Four factor formula

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The four-factor formula, also known as Fermi's four factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in an infinite medium. The formula is[1]

Symbol Name Meaning Formula
Reproduction Factor (Eta)
The thermal utilization factor
The resonance escape probability
The fast fission factor

The six factor formula defines each of these terms in much more detail.


The multiplication factor, k, is defined as (see Nuclear chain reaction):

If k is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially.
If k is less than 1, the chain reaction is subcritical, and the neutron population will exponentially decay.
If k = 1, the chain reaction is critical and the neutron population will remain constant.

In an infinite medium, neutrons cannot leak out of the system and the multiplication factor becomes the infinite multiplication factor, , which is approximated by the four-factor formula.

See also[edit]


  1. ^ Duderstadt, James; Hamilton, Louis (1976). Nuclear Reactor Analysis. John Wiley & Sons, Inc. ISBN 0-471-22363-8.