Nuclear Binding Energy Calculator

How to Use This Calculator

1. Enter Z (protons), N (neutrons), and atomic mass M in unified atomic mass units (u).
2. Simple tier shows mass defect, total BE, and BE/nucleon.
3. Use Common Nuclei presets for Fe-56, He-4, U-235, and others.
4. Professional tier adds SEMF prediction and fission/fusion yield estimate.

Formula

Example

Frequently Asked Questions

• What is nuclear binding energy? ▼
  Binding energy is the energy required to completely disassemble a nucleus into its constituent protons and neutrons. It equals the mass defect times c²: BE = Δm × 931.494 MeV/u. Fe-56 has the highest BE per nucleon (~8.79 MeV), making it the most stable nucleus.
• What is the mass defect? ▼
  The mass of a nucleus is always less than the sum of its free proton and neutron masses. This missing mass (Δm = Z×m_H + N×m_n − M) is the mass defect, and by E=mc², it equals the binding energy.
• Why is Fe-56 the most stable nucleus? ▼
  Fe-56 sits at the peak of the binding energy per nucleon curve (~8.79 MeV/nucleon). Nuclei lighter than Fe release energy by fusion; nuclei heavier than Fe release energy by fission. Both processes produce nuclei closer to Fe-56.
• What is the semi-empirical mass formula? ▼
  The Bethe-Weizsäcker formula models BE as five terms: volume (~15.8A), surface (−17.8A^2/3), Coulomb (−0.711Z(Z-1)/A^1/3), asymmetry (−23.7(N-Z)²/A), and pairing (±11.2/√A). It predicts binding energies within a few MeV.

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