The invention relates to a variable transmission (3) for an electric vehicle and comprising a variator unit (40) for providing a continuously variable speed ratio between an input shaft (44) and an output shaft (45) thereof. According to the invention, the variable transmission (3) further comprises two planetary gear sets (50) respectively provided on a respective axial side of the output shaft (45) and each comprising three coaxially rotatable members (51, 52, 53) including a sun gear (51), a ring gear (52) and a planet carrier (53) rotatably carrying planet gears (54), whereof first members (51, 52, 53) rotate as one with the output shaft (45), whereof second members (51, 52, 53) respectively rotate as one with a respective one of the two driven wheels (2) and whereof third members (51, 52, 53) of each of the planetary gear sets (50) are connectable to a stationary part (39) of the variable transmission (3) via a respective clutch (55).