During an immune response numerous receptor-mediated signals delivered to T cells direct their proliferation, survival and differentiation. Here, we describe a quantitative model and in vitro methods for assessing the "calculus" used by T cells to process these multiple signals. The model reveals how T cells convert independently received signals into linear additive effects on division times which, in turn, amplify T cell number exponentially. These results explain why so many ligands can each appear obligatory for T cell activation and argue for a re-examination of the two-signal theory as the basis for decisions between tolerance and activation.