A coordinates input apparatus, for example, a digitizer, has a vibration propagation medium such as a transparent glass plate for allowing a vibration to propagate therethrough; an input pen for applying vibration to the vibration propagation medium; a vibration detector for detecting vibration applied by the input pen; an envelope output device for producing an envelope signal representing the envelope of the vibration detected by the vibration detector; a differentiator for conducting a differentiation of the envelope signal produced by the envelope output device so as to determine the peak; a controller adapted for determining, as the time of arrival of the vibration, a zero-cross point of the vibration that is located in the vicinity of a zero-cross point of the signal from the differentiator; and a computing device for computing the distance between the input pen and the vibration detector from the time determined by the controller.