The average lifetime of a single neutron in the reactor neutron cloud may be as small as one ten-millionth of a second. This means that in order for the cloud to remain in existence, each neutron must be responsible for producing another neutron in less than one ten millionth of a second. Thus, one second after a neutron is born, its ten-millionth generation descendent is born. (The term neutron generation will be used to refer to the "life" of a group of neutrons from birth to the time they cause fission and produce new neutrons). However, not all of the neutrons produced by fission will have the opportunity to cause new fissions because some will be absorbed by non-fissile material and others will leak out of the reactor. The number of neutrons absorbed or leaking out of the reactor will determine whether a new generation of neutrons is larger, smaller, or the same size as its predecessor. A measure of the increase or decrease in size of the neutron cloud is the ratio of the neutrons produced to the sum of the neutrons absorbed in fission or non-fission reactions, plus those lost in any one generation. This ratio is called the effective multiplication factor and may be expressed mathematically by

If the production of neutrons by one generation is greater than the sum of its absorption and the leakage, k_eff will be greater than 1.0, e.g., 1.1, and the neutron flux will increase with each generation. If, on the other hand, k_eff is less than 1.0, perhaps 0.9, the flux will decrease with each generation. If the size of each successive generation is the same then the production exactly equals the losses by absorption and leakage. k_eff is then exactly 1.0 and the reactor is said to be critical. The multiplication factor can, therefore, also be defined as:

Changes in the neutron flux cause changes in the power level of the reactor. Since the change in power level is directly affected by the multiplication factor, it is necessary to know more about how this factor depends upon the contents and construction of the reactor.

The balance between the production of neutrons, on the one hand, and their absorption in the core and leakage out of the core, on the other hand, determines the value of the multiplication factor. If the leakage is small enough to be neglected, the multiplication factor depends only upon the balance between production and absorption and is called the infinite multiplication factor, k_∞ (an infinitely large core can have no leakage). When the leakage is included, the factor is called the effective multiplication factor (k_eff). Each will be considered. (By definition, the multiplication constants k_eff and k_∞ are dimensionless numbers.)