Systems and methods for determining the elbow or Ct value in a real-time, or kinetic, PCR amplification curve data set. The PCR data set may be visualized in a two-dimensional plot of fluorescence intensity (y-axis) vs. cycle number (x-axis). The data set is transformed to produce a partition table of data points with one column including the fluorescence at cycle (n) and a second column including the fluorescence at cycle (n+i), where i is typically 1 or greater. A cluster analysis process is applied to the partition table data set to determine a plurality of clusters in the partition table data set. In one aspect, the clustering process used includes a k-means clustering algorithm, where k≧3. The data point representing the elbow or Ct value of the PCR curve is identified as an end point of one of the identified clusters, and the cycle number corresponding to this data point is returned or displayed.