Nuclear Binding Energy Calculator
Calculate nuclear binding energy and binding energy per nucleon for any isotope.
Where the Mass Goes
A nucleus weighs less than the sum of its separate protons and neutrons. That missing mass — the mass defect — was converted to energy when the nucleus formed, and it is exactly the energy needed to pull it apart again.
The conversion factor 931.5 MeV per atomic mass unit comes directly from E = mc². A mass defect of just 0.0024 u — about one part in a thousand — corresponds to 2.2 MeV, which is roughly a million times the energy of a chemical bond.
Why Iron Sits at the Peak
Binding energy per nucleon is what matters for stability, and it peaks near iron-56 at about 8.8 MeV per nucleon. The curve rises steeply to that point, then declines slowly.
| Nucleus | BE/A (MeV) | Consequence |
|---|---|---|
| H-2 (deuterium) | 1.11 | Very loosely bound |
| He-4 | 7.07 | Unusually stable for its size |
| Fe-56 | 8.79 | Near the maximum |
| U-235 | 7.59 | Below peak — fission releases energy |
The shape explains both nuclear energy routes. Fusion of light nuclei climbs the steep left side, releasing large energy per nucleon. Fission of heavy nuclei moves right to left down the shallow right side, releasing less per nucleon but from far more massive nuclei. Iron is the endpoint of both — which is why stellar fusion halts there and why iron is so abundant in the universe.
Two competing effects produce the peak. The strong force acts only between neighbouring nucleons, so binding per nucleon saturates. Electrostatic repulsion between protons acts across the whole nucleus and grows with Z², eventually dominating.
Worked Examples
Common Mistakes
Tabulated atomic masses include the electrons. Either use the proton mass and atomic mass consistently, or subtract the electron masses — mixing conventions introduces a small but systematic error.
Uranium has far more total binding energy than iron, but less per nucleon. Stability is governed by the per-nucleon figure.
The neutron count is A minus Z. Using A for both particle counts roughly doubles the calculated mass defect.
Beyond iron, binding energy per nucleon falls. That is precisely why heavy nuclei can release energy by splitting.
Frequently Asked Questions
Formula Explorer connections
Interpretation: This relationship connects isotopic composition, decay, radiation, mass defect or nuclear energy to a measurable quantity. Assumption: Use the correct nuclide, decay constant, branching behavior and time units. Radiation estimates also depend on geometry, shielding and detector response.