An apparatus is provided for measuring wear-induced displacement of a brake lining with respect to an associated brake caliper, comprising a gear mechanism for converting the wear-induced displacement into a rotary movement, having a sensor for detecting the rotary movement, wherein a contact-free coupling is provided for transmitting the rotary movement to the sensor. The apparatus is designed in such a way that the sensor generates an analogue or pulse-width-modulated detection signal for determining the wear-induced displacement of the brake lining, wherein the detection signal corresponds to the respective displacement caused by the rotary movement. The invention also related to a corresponding method for measuring the wear-induced displacement of a brake lining with respect to an associated brake caliper.