Active power can be estimated by digitizing the voltage and current waveforms during an integer number of periods and digitally processing the samples obtained. There are two methods that can be used: Discrete Integration and Spectral Analysis. In the first one the average of the sample by sample product of the two waveforms is computed. In the second one, sine fitting algorithms are used to estimate the amplitude and initial phase of each waveform. The values obtained are then used to compute the active power. Here we derive analytical expressions for the precision of both estimators as a function of the number of samples acquired and the amount of additive random noise present. These are useful to determine the confidence interval for the measurements made. We also compare the two estimators and conclude that the second one, using sine fitting, is sometimes better.