Criticality Calculator

k-effective is the average number of neutrons from one fission that go on to cause another fission, accounting for both absorption and leakage out of the system. k-effective below 1 means the neutron population shrinks over time (subcritical); exactly 1 means a steady, self-sustaining chain reaction (critical); and above 1 means the population grows (supercritical). It's the single most important number in reactor physics and criticality safety.

The four-factor formula, k-infinity = eta x f x p x epsilon, estimates the neutron multiplication factor for an infinitely large medium with no neutron leakage. Eta is neutrons produced per absorption in fuel, f is the fraction of neutrons absorbed in fuel rather than elsewhere, p is the probability a neutron slows down without being captured in a U-238 resonance, and epsilon accounts for extra fissions from fast neutrons. It's a standard building block in introductory reactor-physics texts, used before accounting for real-world neutron leakage.

A sphere has the smallest surface area for a given volume of any shape, so for the same mass it loses proportionally fewer neutrons to leakage out through its surface than a cylinder or slab does. Less leakage means a higher non-leakage probability, which raises k-effective for the same mass -- which is exactly why this calculator's geometry setting treats a sphere as the most reactive shape and a slab as the least reactive.

A reflector -- water, steel, beryllium, or another neutron-scattering material placed around the fissile mass -- scatters some of the neutrons that would otherwise escape back into the core, lowering the effective leakage. That means a reflected configuration can reach the same k-effective with less fissile mass than a bare (unreflected) one, which is why reflector material is treated as a serious safety consideration in real criticality-safety work, not just an engineering detail.

No. This tool uses simplified, illustrative constants to demonstrate the shape of real reactor-physics relationships -- it is not validated against measured cross-section data and has no safety margins built in. Any real question about whether a fissile-material configuration is subcritical must go through qualified nuclear criticality safety engineers using validated transport codes and applicable regulatory limits, never a general-purpose educational calculator like this one.