The TP53 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 TP53 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 TP53 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 affinities of TP53, TP63, and TP73 to 10 TP53 family binding sites across the nucleosome core particle. We find that the affinities of TP53, TP63, and TP73 for nucleosomes are primarily determined by the positioning of TP53 family binding sites within nucleosomes; TP53 family members bind strongly to the more accessible edges of nucleosomes but weakly to the less accessible centers of nucleosomes. Our results further show that the DNA-helical orientation of TP53 family binding sites within nucleosomal DNA impacts the nucleosome-binding affinities of TP53 family members, with binding-site composition impacting the affinity of each TP53 family member only when the binding-site location is accessible. Taken together, our results show that the accessibility, composition, and helical orientation of TP53 family binding sites collectively determine the nucleosome-binding affinities of TP53, TP63, and TP73. These findings help explain the rules underlying TP53 family-nucleosome binding and thus provide requisite insight into how we may better control gene expression changes involved in development and tumor suppression.