Nuclear Binding Energy Calculator
Calculates an isotope's nuclear binding energy in MeV from its mass defect, and the binding energy per nucleon used to compare how tightly nuclei are bound.
Last updated: October 2026
Binding Energy
492.26 MeV
Formula below · 3 sources (physics.nist.gov, spark.iop.org, Wikipedia) · Updated Oct 2026
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About this calculator
Binding energy is the energy needed to pull a nucleus apart into free protons and neutrons. A bound nucleus weighs less than its separate parts, and the missing mass (the mass defect) times c² is the binding energy:
BE (MeV) = [Z × m(¹H) + (A − Z) × mₙ − M] × 931.494
Here Z is the atomic number, A the mass number, M the atomic mass of the isotope in unified atomic mass units (u), m(¹H) = 1.00782503 u the mass of a hydrogen atom, mₙ = 1.00866492 u the neutron mass, and 931.494 MeV is the energy equivalent of 1 u (CODATA 2022: 931.49410372 MeV).
Why the hydrogen-atom mass
Tables list atomic masses, which include Z electrons. Using Z hydrogen atoms on the other side brings in the same Z electrons, so the electron masses cancel. Using the bare proton mass with an atomic mass would understate the binding energy by about 0.511 MeV per proton.
Per nucleon
Dividing by A gives the binding energy per nucleon, the figure used to compare nuclei. It rises from about 7.07 MeV for helium-4 to a peak of about 8.79 MeV near iron-56, then falls slowly for heavier nuclei. That shape is why fusing light nuclei and splitting heavy ones both release energy.
How to use
Enter the mass number A, the atomic number Z and the isotope's atomic mass from a mass table. Use the mass of the specific isotope, not the element's standard atomic weight (55.845 for iron averages several isotopes). Default, iron-56: Z = 26, A = 56, M = 55.934936 u. Constituents: 26 × 1.00782503 + 30 × 1.00866492 = 56.46340 u. Mass defect: 56.46340 − 55.934936 = 0.52846 u. BE = 0.52846 × 931.494 ≈ 492.26 MeV, or 8.79 MeV per nucleon. Helium-4: Z = 2, A = 4, M = 4.002602 u gives a mass defect of 0.030378 u and BE ≈ 28.30 MeV, about 7.07 MeV per nucleon.
Frequently asked questions
Why does the calculator use the hydrogen-atom mass instead of the proton mass?
Because you enter an atomic mass, which includes the electrons. Z hydrogen atoms carry the same Z electrons, so the electron masses cancel and only the tiny electron binding energy is left over. With the bare proton mass you would understate the result by about 0.511 MeV per proton, roughly 13 MeV for iron-56.
What does binding energy per nucleon tell me?
It is the average energy holding each nucleon in the nucleus. It peaks at about 8.79 MeV near iron-56. Light nuclei release energy when they fuse toward that peak, and heavy nuclei release energy when they split toward it.
Can I use the standard atomic weight from the periodic table?
No. The standard atomic weight is an average over the element's natural isotopes. Use the atomic mass of the single isotope you are interested in, with at least six decimal places, because the calculation subtracts two nearly equal numbers.
What if the result is negative?
A bound nucleus always has a positive binding energy, so a negative result means the inputs do not match: check that A and Z belong to the isotope whose mass you entered.
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