A parking assistance system for outputting parking instructions to the driver of a vehicle has a sensor device which is designed for performing a parking space measurement on the basis of parking space limits and generating parking space information on the basis of the parking space measurement; a program-controlled device which calculates the driving trajectory to be traveled on the basis of the parking space information generated and calculates a time to collision and/or a distance to collision, within which the vehicle will presumably collide with one of the parking space limits, from the parking space information generated and the calculated driving trajectory; and a warning signal transducer which generates a warning signal if the calculated period of time is less than a first limit value and/or the calculated distance to collision is less than a second limit value.