Nuclear Binding Energy Calculator

Nuclear binding energy is the energy required to completely separate all the nucleons (protons and neutrons) in a nucleus. It arises because the measured mass of a nucleus is always slightly less than the sum of its individual nucleon masses — this 'missing' mass (the mass defect) is converted into binding energy via Einstein's E = Δm·c².

Mass defect is the difference between the expected mass of an atom (calculated from the sum of its protons, neutrons, and electrons as separate hydrogen atoms and neutrons) and its actual measured atomic mass. The formula is: Δm = Z·m(¹H) + N·mₙ − m_atom, where m(¹H) = 1.00782503207 u and mₙ = 1.00866491600 u.

BE/A is the total binding energy divided by the mass number A. It measures how tightly each nucleon is bound on average, making it a universal measure of nuclear stability. Iron-56 has one of the highest BE/A values (~8.79 MeV/nucleon), which is why it sits at the peak of the nuclear stability curve.

Nuclear-scale energies are extremely small in Joules but conveniently sized in mega-electron volts (MeV). Using the conversion 1 u = 931.494 MeV/c², the mass defect in atomic mass units maps directly to binding energy in MeV, making calculations far more practical. One MeV equals approximately 1.602 × 10⁻¹³ Joules.

You need three values: the atomic number Z (number of protons), the mass number A (total protons + neutrons), and the precise atomic mass of the nuclide in unified atomic mass units (u). Atomic masses can be found in standard nuclear data tables or isotope charts.

Yes. The binding energy values produced here are directly applicable to fission and fusion calculations. In fission, a heavy nucleus splits into fragments with higher BE/A, releasing energy. In fusion, light nuclei combine into a product with higher BE/A, also releasing energy. The energy released equals the difference in total binding energies.

This calculator uses the liquid-drop / semi-empirical approach based on measured atomic masses. It assumes the input atomic mass is accurate to at least 6 decimal places. It does not account for excited nuclear states or shell-model corrections beyond what is embedded in the measured mass. For exotic or very short-lived nuclides, precise atomic masses may not be available.

Iron-56 (Z=26, A=56, atomic mass ≈ 55.934939 u) and Nickel-62 (Z=28, A=62) are often cited as having the highest BE/A values, around 8.79 MeV/nucleon. This is why stellar nucleosynthesis stops at the iron-nickel peak — fusing these nuclei further would consume rather than release energy.