Many biological networks respond to various inputs through a common signaling molecule that triggers distinct cellular outcomes. One potential mechanism for achieving specific input-output relationships is to trigger distinct dynamical patterns in response to different stimuli. Here we focused on the dynamics of p53, a tumor suppressor activated in response to cellular stress. We quantified the dynamics of p53 in individual cells in response to UV and observed a single pulse that increases in amplitude and duration in proportion to the UV dose. This graded response contrasts with the previously described series of fixed pulses in response to γ-radiation. We further found that while γ-triggered p53 pulses are excitable, the p53 response to UV is not excitable and depends on continuous signaling from the input-sensing kinases. Using mathematical modeling and experiments, we identified feedback loops that contribute to specific features of the stimulus-dependent dynamics of p53, including excitability and input-duration dependency. Our study shows that different stresses elicit different temporal profiles of p53, suggesting that modulation of p53 dynamics might be used to achieve specificity in this network.