The main objective of this work is to obtain an empirical relationship between the root-mean-square and the quasi-peak spectra of voltage recordings in the electrical grid, based on a statistical analysis of a set of on-field measurements for the CISPR Band A (9–150 kHz). The lack of a relationship between the weighting root-mean-square and quasi-peak detectors implies the impossibility of calculating quasi-peak (QP) spectra from root-mean-square (RMS) measurements. It is of great interest that quasi-peak values can be estimated by simple calculations from RMS values, so that comparison to compatibility levels could be applied. This work defines an empirical relationship between the statistical variation of instantaneous RMS values over time, the maximum RMS value of these instantaneous values and the QP output. This relationship is described in the form of a simple equation that can be applied to RMS provided by the RM-A method, specifically developed for the CISPR Band A. A method for the fast assessment of QP values from simple RMS receivers is proposed as a potential application of the numerical RMS-QP relationship. Both the numerical RMS-QP relationship and its application as a simple and fast assessment method are evaluated with disturbances recorded in the low voltage grid.