TP53 is a transcription factor that controls multiple cellular processes, including cell cycle arrest, DNA repair and apoptosis. The relation between TP53 binding site architecture and transcriptional output is still not fully understood. Here, we systematically examined in three different cell lines the effects of binding site affinity and copy number on TP53-dependent transcriptional output, and also probed the impact of spacer length and sequence between adjacent binding sites, and of core promoter identity. Paradoxically, we found that high-affinity TP53 binding sites are less potent than medium-affinity sites. TP53 achieves supra-additive transcriptional activation through optimally spaced adjacent binding sites, suggesting a cooperative mechanism. Optimally spaced adjacent binding sites have a ∼10-bp periodicity, suggesting a role for spatial orientation along the DNA double helix. We leveraged these insights to construct a log-linear model that explains activity from sequence features, and to identify new highly active and sensitive TP53 reporters.