This paper describes a method for the calculation of confidence intervals of simulation throughputs and utilizations. The method is based on the delta method and uses only a single simulation, where the variation of the underlying means is used to determine the variation of the performance function by using the first derivative of the performance function. While the delta method requires inde-pendent distributed data, such data is frequently available for many performance measures, allowing the practical application of the method. In addition, the method can also be used for short simulations or rare event applications, where methods based on batch means fail. This method can easily be implemented into existing simulation software.