The ability to accurately estimate bite force (BF) in extant and fossil primates is valuable to biological anthropologists. BF is generally evaluated using complex jaw musculature and lever arm analyses employing numerous assumptions and requiring complete cranial morphology. Here, a simple method to determine BF from data measured on histological sections of fossil teeth is proposed. Published sections of molar teeth encompassing 27 different extinct and extant primates dating back to as early as 17 million years ago were examined. Focusing on the cusp region, the extracted data include characteristic enamel thickness dc and dentin horn angle φ. The occlusal force needed to fracture a cusp, PF , was determined from these variables with the aid of a finite element stress analysis similarly to a previous study on postcanine human teeth. The bite force was obtained by linking BF to PF using a universal constant. The measured variables dc and φ are conclusively linked. This link produces a virtually constant fracture force PF and in turn bite force BF for all cusps in the molar row. An explicit formula tying BF to dc and φ was derived. For nonhominin taxa the bite force, molar crown area, and body mass are found to be intimately related. The case of hominins is more involved. The so determined BF is gender-averaged, with the bite force of males estimated to be ≈12% greater than that of females. The use of "fracture mechanics" concepts from mechanics of materials facilitates determination of critical bite force in primates based on characteristic enamel thickness dc and dentin horn angle φ as extracted from histological sections of molar teeth. This novel approach enables quantitative insight into the role played by crown area, body mass and bite force on evolutionary trends. The conclusive link between cuspal enamel thickness and dentin horn angle facilitates optimal food processing without hindering cusp resilience. The proposed approach may be extended to mammals having asymmetric cusp structures.