MotionLab

Nuclear Binding Energy Calculator

Why iron-56 is the most stable nucleus and why both fission and fusion release energy.

Protons (Z)

Neutrons (N)

Binding energy (MeV)

495.184

Semi-empirical mass formula (Weizsäcker)

Per nucleon (MeV): 8.843

What you entered

Protons (Z): 26Neutrons (N): 30

1
Volume term (avA)
15.56 × 56= 871.36 MeV
2
Surface term (−asA^⅔)
−17.23 × 56^(2/3)= -252.1993 MeV
3
Coulomb term (−acZ(Z−1)/A^⅓)
−0.7 × 26(26−1) ÷ 56^(1/3)= -118.9274 MeV
4
Asymmetry term (−aa(A−2Z)²/A)
−23.285 × (56−2×26)² ÷ 56= -6.6529 MeV
5
Total binding energy
sum of all terms + pairing δ=1.6036= 495.1839 MeV
6
Binding energy per nucleon
495.1839 ÷ 56= 8.8426 MeV

Result

Binding energy (MeV): 495.184

A nucleus with Z = 26, N = 30 (A = 56) has a total binding energy of 495.18 MeV (8.843 MeV/nucleon).

Nuclear binding energy by nucleus

Total binding energy and binding energy per nucleon, from the semi-empirical mass formula.

Protons	Neutrons	Nucleus	Total binding (MeV)	Per nucleon (MeV)
2	2	Helium-4	23.941	5.9853
6	6	Carbon-12	90.701	7.5584
26	30	Iron-56	495.184	8.8426
92	146	Uranium-238	1811.394	7.6109

Binding energy per nucleon peaks near iron-56 at about 8.84 MeV, which is the single most consequential curve in nuclear physics: lighter nuclei release energy by fusing toward iron and heavier ones by fissioning toward it, and nothing releases energy by going past it. That is why stars fuse up to iron and then stop, and why uranium at 7.61 MeV per nucleon is fissile. A caution on the model: the semi-empirical mass formula is a liquid-drop approximation fitted to heavy nuclei and becomes unreliable for very light ones - it returns a negative binding energy for deuterium, where the true value is about 2.22 MeV.

The binding energy curve explains nuclear power

Binding energy per nucleon peaks near iron-56 (~8.8 MeV/nucleon) — lighter nuclei release energy by fusing toward iron (fusion, powering stars), while heavier nuclei release energy by splitting apart toward iron (fission, powering nuclear reactors). Both processes move toward greater stability.

Five competing effects in one formula

The semi-empirical mass formula balances five terms: volume (bulk nuclear attraction), surface (fewer neighbors at the surface), Coulomb (proton-proton repulsion), asymmetry (neutron-proton imbalance penalty), and pairing (even numbers of nucleons are more stable).

Frequently asked questions

Why does iron-56 have the highest binding energy per nucleon?

Iron-56 sits at the peak of the binding energy curve (~8.8 MeV/nucleon). Lighter nuclei can release energy by fusing toward iron (powering stars). Heavier nuclei release energy by fissioning toward iron (powering nuclear reactors). Iron is the 'ash' of nuclear reactions — you can't extract energy from it.

How much energy does uranium-235 fission release?

U-235 fission products have higher binding energy per nucleon than U-235 itself. The difference is about 0.9 MeV/nucleon × 235 nucleons ≈ 200 MeV per fission. That's 3.2×10⁻¹¹ J per atom — tiny, but 1 kg of U-235 contains 2.56×10²⁴ atoms, yielding ~82 TJ (equivalent to 20 kilotons of TNT).

Why is fusion more energetic per kilogram than fission?

Fusion of hydrogen to helium gains about 6.3 MeV/nucleon, while fission of uranium gains about 0.9 MeV/nucleon. Per unit mass, fusion releases roughly 4× more energy. Plus hydrogen is abundant and produces no radioactive waste — which is why fusion is the 'holy grail' of energy research.

What is the mass defect?

A nucleus weighs less than the sum of its individual protons and neutrons. The 'missing' mass was converted to binding energy via E = mc². For helium-4: mass defect = 0.03038 u = 28.3 MeV. This mass-energy equivalence is directly measurable and confirms Einstein's famous equation.