Nuclear Binding Energy Calculator
Calculate the mass defect and nuclear binding energy of any nucleus from its proton number, neutron number and atomic mass, in MeV, MeV per nucleon, joules and kJ/mol — with presets from deuterium to uranium-238.
How it works
Δm = Z · m(¹H) + N · m(n) − M(atom) · m(¹H) = 1.00782503 u, m(n) = 1.00866492 u · E_B = Δm × 931.494 MeV/u (E = mc²) · binding energy per nucleon = E_B ÷ A · 1 MeV = 1.602177 × 10⁻¹³ J
A nucleus weighs less than the protons and neutrons it is made of; the missing mass (the mass defect) is the binding energy that would be needed to pull it apart, through E = mc². Using the mass of a hydrogen atom for each proton makes the electron masses cancel against the neutral-atom mass found in tables. Binding energy per nucleon peaks near iron and nickel (about 8.8 MeV), which is why fusion of light nuclei and fission of heavy ones both release energy. Masses are from the Atomic Mass Evaluation 2020 and constants from CODATA 2018.
Worked example
Helium-4 has Z = 2 and N = 2 and an atomic mass of 4.002603 u. The mass defect is 2 × 1.007825 + 2 × 1.008665 − 4.002603 = 0.030377 u, so the binding energy is 0.030377 × 931.494 = 28.296 MeV, or 7.0739 MeV per nucleon.
Sources: IAEA — Atomic Mass Evaluation 2020 (AME2020) · NIST CODATA — Fundamental physical constants · HyperPhysics — Nuclear binding energy
Frequently asked questions
What is the mass defect?
It is the difference between the total mass of the separate protons and neutrons and the measured mass of the nucleus. Multiplied by c² (931.494 MeV per atomic mass unit) it gives the binding energy.
Which nucleus has the highest binding energy per nucleon?
Nickel-62, at about 8.795 MeV per nucleon, just above iron-58 and iron-56 (about 8.790 MeV). That is why stars build elements by fusion only up to the iron group.
Why use atomic masses instead of nuclear masses?
Tables list neutral-atom masses. Using the hydrogen-atom mass for each proton adds Z electrons on one side to match the Z electrons in the atomic mass, so they cancel (apart from tiny electron binding energies).
How much energy does fission of uranium-235 release?
Splitting ²³⁵U into medium-mass nuclei raises the binding energy per nucleon from about 7.6 to about 8.5 MeV, releasing roughly 200 MeV per fission.
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This calculator is for educational purposes. Double-check important results before acting on them.