A method operates a hearing device. The hearing device has a microphone by which ambient sound is picked up and is converted into an input signal that has a wanted component and a noise component. A stationarity of the input signal is determined. A signal-to-noise ratio of the input signal is determined on a basis of a scaling factor. The scaling factor is determined on a basis of the stationarity, namely on a basis of a function that indicates the scaling factor on a basis of the stationarity of the input signal. A corresponding hearing device implements such a method.