Today's Fission Reactors Already Beat Tomorrow's Fusion Reactors in Volumetric Power Density by a Factor of Nine

The binding-energy-per-nucleon curve is widely cited as evidence for the energetic superiority of fusion over fission, but it describes the nuclear reactions in isolation and cannot answer questions about power reactors. The appropriate figure of merit for reactor design is the volumetric power density, the product of reactant number densities, velocity-averaged reaction cross-section, and energy released per reaction. I derive this expression from first principles and evaluate it for D-T fusion at the temperature of maximum Maxwellian-averaged reactivity, using the Bosch-Hale parametrization and the Greenwald density limit at ITER scale, and for U-235 thermal fission at the core-averaged conditions of a commercial pressurized water reactor (PWR), using ENDF/B-VIII.0 data. The comparison is asymmetric in fusion's favor by design: fusion receives its theoretical maximum, fission its currently deployed operating parameters, far below fission's own theoretical maximum. Even so, the calculated fission value of approximately 250 MW/m³ exceeds the calculated fusion ceiling of approximately 11.2 MW/m³ by a factor of 22, and decomposition shows that the reactant density product, not the cross-section or the energy per reaction, is the largest of the three factor ratios. The more conservative comparison stated in the title uses no input from this paper's calculations: commercial PWRs deployed today operate continuously at reported core-averaged power densities of approximately 100 MW/m³, nine times the fusion ceiling. Raising the magnetic field relaxes the fusion bound as the fourth power of the field but saturates at magnet stress limits, and published high-field design points remain one to two orders of magnitude below operational fission practice. The analysis is restricted to magnetic confinement and volumetric power density; fuel cycle, cost, safety, and waste lie outside its scope.