Academic self-concept is a prominent construct in educational psychology that predicts future achievement. Similarly, peer ratings of competence predict future achievement as well. Yet do self-concept ratings have predictive value over and above peer ratings of competence? In this study, the interpersonal approach (Kwan, John, Kenny, Bond, & Robins, 2004) was applied to academic self-concept. The interpersonal approach decomposes the variance in self-concept ratings into a “method” part that is due to the student as the rater (perceiver effect), a shared “trait” part that is due to the student’s perceived achievement (target effect), and an idiosyncratic self-view (self-enhancement). In a round-robin design of competence ratings in which each student in a class rated every classmate’s competence, a total of 2,094 school students in 89 classes in two age cohorts rated their own math competence and the math competence of their classmates. Three main results emerged. First, self-concept ratings and peer ratings of competence had a substantial overlap in variance. Second, the shared “trait” part of the competence ratings was highly correlated with achievement and predicted gains in achievement. Third, the idiosyncratic self-view had a small positive association with (future) achievement. Altogether, this study introduces the interpersonal approach as a general framework for studying academic self-concept and peer ratings of competence in an integrated way.