Tcell responses are initiated by antigen and promoted by a range of costimulatory signals. Understanding how Tcells integrate alternative signal combinations and make decisions affecting immune response strength or tolerance poses a considerable theoretical challenge. Here, we report that Tcell receptor (TCR) and costimulatory signals imprint an early, cell-intrinsic, division fate,whereby cells effectively count through generations before returning automatically to a quiescent state. This autonomous program can be extended by cytokines. Signals from the TCR, costimulatory receptors, and cytokines add together using a linear division calculus, allowing the strength of a Tcell response to be predicted from the sum of the underlying signal components.These data resolve a long-standing costimulation paradox and provide a quantitative paradigm for therapeutically manipulating immune response strength.