We reassess the relation between students’ socioeconomic status (SES) and their achievement by treating SES as multidimensional instead of unidimensional. We use data from almost 600,000 students in 77 countries participating in the 2018 PISA assessment of student achievement in math, science, and reading. The composite measure of SES that PISA uses can be broken down into six component variables that we here use as simultaneous predictors of achievement. This analysis yields several new insights. First, in the typical society, two predictors (books at home and parents’ highest occupational status) clearly outperform the rest. Second, a new composite measure based only on these two components often reveals substantially larger achievement gaps than those reported by PISA. Third, the analysis revealed remarkable differences between societies in the relation between achievement and wealth possessions. In most societies, the independent effect of wealth possessions on student achievement was zero or even slightly negative—but in the least developed societies it was strongly positive. These findings have implications for how SES achievement gaps should be measured and interpreted. Copyright © 2021 Eriksson, Lindvall, Helenius and Ryve.