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Nuclear Fission Chain Reaction Simulation

Reading time: 6 minConfidence: HighLast verified: July 2026

This simulation lets you adjust the neutron multiplication factor (k) of a fission chain reaction and watch, generation by generation, whether the reaction dies out (subcritical), holds steady (critical), or grows explosively (supercritical).

Interactive simulation

Generation: 0
Neutrons this generation: —
Reactor state: —

The physics behind this simulation

Each fission event releases on average k neutrons that go on to cause further fission (after accounting for neutrons lost to absorption or escape). Starting from N₀ neutrons, the neutron population after g generations is:

N(g) = N₀ · k^g

When k < 1 (subcritical), each generation produces fewer neutrons than the last, and the reaction dies out. When k = 1 (critical), the neutron population stays constant generation after generation — this is the condition maintained in a controlled nuclear power reactor. When k > 1 (supercritical), the neutron population — and the energy release rate — grows exponentially with each generation, the regime used (in a carefully engineered, extremely fast, uncontrolled form) in nuclear weapons.

Common mistakeReal reactors are operated extremely close to k = 1, with control rods making tiny adjustments to keep k within an exceptionally narrow band — a small, deliberately introduced supercriticality (k just barely above 1) is used only for briefly and safely raising reactor power, never anything resembling weapon-level supercriticality, which relies on an entirely different, much faster, and far more extreme physical regime.

Sources

  • Krane, K.S. (1987). Introductory Nuclear Physics. Wiley, Ch. 13.
Last verified: July 2026 · Source: Krane (1987) · Confidence: high