The p53 family of transcription factors plays key roles in driving development and combating cancer by regulating gene expression. TP53, TP63, and TP73-the three members of the p53 family-regulate gene expression by binding to their DNA binding sites, many of which are situated within nucleosomes. To thoroughly examine the nucleosome-binding abilities of the p53 family, we used Pioneer-seq, a technique that assesses a transcription factor's binding affinity to its DNA binding sites at all possible positions within the nucleosome core particle. Using Pioneer-seq, we analyzed the binding affinity of TP53, TP63, and TP73 to 10 p53-family binding sites across the nucleosome core particle. We found that the affinity of TP53, TP63, and TP73 for nucleosomes was largely determined by the positioning of p53-family binding sites within nucleosomes; p53-family members bind strongly to the more accessible edges of nucleosomes but weakly to the less accessible centers of nucleosomes. We also found that the DNA-helical orientation of p53-family binding sites within nucleosomal DNA impacted the nucleosome-binding affinity of p53-family members. The composition of their binding sites also impacted each p53-family member's nucleosome-binding affinities only when the binding site was located in an accessible location. Taken together, our results show that the accessibility, composition, and helical orientation of p53-family binding sites collectively determine the nucleosome-binding affinities of TP53, TP63, and TP73. These findings help explain the rules underlying p53-family-nucleosome binding and thus provide requisite insight into how we may better control gene-expression changes involved in development and tumor suppression.