A steering angle sensor and a vehicle system having the sensor are disclosed. The steering angle sensor for mounting on a vehicle comprises a main gear coupled to and rotated with a steering column; a first auxiliary gear and a second auxiliary gear meshed with the main gear, respectively; angular detection means mounted adjacent to the first and the second auxiliary gears respectively for generating electric signals in concert with rotations of the first and the second auxiliary gears; and a calculation/control module for calculating steering angles from the electric signals generated by theangular detection means, determining a duty ratio corresponding to the steering angle and generating a rough gain pulse width modulation signal and a fine gain pulse width modulation signal.