Nuclear Binding Energy Calculator

Work out nuclear binding energy instantly with clear inputs, formula shown and shareable results.

About Nuclear Binding Energy Calculator

A nucleus weighs less than its separated parts, and that missing mass is the binding energy by E = mc^2. Adding hydrogen atom masses for the protons and neutron masses for the neutrons, then subtracting the measured atomic mass, gives the defect in atomic mass units; one u is 931.494 MeV. Iron-56 comes out near 492 MeV total, about 8.79 MeV per nucleon - the peak of nuclear stability.

Formulas

Mass defect

defect = Z x m(H) + N x m(n) - measured atomic mass

Binding energy

BE = defect x 931.494 MeV/u

Worked example

With the default values below, Nuclear Binding Energy Calculator returns Total Binding Energy of 492.260. Change any input above and every figure here is recalculated in your browser.

Inputs used

Protons Zminimum 1: 26
Neutrons Nminimum 0: 30
Measured atomic massminimum 0 u: 55.934936 u

Results

Total Binding Energy: 492.260 MeV
Mass Defect: 0.528462 u
Binding Energy Per Nucleon: 8.7903 MeV
Mass Number A: 56

Step by step

1Values used
2Mass defect
3Binding energy
4Total Binding Energy= 492.260 MeV
5Mass Defect= 0.528462 u
6Binding Energy Per Nucleon= 8.7903 MeV
7Mass Number A= 56

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why use the hydrogen atom mass rather than the proton mass?

Because the measured atomic mass includes the electrons. Using hydrogen atoms cancels them out on both sides.

Why does iron-56 matter?

It sits at the maximum binding energy per nucleon, so fusion releases energy below it and fission releases energy above it. Stars cannot gain energy past iron.