Mass Defect Calculator
Enter proton count, neutron count and actual nuclear mass to compute the mass defect, binding energy and binding energy per nucleon.
Input Data
Results
At a glance:The mass defect Δm is the shortfall between the sum of the masses of the separated constituent nucleons (Z protons at m_p = 1.007276 u, N neutrons at m_n = 1.008665 u) and the actual mass of the bound nucleus: Δm = Z·m_p + N·m_n − m_nucleus. This 'missing' mass is the nuclear binding energy E_B = Δm·c² (1 u = 931.494 MeV/c²). Dividing by A = Z+N gives the binding energy per nucleon, which peaks near iron-56 (~8.8 MeV/nucleon) — the most stable nuclei. Fusion of light nuclei and fission of heavy nuclei both move toward iron, releasing the binding-energy difference. This tool computes Δm, E_B and per-nucleon BE from Z, N and actual mass.
Formula
Δm = Z·m_p + N·m_n − m_nucleus
E_B = Δm·c²
BE per nucleon = E_B/(Z+N)
1 u = 931.494 MeV/c²
$$\Delta m = Z m_H + N m_n - m_{\text{atom}}, \quad E_B = \Delta m \cdot c^2, \quad \frac{E_B}{A} \text{ peaks at } ^{56}\text{Fe} (8.79 \text{ MeV})$$How to Use
- Enter proton count Z and neutron count N.
- Enter the actual nuclear mass (u).
- The calculator returns Δm, E_B (J and MeV) and binding energy per nucleon.
Case Studies
Helium-4
Z=2, N=2, m = 4.001506 u.
Δm = 2×1.007276+2×1.008665−4.001506 = 0.03038 u.
E_B ≈ 28.3 MeV, ~7.07 MeV/nucleon.
FAQ
Where does the mass defect go?
It is converted to binding energy holding the nucleus together (E_B = Δmc²); the bound system has less rest mass than its free parts. It is released in fission/fusion as kinetic energy/radiation.
Why is iron the most stable?
Iron-56 has the highest binding energy per nucleon (~8.8 MeV). Both lighter and heavier nuclei can release energy by moving toward A≈56.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.