Nuclear Binding Energy Calculator (Mass Defect and Energy per Nucleon)
The energy that holds a nucleus together, from its measured atomic mass: the mass defect, the total binding energy in MeV and the binding energy per nucleon.
Results
Total binding energy
492.260
MeV
Binding energy per nucleon
8.7903
MeV
Mass defect
0.528462
u
Share of the atom's mass that is missing
0.9448
%
What this tool does
A nucleus weighs less than its separate protons and neutrons, and the missing mass, turned into energy with E = mc², is the binding energy that would be needed to pull it apart. Per nucleon it rises quickly to about 8.8 MeV near iron-56 and nickel-62 and falls slowly for the heaviest nuclei — which is why fusing light nuclei and splitting very heavy ones both release energy. Use the mass of the neutral atom, as tabulated, and the tool subtracts the electrons by using hydrogen-atom masses for the protons.
Formula
Δm = Z m_H + N m_n − M_atom · E_B = Δm × 931.494 MeV/u · E_B ÷ A
Variables
| Symbol | Meaning | Unit |
|---|---|---|
z | Protons in the nucleus (atomic number Z) | — |
a | Protons plus neutrons (mass number A) | — |
m | Mass of the neutral atom | u |
EB | Total binding energy | MeV |
EA | Binding energy per nucleon | MeV |
DM | Mass defect | u |
SH | Share of the atom's mass that is missing | % |
Worked example
- Protons in the nucleus (atomic number Z)26
- Protons plus neutrons (mass number A)56
- Mass of the neutral atom55.9349 u
- Total binding energy492.260 MeV
- Binding energy per nucleon8.7903 MeV
- Mass defect0.528462 u
- Share of the atom's mass that is missing0.9448 %
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.