Bite forces play a key role in animal ecology: they affect mating behaviour, fighting success, and the ability to feed. Although feeding habits of arthropods have a significant ecological and economical impact, we lack fundamental knowledge on how the morphology and physiology of their bite apparatus controls bite performance, and its variation with mandible gape. To address this gap, we derived a biomechanical model that characterizes the relationship between bite force and mandibular opening angle from first principles. We validate this model by comparing its geometric predictions with morphological measurements on the muscoloskeletal bite apparatus of Atta cephalotes leaf-cutter ants, using computed tomography (CT) scans obtained at different mandible opening angles. We then demonstrate its deductive and inductive utility with three examplary use cases: Firstly, we extract the physiological properties of the leaf-cutter ant mandible closer muscle from in vivo bite force measurements. Secondly, we show that leaf-cutter ants are specialized to generate extraordinarily large bite forces, equivalent to about 2600 times their body weight. Thirdly, we discuss the relative importance of morphology and physiology in determining the magnitude and variation of bite force. We hope that a more detailed quantitative understanding of the link between morphology, physiology, and bite performance will facilitate future comparative studies on the insect bite apparatus, and help to advance our knowledge of the behaviour, ecology and evolution of arthropods.