Binding Energy Per Nucleon Calculator: Nuclear P...
Calculate the nuclear binding energy per nucleon using Einstein's mass-energy equivalence. Understand nuclear stability, fission, and fusion with worked examples.
What is Nuclear Binding Energy?
Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. The binding energy per nucleon (BEN) measures nuclear stability — larger BEN means a more stable nucleus. Iron-56 has the highest BEN (~8.8 MeV/nucleon), which is why it is the most stable element.
⚛️ Binding Energy Per Nucleon Calculator
Use our free calculator for instant, accurate results.
📐 Formula
BE = Δm × c² = Δm × 931.5 MeV/u
Δm = mass defect = (Z×mₚ + N×mₙ) − m_nucleus. BEN = BE / A (A = mass number).
📝 Worked Example
Helium-4 (⁴He): Z=2, N=2, A=4
Δm = (2×1.00728 + 2×1.00867) − 4.00260 = 0.03038 u
BE = 0.03038 × 931.5 = 28.3 MeV
BEN = 28.3/4 = 7.07 MeV/nucleon
📝 How to Use the Calculator
❓ FAQ
Why is iron the most stable element?
Iron-56 has the peak binding energy per nucleon (~8.8 MeV). Both fission of heavier elements and fusion of lighter ones move toward iron on the stability curve.
What is the mass defect?
The mass of a nucleus is always less than the sum of its individual protons and neutrons. This missing mass (Δm) is converted to binding energy via E=mc².
Veer Kumavat
Founder & AuthorVeer is a 14-year-old student from Nashik, Maharashtra, who built SciFi Calculators to help students worldwide master STEM subjects. He is passionate about making complex science and math problems accessible through intuitive digital tools.