Ideological polarization matters, both as a key quality of democracy and as a source of concern about growing divisions in today’s political landscape. Reliable measures are needed to evaluate changes in party system polarization. However, current indicators remain largely unidimensional in nature, despite a wide acceptance of the multidimensionality of contemporary European politics. We introduce a novel measure of multidimensional polarization that is based on the variance-covariance matrix of party positions. To account for the possibility that party positions are correlated across dimensions rather than orthogonal, we compare the effective dimensionality of a landscape to its assumed dimensionality. We highlight the advantages of this approach with artificial data, before focusing on estimates derived from the Chapel Hill Expert Survey (1999-2019). We then explore the correlates of multidimensional polarization discussed in previous research and compare our findings to existing unidimensional measures. By offering a tool to evaluate how condensed or dispersed a party system is on multiple dimensions—both cross-sectionally and temporally—this study has important implications for our understanding of party strategy and democratic representation.