The question of how to quantify the intensity of extratropical cyclones does not have a simple answer. To offer some perspective on this issue, multiple measures of intensity are analyzed in this study for North Atlantic and European extratropical cyclones for the extended winter season between 1979 and 2022 using ERA5 reanalysis data. The most relevant intensity measures are identified by investigating relationships between them and by performing sparse principal component analysis on the set of measures. We show that dynamical intensity measures correlate strongly with each other, while correlations are weaker for impact-relevant measures. Based on the correlations and the sparse principal component analysis, we find that five intensity measures, namely 850 hPa relative vorticity, 850 hPa wind speed, wind footprint, precipitation, and a storm severity index, describe cyclone intensity comprehensively and non-redundantly. Using these five measures as input, we objectively classify the extratropical cyclones with a cluster analysis based on a Gaussian mixture model. The cluster analysis is able to produce four clusters between which cyclones differ in terms of their intensity, life cycle characteristics such as deepening rate and lifetime, and geographical location. A clear majority (81 %) of investigated impactful storms belong to the most intense cluster, which demonstrates the ability of the method to identify potentially damaging extratropical cyclones.