An apparatus for feeding sheets from a stack to a machine that processes the sheets and a method of determining the vertical position of stacked sheets. The method enables the vertical position of the topmost sheet resting on the sheet stack to be determined using a sensor device. Ultrasonic pulses are applied to a longitudinal side of the sheet stack such that the pulses strike the longitudinal side of the stack at an angle, and the position of the upper edge of the stack is determined by means of an ultrasonic propagation time measurement.