Nuclear Criticality Safety Calculator
Background on nuclear criticality safety margins (k-eff, upper subcritical limits, ANSI/ANS-8.1). It deliberately does not compute a margin from simplified inputs, because no shortcut formula is safe for that purpose.
Last updated: September 2026
Formula below · 2 sources (nrc.gov, Wikipedia) · Updated Sep 2026
Compare with similar
About this calculator
Criticality occurs when a fissile assembly sustains a self-perpetuating chain reaction, characterized by an effective neutron multiplication factor k_eff = 1. For safety, all handling and storage configurations must maintain k_eff well below 1 (typically k_eff ≤ 0.95 under NRC/IAEA standards). This page previously reported a 'margin' from an invented product of these inputs. No such shortcut exists: k_eff depends on the fissile nuclide, enrichment, mass, moderation, geometry and reflection together and must come from a validated transport calculation or from the published subcritical limits in ANSI/ANS-8.1 and the criticality handbooks. The calculator therefore no longer returns a number. The fissile concentration drives neutron production; geometry affects neutron leakage (spheres are most reactive). Moderator ratio governs neutron thermalization; reflectors return escaping neutrons back to the core; and temperature introduces Doppler broadening that tends to absorb resonance neutrons. Never use a simplified index to decide that fissile material is safe to handle.
How to use
Use this page as background only. To assess a real configuration: (1) model it in a validated code (MCNP, SCALE/KENO) or compare it with the single-parameter limits in ANSI/ANS-8.1 (for example minimum critical masses, volumes and concentrations for U-235 and Pu-239 solutions); (2) apply the upper subcritical limit your licence requires (often k_eff + 2σ ≤ 0.95); (3) apply the double-contingency principle so that no single credible upset can cause criticality. Have a qualified criticality-safety engineer review the result.
Frequently asked questions
What does the neutron multiplication factor k_eff mean in nuclear criticality safety?
k_eff is the ratio of neutrons produced in one fission generation to the number consumed or lost in the preceding generation. When k_eff equals exactly 1, the chain reaction is self-sustaining (critical). Values below 1 mean more neutrons are lost than produced, so the reaction dies out (subcritical). Values above 1 indicate a growing, potentially uncontrolled reaction (supercritical). Nuclear safety standards require that fissile material handling and storage maintain k_eff ≤ 0.95 under all normal and credible abnormal conditions to provide a safety margin.
How does geometry affect the criticality of a fissile material assembly?
Geometry determines how many neutrons escape the assembly before causing additional fissions. A sphere has the smallest surface-area-to-volume ratio of any shape, meaning fewer neutrons escape per unit of fissile material — making it the most reactive geometry. Flat slabs and long cylinders have larger relative surface areas and therefore higher neutron leakage, reducing k_eff. Criticality safety programs often use geometry controls — limiting slab thickness or cylinder diameter — as one of the primary administrative and engineering safeguards in fissile material processing facilities.
Why is moderator-to-fuel ratio important in criticality safety assessments?
Moderators slow fast neutrons down to thermal energies where fission cross-sections of uranium-235 and plutonium-239 are dramatically higher, making a chain reaction much more likely. An optimal moderator-to-fuel ratio (often called the optimal hydrogen-to-fissile ratio) can produce a significantly more reactive system than either under- or over-moderated configurations. This is why accidentally flooding a fissile storage area with water is a serious criticality concern — water is an effective moderator. Criticality safety evaluations must consider the most reactive credible moderation condition, not just normal operating geometry.