Binding Energy Per Nucleon Calculator

Calculate binding energy per nucleon from mass defect and nucleon count, or derive mass defect and total binding energy from isotope mass.

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Binding Energy Per Nucleon Formula

The following formula is used to calculate the binding energy per nucleon.

BE = (Δm \times c²) / A

Variables:

BE is the binding energy per nucleon (MeV)
Δm is the mass defect (atomic mass units)
c is the speed of light, exactly 299,792,458 m/s. The conversion is 1 u × c² ≈ 931.49410372 MeV; this energy factor is not a speed.
A is the number of nucleons (protons and neutrons in the nucleus)

To calculate the binding energy per nucleon, multiply the mass defect by the speed of light squared conversion factor and divide by the number of nucleons.

What is Binding Energy Per Nucleon?

Binding energy per nucleon is the total energy needed to separate a nucleus into individual protons and neutrons, divided by its nucleon count. It helps explain nuclear fission and fusion but does not by itself determine radioactive stability or half-life. The isotope-mass mode uses neutral atomic masses and neglects electron binding-energy differences.

How to Calculate Binding Energy Per Nucleon?

The following steps outline how to calculate the Binding Energy Per Nucleon.

First, select the quantity to solve for. For energy per nucleon, enter the mass defect (Δm) in atomic mass units or kilograms.
Next, determine the number of nucleons (A) in the nucleus.
Use BE ≈ Δm × 931.49410372 / A for mass defect in u and energy per nucleon in MeV. For SI units, use Δm in kg and c = 299,792,458 m/s to obtain joules per nucleon.
Finally, calculate the Binding Energy Per Nucleon (BE) in MeV.
After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Mass defect (Δm) = 0.030 atomic mass units

Number of nucleons (A) = 56

Binding Energy Per Nucleon Calculator screenshot