Human neutrophils play an essential role in the immune system, acting as first responders to infection by migrating through tissue along chemical gradients and consuming foreign objects such as pathogens. These processes, known as chemotaxis and phagocytosis respectively, require neutrophils to deform in a controlled manner, balancing adhesion to surfaces and protrusive forces exerted by the cell’s own cytoskeleton. Bursts in the concentration of intracellular calcium ions (Ca2+) are commonly observed during such deformations, but the link between neutrophil mechanics and Ca2+ bursts remains unclear. In this work, we first examine the mechanical underpinnings of neutrophil phagocytic spreading, and then study the causes and the effects of Ca2+ bursts during neutrophil chemotaxis and phagocytosis. Throughout, we use a combination of biophysical experiments and computational models to answer fundamental questions about neutrophil biology. In initial experiments, we deposit human neutrophils onto surfaces coated with different densities of IgG antibodies to probe the roles of adhesion and protrusion in phagocytic spreading. These experiments, in combination with computational models of cell deformation, demonstrate that frustrated phagocytic spreading is driven by cell protrusion, but the maximum contact area to which the cell can spread is limited by the availability of adhesion sites. We then turn our attention to the causes and effects of Ca2+ bursts in neutrophil chemotaxis and phagocytosis. Using single-cell biophysics experiments, we show that neutrophil chemotactic protrusion alone neither requires nor causes Ca2+ bursts. On the other hand, we find that phagocytic spreading is consistently accompanied by Ca2+ bursts, and the timing and magnitude of these bursts are determined in part by the density of ligands on a pathogenic surface. We develop a computational model of these Ca2+ bursts in phagocytosis and show that the model agrees with our experimental data. Finally, we determine the effects of altering intracellular or extracellular Ca2+ on the dynamics of phagocytosis. Remarkably, we find that eliminating Ca2+ bursts by depleting intracellular Ca2+ stores does not prevent phagocytosis of IgG-coated targets but does result in slower cell spreading and lower maximum contact areas in frustrated phagocytosis experiments. Removing all extracellular divalent cations has only a small effect on Ca2+ bursts but does lead to altered cell morphology in phagocytosis; we attribute this to the general ability of divalent cations to modify the binding affinity of cell adhesion receptors such as integrins. Overall, our work shows that Ca2+ bursts, while not strictly required for neutrophil protrusion, do facilitate efficient spreading over pathogenic surfaces during phagocytosis.