Physics • Senior secondary • Nuclear binding

Binding Energy Calculator

Calculate a nuclide’s mass defect, total binding energy, and binding energy per nucleon. The calculator makes the mass convention explicit so atomic masses are not accidentally mixed with bare-proton masses.

Choose the mass convention first

If your isotope table gives the mass of a neutral atom, use Atomic-mass mode. The calculator then uses the hydrogen-atom mass for each proton so the electron masses cancel consistently.

If your source gives the mass of the bare nucleus, use Nuclear-mass mode. The calculator then uses the bare-proton mass.

Never mix the two conventions.

Nuclide

Protons, Z Neutrons, N Mass supplied Measured bound mass, u

Example defaults are helium-4 in atomic-mass mode. Replace them with values supplied by your source or question.

Constants used

Hydrogen-atom mass, u Proton mass, u Neutron mass, u Energy equivalent, MeV per u

Constants are editable so a kaiako can require the rounded values supplied in a particular question.

Mass defect, Δm—

Total binding energy—

Binding energy / nucleon—

What the calculator is doing

Atomic mode: Δm = Z·m(H) + N·m(n) − m(atom)

Binding energy = Δm × (MeV/u conversion)

Binding energy per nucleon = binding energy ÷ (Z + N)

A positive mass defect means the separated constituents have more mass than the bound system. The corresponding energy is the binding energy associated with assembling the nucleus from those constituents.

Interpretation checks

If Δm is negative, stop: a mass convention, isotope mass, particle count or unit is probably inconsistent.
Do not compare total binding energy alone when nuclei have different nucleon counts; binding energy per nucleon is usually the more informative comparison for how tightly bound the average nucleon is.
This tool calculates from supplied masses. It does not decide which nuclear reaction is possible or replace conservation-of-charge, nucleon-number and energy reasoning.

Show the reasoning, not only the button

Write Z and N.
Name whether your supplied isotope mass is atomic or nuclear.
Write the mass-defect expression with substituted values.
Convert Δm to energy.
Divide by A = Z + N if comparing binding per nucleon.
Explain in words what your result says about the bound nucleus.