyst provided proton to promote esterification as revealed by DFT.•The acid microsphere was recycled with constant activity in 5 consecutive times.•Satisfactory activity and generality in biodiesel synthesis with various feedstocks.