Binding Energy per Nucleon Calculator

Nuclear stability is measured by how tightly protons and neutrons are bound together — the Binding Energy per Nucleon Calculator quantifies that energy for any atom. Enter the Atomic Number (Z) and Mass Number (A) — and optionally the Atomic Mass in amu — to get the Binding Energy per Nucleon (BE/A) in MeV/nucleon. Secondary outputs include Total Binding Energy, Mass Defect (in both amu and MeV), and the neutron count. Also try the use the Atomic Number Calculator.

Results

Binding Energy per Nucleon (BE/A)

Total Binding Energy

Mass Defect

Mass Defect (Energy)

Number of Neutrons (N)

What is nuclear binding energy?

Nuclear binding energy is the energy required to completely disassemble a nucleus into its individual protons and neutrons. It represents how tightly the nucleons are held together by the strong nuclear force. See also our calculate Electronegativity.

Why is binding energy per nucleon (BE/A) important?

BE/A allows comparison of nuclear stability across different nuclei. Higher values typically indicate more stable nuclei, with iron-56 having one of the highest BE/A values at about 8.8 MeV/nucleon.

What is mass defect and how is it calculated?

Mass defect is the difference between the expected mass of separated nucleons and the actual atomic mass. It's calculated as Δm = [Z × m_proton + N × m_neutron] - M_atom, where the 'missing' mass converts to binding energy.

How accurate are binding energy calculations?

Calculations using experimental atomic masses are very accurate. When atomic mass is not provided, the calculator uses semi-empirical mass formula estimates, which are reasonably accurate for most nuclei but less precise for very light or very heavy elements. You might also find our Radioactive Decay Calculator (Biology) useful.

What does the conversion factor 931.494 MeV/amu represent?

This is Einstein's mass-energy equivalence (E=mc²) expressed in nuclear physics units. One atomic mass unit (amu) of mass converts to 931.494 MeV of energy, allowing conversion between mass defect and binding energy.

Which nuclei have the highest binding energy per nucleon?

Iron-56 and nickel-62 have the highest BE/A values (around 8.8 MeV/nucleon), making them among the most stable nuclei. This is why fusion reactions release energy for light nuclei and fission releases energy for heavy nuclei.

How does binding energy relate to nuclear stability?

Generally, nuclei with higher binding energy per nucleon are more stable and less likely to undergo radioactive decay. The BE/A curve peaks around mass number 56, which explains why elements like iron are so abundant in the universe.