In nuclear physics, the valley of stability (also called the belt of stability, nuclear valley, energy valley, or beta stability valley) is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclides are composed of protons and neutrons. The shape of the valley refers to the profile of binding energy as a function of the numbers of neutrons and protons, with the lowest part of the valley corresponding to the region of most stable nuclei. The line of stable nuclides down the center of the valley of stability is known as the line of beta stability. The sides of the valley correspond to increasing instability to beta decay (β⁻ or β⁺). The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the nuclear drip lines, where nuclides become so unstable they emit single protons or single neutrons. Regions of instability within the valley at high atomic number also include radioactive decay by alpha radiation or spontaneous fission. The shape of the valley is roughly an elongated paraboloid corresponding to the nuclide binding energies as a function of neutron and atomic numbers.

The nuclides within the valley of stability encompass the entire table of nuclides. The chart of those nuclides is also known as a Segrè chart, after the physicist Emilio Segrè. The Segrè chart may be considered a map of the nuclear valley. The region of proton and neutron combinations outside of the valley of stability is referred to as the sea of instability.

Scientists have long searched for long-lived heavy isotopes outside of the valley of stability, hypothesized by Glenn T. Seaborg in the late 1960s. These relatively stable nuclides are expected to have particular configurations of "magic" atomic and neutron numbers, and form a so-called island of stability.

All atomic nuclei are composed of protons and neutrons bound together by the nuclear force. There are 286 primordial nuclides that occur naturally on earth, each corresponding to a unique number of protons, called the atomic number, Z, and a unique number of neutrons, called the neutron number, N. The mass number, A, of a nuclide is the sum of atomic and neutron numbers, A = Z + N. Not all nuclides are stable, however. According to Byrne, stable nuclides are defined as those having a half-life greater than 10¹⁸ years, and there are many combinations of protons and neutrons that form nuclides that are unstable. A common example of an unstable nuclide is carbon-14 that decays by beta decay into nitrogen-14 with a half-life of about 5,730 years:

In this form of decay, the original element becomes a new chemical element in a process known as nuclear transmutation and a beta particle and an electron antineutrino are emitted. An essential property of this and all nuclide decays is that the total energy of the decay product is less than that of the original nuclide. The difference between the initial and final nuclide binding energies is carried away by the kinetic energies of the decay products, often the beta particle and its associated neutrino.

The concept of the valley of stability is a way of organizing all of the nuclides according to binding energy as a function of neutron and proton numbers. Most stable nuclides have roughly equal numbers of protons and neutrons, so the line for which Z = N forms a rough initial line defining stable nuclides. The greater the number of protons, the more neutrons are required to stabilize a nuclide; nuclides with larger values for Z require an even larger number of neutrons, N > Z, to be stable. The valley of stability is formed by the negative of binding energy, the binding energy being the energy required to break apart the nuclide into its proton and neutron components. The stable nuclides have high binding energy, and these nuclides lie along the bottom of the valley of stability. Nuclides with weaker binding energy have combinations of N and Z that lie off of the line of stability and further up the sides of the valley of stability. Unstable nuclides can be formed in nuclear reactors or supernovas, for example. Such nuclides often decay in sequences of reactions called decay chains that take the resulting nuclides sequentially down the slopes of the valley of stability. The sequence of decays take nuclides toward greater binding energies, and the nuclides terminating the chain are stable. The valley of stability provides both a conceptual approach for how to organize the myriad stable and unstable nuclides into a coherent picture and an intuitive way to understand how and why sequences of radioactive decay occur.

The protons and neutrons that comprise an atomic nucleus behave almost identically within the nucleus. The approximate symmetry of isospin treats these particles as identical, but in a different quantum state. This symmetry is only approximate, however, and the nuclear force that binds nucleons together is a complicated function depending on nucleon type, spin state, electric charge, momentum, etc. and with contributions from non-central forces. The nuclear force is not a fundamental force of nature, but a consequence of the residual effects of the strong force that surround the nucleons. One consequence of these complications is that although deuterium, a bound state of a proton (p) and a neutron (n) is stable, exotic nuclides such as diproton or dineutron are unbound. The nuclear force is not sufficiently strong to form either p-p or n-n bound states, or equivalently, the nuclear force does not form a potential well deep enough to bind these identical nucleons.^{[citation needed]}

Stable nuclides require approximately equal numbers of protons and neutrons. The stable nuclide carbon-12 (¹²C) is composed of six neutrons and six protons, for example. Protons have a positive charge, hence within a nuclide with many protons there are large repulsive forces between protons arising from the Coulomb force. By acting to separate protons from one another, the neutrons within a nuclide play an essential role in stabilizing nuclides. With increasing atomic number, even greater numbers of neutrons are required to obtain stability. The heaviest stable element, lead (Pb), has many more neutrons than protons. The stable nuclide ²⁰⁶Pb has Z = 82 and N = 124, for example. For this reason, the valley of stability does not follow the line Z = N for A larger than 40 (Z = 20 is the element calcium). Neutron number increases along the line of beta stability at a faster rate than atomic number.