Nuclear reactor physics is the field of physics that studies and deals with the applied study and engineering applications of chain reaction to induce a controlled rate of fission in a nuclear reactor for the production of energy.

Most nuclear reactors use a chain reaction to induce a controlled rate of nuclear fission in fissile material, releasing both energy and free neutrons. A reactor consists of an assembly of nuclear fuel (a reactor core), usually surrounded by a neutron moderator such as regular water, heavy water, graphite, or zirconium hydride, and fitted with mechanisms such as control rods which control the rate of the reaction.

The physics of nuclear fission has several quirks that affect the design and behavior of nuclear reactors. This article presents a general overview of the physics of nuclear reactors and their behavior.

In a nuclear reactor, the neutron population at any instant is a function of the rate of neutron production (due to fission processes) and the rate of neutron losses (due to non-fission absorption mechanisms and leakage from the system). When a reactor's neutron population remains steady from one generation to the next (creating as many new neutrons as are lost), the fission chain reaction is self-sustaining and the reactor's condition is referred to as "critical". When the reactor's neutron production exceeds losses, characterized by increasing power level, it is considered "supercritical", and when losses dominate, it is considered "subcritical" and exhibits decreasing power.

The "Six-factor formula" is the neutron life-cycle balance equation and takes the form ${\displaystyle k=\eta fp\varepsilon P_{FNL}P_{TNL}}$. The parameter k is known as the effective multiplication factor (also denoted by ${\displaystyle K_{eff}}$), and defined to be k = ⁠number of neutrons in one generation/number of neutrons in preceding generation⁠. As indicated by its name, the Six-factor formula accounts for six factors in the fission reaction process:

When ${\displaystyle k=1}$, the reactor is said to be critical; when ${\displaystyle k<1}$, the reactor is subcritical; and when ${\displaystyle k>1}$, the reactor is supercritical.

Reactivity, expressed as either ${\displaystyle \rho }$ or ${\textstyle {\frac {\Delta k}{k}}}$ and given by the equation ${\textstyle \rho ={\frac {k-1}{k}}}$, is an expression of the departure from criticality. When ${\displaystyle \rho =0}$, the reactor is critical. When ${\displaystyle \rho <0}$, the reactor is subcritical. When ${\displaystyle \rho >0}$, the reactor is supercritical. Reactivity is commonly expressed in decimals, percentages, or pcm (per cent mille) of ${\textstyle \rho }$. When reactivity is expressed in units of the delayed neutron fraction ${\displaystyle \beta }$, the unit is called the dollar.

If we write N for the number of free neutrons in a reactor core and ${\displaystyle \tau }$ for the average lifetime of each neutron (before it either escapes from the core or is absorbed by a nucleus), then the reactor will follow the differential equation (evolution equation).