Nuclear Binding Energy Calculator
The nuclear binding energy calculator computes the mass defect and total binding energy of an atomic nucleus from the number of protons, neutrons, and the measured atomic mass. Using Einstein's mass-energy equivalence (E = mc2), the mass deficit between the free nucleons and the actual nucleus reveals the nuclear binding energy in MeV and binding energy per nucleon. This quantity determines nuclear stability, explains why fusion releases energy for light elements and fission releases energy for heavy elements, and underlies all nuclear energy technologies. Enter Z, N, and the atomic mass (in atomic mass units) to calculate the binding energy.
Nuclear binding energy formula
Mass defect: delta_m = Z*m_H + N*m_n - M_atom
m_H (hydrogen atom) = 1.007825 u
m_n (neutron) = 1.008665 u
1 u = 931.494 MeV/c^2
BE = delta_m * 931.494 MeV
BE/A = BE / (Z + N)
Notable binding energies
- H-2 (deuterium): BE = 2.22 MeV, BE/A = 1.11 MeV/nucleon
- He-4 (alpha): BE = 28.30 MeV, BE/A = 7.07 MeV/nucleon
- Fe-56 (iron): BE = 492.26 MeV, BE/A = 8.79 MeV/nucleon (peak)
- U-238 (uranium): BE = 1,801.7 MeV, BE/A = 7.57 MeV/nucleon
Nuclear binding energy: frequently asked questions
What is nuclear binding energy?
Nuclear binding energy is the energy required to completely separate a nucleus into its individual protons and neutrons. Equivalently, it is the energy released when those nucleons come together to form the nucleus. It arises because the nuclear mass is less than the sum of free proton and neutron masses. This mass difference (mass defect) converts to energy via E = delta_m * c^2.
What is mass defect?
Mass defect (delta_m) = Z*m_p + N*m_n - M_nucleus, where Z is the proton number, N is the neutron number, m_p = 1.007276 u (proton mass), m_n = 1.008665 u (neutron mass), and M_nucleus is the actual nuclear mass. 1 u = 931.494 MeV/c^2. The binding energy BE = delta_m * 931.494 MeV/u (or delta_m * c^2 in SI: c = 2.998e8 m/s).
What is binding energy per nucleon?
Binding energy per nucleon (BE/A) is the binding energy divided by mass number A = Z + N. It peaks near iron (Fe-56) at about 8.79 MeV/nucleon, which is why iron is the most stable nucleus. Light nuclei release energy by fusion (combining to approach iron); heavy nuclei release energy by fission (splitting toward iron).
How does nuclear binding energy relate to E=mc2?
Einstein's mass-energy equivalence E = mc^2 is the direct relationship. The mass defect in kg converts to energy in joules: E = delta_m * c^2 (c = 2.998e8 m/s). In nuclear units: 1 atomic mass unit (u) = 931.494 MeV. So delta_m in u gives BE in MeV directly by multiplying by 931.494. One MeV = 1.602e-13 J.
What is the semi-empirical mass formula?
The semi-empirical (Bethe-Weizsacker) mass formula estimates nuclear binding energy: BE = a_V*A - a_S*A^(2/3) - a_C*Z^2*A^(-1/3) - a_A*(A-2Z)^2/A + delta, where a_V = 15.85 MeV (volume), a_S = 18.34 MeV (surface), a_C = 0.71 MeV (Coulomb), a_A = 23.21 MeV (asymmetry), and delta is the pairing term. It predicts the liquid-drop model binding energy.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.