Nuclear Binding Energy Calculator
The binding energy of a nucleus from its measured atomic mass and its proton and neutron counts — the mass defect converted by E = mc² — with the energy per nucleon that decides which nuclei can release energy by fusion or fission.
A nucleus weighs less than its protons and neutrons weigh separately.
How the nuclear binding energy calculator works
A nucleus weighs less than its protons and neutrons weigh separately. The missing mass — the mass defect — is the energy that holds it together, at 931.5 MeV per atomic mass unit. Divide by the nucleon count and you have the binding energy per nucleon: about 7.1 MeV for helium-4, 8.8 for iron-56 at the peak of the curve, 7.6 for uranium.
Energy is released by moving toward the peak: fusing light nuclei, splitting heavy ones. The curve's shape is the whole of nuclear energy.
Formula: Δm = Z m_H + N m_n − M_atom; BE = Δm × 931.494 MeV; per nucleon = BE / (Z + N)
Worked examples
| Inputs | Binding energy per nucleon (MeV) | Note |
|---|---|---|
| Iron-56 | 8.7903 | 8.79 MeV per nucleon — the peak |
| Helium-4 | 7.0739 | 7.07 |
| Uranium-235 | 7.5909 | 7.59 |
FAQFrequently asked questions
What is binding energy?
The energy needed to pull a nucleus apart into free protons and neutrons — equivalently, the energy released when they come together. It shows up as missing mass.
Why use the atomic mass and the hydrogen mass?
Because measured masses are of neutral atoms, electrons included. Using the hydrogen atom for each proton cancels the electrons out, to within their tiny binding energy.
Why is iron the peak?
Below it, adding nucleons lets the strong force bind each more tightly; above it, the protons' mutual repulsion grows faster than the short-range attraction. Iron-56 and nickel-62 sit at the top.
How does this give fission energy?
Uranium at 7.6 MeV per nucleon splits into fragments near 8.5. The difference, about 0.9 MeV per nucleon over 235 nucleons, is the 200 MeV a fission releases.
Where do I find atomic masses?
The AME atomic mass evaluation, or any isotope table. They are given to eight or nine significant figures because the defect is a small difference of large numbers.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.