Systems and methods for determining the elbow or Ct value in a real-time, or kinetic, PCR amplification curve data set. A PCR data set may be visualized in a two-dimensional plot of fluorescence intensity vs. cycle number. The data set may be adjusted to have a zero slope. In one aspect, a data set is fit to a double sigmoid curve function with the function parameters determined using a Levenberg-Marquardt regression process. The determined parameters are used to subtract off the linear growth portion from the data set to provide a modified data set. For multiple data sets, all the data curves can be aligned in this manner to have a common baseline slope, e.g., a slope of zero. A rotation transform is applied to a modified data set to rotate the data about a defined coordinate such as the origin so that the data point representing the Ct value becomes a minimum or a maximum along the intensity axis. The data point representing the elbow or Ct value of the curve is identified, and this data point is then rotated back and the cycle number of the data point is returned or displayed.