Progress in electronic vehicle control has created the need for contactless detection of rotation angles up to 360 degrees, such as for engine control valves or vehicle control steering. Conventional contactless sensors that can detect rotation angles up to 360 degrees have been optical or magnetic rotary encoders, which are large and expensive for use in automobiles. The authors developed a small and low-cost sensor that is suited for mass production and able to detect rotation angles up to 360 degrees by combining MRE sensors with a membrane coil.