What is nuclear binding energy?

Nuclear binding energy is the energy required to completely separate all protons and neutrons in a nucleus. It arises because the bound nucleus has less mass than its free constituents — the difference (mass defect) converts to energy via E = Δm·c².

What units does this calculator use?

Nuclear mass is entered in atomic mass units (u). The result is displayed in MeV (megaelectronvolts) using the conversion 1 u = 931.494 MeV/c².

Where do I find the nuclear mass of an isotope?

Nuclear masses are tabulated in the Atomic Mass Evaluation (AME). Note that nuclear mass = atomic mass − Z·(electron mass). The electron mass is 0.000549 u, so nuclear mass ≈ atomic mass − 0.000549·Z.

What is binding energy per nucleon (BE/A)?

BE/A is the average binding energy for each nucleon in the nucleus. It peaks around iron-56 (~8.8 MeV/nucleon), which is why iron is the most stable nucleus. Lighter nuclei release energy via fusion; heavier nuclei release energy via fission.

What proton and neutron masses does this calculator use?

Proton rest mass: 1.007276 u. Neutron rest mass: 1.008665 u. These are standard CODATA values.

Nuclear Binding Energy Calculator

Enter proton count, neutron count, and nuclear mass to calculate binding energy, binding energy per nucleon, and mass defect.

Isotope Parameters

Protons (Z)

Atomic number — number of protons in the nucleus.

Neutrons (N)

Number of neutrons in the nucleus.

Nuclear Mass (u)

Nuclear mass in atomic mass units. Nuclear mass = atomic mass − Z × 0.000549 u.

Quick Examples

Results

Enter isotope parameters and click Calculate.

Summary

Enter proton count, neutron count, and nuclear mass to calculate binding energy, binding energy per nucleon, and mass defect.

How it works

Enter the number of protons (Z) and neutrons (N) for the isotope.
Enter the nuclear mass in atomic mass units (u).
The calculator computes the mass defect: Δm = Z·mp + N·mn − M_nucleus.
Binding energy is derived from the mass defect via E = Δm × 931.494 MeV/u.
Binding energy per nucleon (BE/A) is binding energy divided by mass number A = Z + N.

Use cases

Check binding energy values for homework or exam problems in nuclear physics.
Compare BE/A across isotopes to understand nuclear stability trends.
Verify calculations for fission and fusion energy release estimates.
Explore how mass defect relates to the strong nuclear force.
Use alongside a nuclide chart to study valley-of-stability patterns.
Teach or demonstrate the Einstein mass-energy equivalence (E=mc²) concept.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu