Binding Energy per Nucleon Calculator
The binding energy per nucleon is a measure of nuclear stability: the energy per proton or neutron that holds the nucleus together. It is computed from the mass defect, which is the difference between the sum of masses of free protons and neutrons and the actual nuclear mass. Using E = mc^2 with the conversion 1 atomic mass unit = 931.494 MeV/c^2, the total binding energy in MeV is the mass defect in atomic mass units times 931.494. Dividing by the mass number A gives the binding energy per nucleon. Iron-56 has the highest value at about 8.79 MeV/nucleon, explaining its role as the endpoint of stellar nucleosynthesis. Enter Z (proton number), A (mass number), and the atomic mass in atomic mass units.
Binding energy formula
delta_m = Z * m_H + (A - Z) * m_n - M_atom
BE = delta_m * 931.494 MeV/u
BE/A = BE / A
m_H = 1.007825032 u (hydrogen atom mass, including electron), m_n = 1.008664916 u (neutron mass), M_atom is the atomic mass from tables. The electron masses largely cancel when using atomic (not nuclear) masses, with small correction for binding energies of electrons (negligible for this calculation).
Binding energy per nucleon for key nuclides
- Helium-4: 7.074 MeV/nucleon (the doubly-magic alpha particle).
- Carbon-12: 7.680 MeV/nucleon.
- Iron-56: 8.790 MeV/nucleon (near-maximum, most stable per nucleon).
- Uranium-235: 7.591 MeV/nucleon (fission releases energy toward iron-like products).
- Deuterium (H-2): 1.112 MeV/nucleon (least stable stable nucleus, fusion is energetically favorable).
Binding energy: frequently asked questions
What is nuclear binding energy?
Nuclear binding energy is the energy required to completely separate a nucleus into its constituent protons and neutrons. It arises because the actual nuclear mass is less than the sum of the masses of free protons and neutrons. This mass defect delta_m is converted to energy via E = delta_m * c^2.
What is the mass defect?
The mass defect is delta_m = Z * mp + (A - Z) * mn - M_nucleus, where Z is the number of protons, A is the mass number (total nucleons), mp is the proton mass, mn is the neutron mass, and M_nucleus is the actual nuclear mass (often given as atomic mass minus Z electron masses).
Why is iron-56 the most stable nucleus?
Iron-56 (and nickel-62) have the highest binding energy per nucleon, about 8.8 MeV/nucleon. Nuclei lighter than iron can gain energy by fusion (combining to form iron-like nuclei); nuclei heavier than iron can gain energy by fission (splitting toward iron-like fragments). This is why stellar fusion stops at iron.
What units are used for binding energy in nuclear physics?
Binding energy is typically expressed in megaelectronvolts (MeV). 1 MeV = 1.602176634 x 10^-13 J. One atomic mass unit (u = 1.66054 x 10^-27 kg) corresponds to 931.494 MeV via E = mc^2. This conversion, 1 u = 931.494 MeV/c^2, is fundamental to nuclear mass calculations.
How does binding energy per nucleon explain nuclear energy release?
Fission of uranium-235 releases about 0.9 MeV/nucleon as fragments near iron are formed from a nucleus with lower binding energy per nucleon (7.6 MeV/nucleon for U-235). Fusion of hydrogen to helium releases even more per nucleon: from 1.1 MeV/nucleon (deuterium) to 7.1 MeV/nucleon (helium-4).
Official sources
- NIST: Atomic Weights and Isotopic Compositions.
- OpenStax University Physics Vol. 3: Nuclear Structure.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.