A flow measuring device detecting a fluid volume quantity since a start of a measurement includes a processing device determining a current flow rate parameter at measurement times using measurement data of a sensor, to increase a volume quantity based on a current flow rate parameter when operating in a first operating mode, and to keep the volume quantity constant when operating in a second mode. The processing device stores the current flow rate parameter for each measurement time in a data memory, resulting after several measuring times in storing previous flow rate parameters determined at these measuring times. Upon satisfying a switchover condition, depending on the current flow rate parameter, during operation in the second mode, the processing unit switches over to the first mode, and the volume quantity increases as a function of the current flow rate parameter and a predefined number of previous flow rate parameters.