Nuclear binding energy calculator
Pick a nuclide or enter the number of protons and neutrons and the atomic mass in unified atomic mass units. The calculator finds the mass defect, the mass that disappears when the nucleons bind, and turns it into the binding energy with E = mc².
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Pick a nuclide from the list, or choose “Other nuclide”.
- For another nuclide, enter Z, N and its atomic mass in u from a table of nuclides.
- Read the binding energy, the energy per nucleon and the mass defect.
- Mass defect: Δm = Z × 1.00782503223 u + N × 1.00866491595 u − M(atom).
- Binding energy: E = Δm × 931.49410242 MeV/u. Per nucleon: E ÷ A, with A = Z + N.
- 1 u = 1.66053906660 × 10⁻²⁷ kg, 1 MeV = 1.602176634 × 10⁻¹³ J.
Worked example
Helium-4 has 2 protons, 2 neutrons and an atomic mass of 4.002603 u. Δm = 2 × 1.00782503223 + 2 × 1.00866491595 − 4.002603 = 0.030377 u, so the binding energy is 0.030377 × 931.494 = 28.296 MeV, or 7.074 MeV per nucleon.
Iron-56 gives 492.26 MeV in all and 8.7903 MeV per nucleon, uranium-238 gives 1,801.69 MeV and 7.5701 MeV per nucleon.
Notes
- Preset masses are atomic masses rounded to six decimals; the results agree with full-precision values to about 0.001 MeV.
- Electron binding energies are neglected: tens of eV for the lightest atoms, under 1 MeV in total even for uranium.
- Use the E = mc² calculator to turn any other mass difference into energy.
Frequently asked questions
What is nuclear binding energy?
It is the energy needed to pull a nucleus apart into its separate protons and neutrons. The same energy is released when the nucleus forms, and it shows up as a missing mass, the mass defect, by E = mc².
How do you calculate the mass defect?
Δm = Z × m(¹H) + N × m(n) − M(atom). Using the mass of hydrogen atoms instead of bare protons makes the electron masses cancel, so you can use tabulated atomic masses directly. For helium-4, 2 × 1.007825 + 2 × 1.008665 − 4.002603 = 0.030377 u.
How do I convert the mass defect to MeV?
Multiply by 931.494 MeV per unified atomic mass unit. Helium-4's 0.030377 u gives 28.296 MeV, or 7.074 MeV per nucleon.
Why is iron-56 special?
Nuclei around iron and nickel have the highest binding energy per nucleon, about 8.8 MeV. Fusing lighter nuclei or splitting heavier ones moves toward that peak, which is why both fusion and fission release energy.