Nuclear Binding Energy Calculator: Mass Defect, Binding Energy per Nucleon and Energy Released (E = mc2)

How tightly a nucleus is bound, and how much energy a nuclear reaction releases.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose a nucleus or a reaction.

For a nucleus pick it from the list, or enter Z, A and the atomic mass. For a reaction enter the total mass before and after.

The calculator gives the mass defect, the binding energy in MeV and joules, and the binding energy per nucleon.

Formulas used

  • \Delta m = Zm_H + (A - Z)m_n - M_{atom}
  • BE = \Delta m\,c^2
  • 1\,\mathrm{u} = 931.494\,\mathrm{MeV}/c^2

Worked example

With the default numbers in the calculator above:

  1. Mass of the separate parts: Z hydrogen atoms (protons with their electrons) and A - Z neutrons: 4.0329799 u
  2. Mass defect: the parts are heavier than the nucleus: 0.03037665 u
  3. Binding energy: 28.2957 MeV (4.5335e-12 J)
  4. Binding energy per nucleon: 7.0739 MeV per nucleon

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: The nucleus Iron-56.

  1. Mass of the separate parts: Z hydrogen atoms (protons with their electrons) and A - Z neutrons: 56.463398 u
  2. Mass defect: the parts are heavier than the nucleus: 0.528462 u
  3. Binding energy: 492.259 MeV (7.8869e-11 J)
  4. Binding energy per nucleon: 8.7903 MeV per nucleon

Common questions

What is the mass defect?

The difference between the mass of the separate protons and neutrons and the mass of the nucleus. The missing mass became the binding energy.

Which nucleus is most stable?

Iron-56 and nickel-62 have the highest binding energy per nucleon, about 8.8 MeV.

Why do fusion and fission release energy?

Both change the nuclei into ones with a higher binding energy per nucleon, and the mass difference is released as energy.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Atomic masses from standard isotope mass tables. Any first-year physics text (nuclear physics).

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