An apparatus for determining a threshold value (e.g., a threshold cycle number or a time value) in a nucleic acid amplification reaction comprises a detection mechanism for measuring, at a plurality of different times during the amplification reaction, at least one signal whose intensity is related to the quantity of a nucleic acid sequence being amplified in the reaction. A controller in communication with the detection mechanism is programmed to store signal values defining a growth curve for the nucleic acid sequence, determine a derivative of the growth curve, and calculate a cycle number or time value associated with a characteristic of the derivative.