In a transmission device with switchable gear ratios, a driving gear is disposed onto an output shaft of a motor, a rocker arm is pivoted on the output shaft through an electromagnetic clutch, a rocker arm gear mounted on the rocker arm is driven by the driving gear, a first gear set is driven by the rocker arm gear when the rocker arm is at a first position, a second gear set is driven by the rocker arm gear when the rocker arm is at a second position, and the first gear set and the second gear set have different output rotating speeds. In addition, a first magnetic element attracts the rocker arm at the first position, and a second magnetic element attracts the rocker arm at the second position. Thus, the gear ratio may be switched according to interactions between the electromagnetic clutch and the magnetic elements.