Ammonoid cephalopods were Earth's most abundant oceanic carnivores for hundreds of millions of years, yet their probable range of swimming capabilities is poorly constrained. We investigate potential hydrodynamic costs and advantages provided by different conch geometries using computational fluid dynamics simulations. Simulations of raw drag demonstrate expected increases with velocity and conch inflation, consistent with published experimental data. Analysis at different scales of water turbulence (via Reynolds number) reveals dynamic trade-offs between conch shape, size, and velocity. Among compressed shells, the cost of umbilical exposure makes little difference at small sizes (and/or low velocity) but is profound at large sizes (and/or high velocity). We estimate that small ammonoids could travel one to three diameters per second (i.e., a typical ammonoid with a 5-cm-diameter shell could travel 5–15 cm/s), but that large ammonoids faced greater discrepancies (a 10 cm serpenticone likely traveled <30 cm/s, while a 10 cm oxycone might achieve >40 cm/s). All of these velocities are proposed only for short bursts of jet propulsion, lasting only a few seconds, in the service of dodging a predator or conspecific rival. These analyses do not include phylogeny, taxonomy, second-order conch architecture (ribs, ornament, etc.), or hydrostatic consequences of internal anatomy (soft body, suture complexity). For specific paleoecological context, we consider how these results inform our reconstruction of Jurassic ammonite recovery from the end-Triassic mass extinction. Greater refinements will come with additional simulations that measure how added mass is influenced by individual shape-trait variations, ornament, and subtle body extensions during a single jet motion.