Mass defect (Δm) is the difference between the total mass of the free protons and neutrons that make up a nucleus and the actual measured mass of that nucleus. The "missing" mass is converted to the binding energy that holds the nucleus together.

Should I enter the nuclear mass or the atomic mass?

Enter the neutral atomic mass listed in isotope mass tables. The calculator uses the neutral hydrogen-atom mass for each proton, so electron masses cancel consistently; do not subtract electron masses yourself.

What reference masses are used?

The calculator uses mH = 1.00782503223 u for a neutral hydrogen atom and mn = 1.00866491595 u for a neutron. This is the standard atomic-mass form of the binding-energy calculation.

Why is the mass defect always positive?

Bound nuclei are lower-energy states than free nucleons. The nucleus always has less mass than the sum of its parts, so Δm is always positive (for a stable nucleus). A negative result usually indicates an incorrect mass value was entered.

What is 931.494 MeV/u?

This is the energy equivalent of one atomic mass unit: 1 u × c² = 931.494 MeV. It comes directly from E = mc² with 1 u = 1.66054 × 10⁻²⁷ kg and c = 2.998 × 10⁸ m/s.

Mass Defect Calculator

Enter proton count, neutron count, and isotope atomic mass to get the mass defect in atomic mass units and binding energy in MeV.

Nucleus Parameters

Z — Number of Protons

N — Number of Neutrons

M — Atomic Mass (u)

Enter the neutral isotope atomic mass from a mass table; do not subtract electron masses.

Quick Examples

Enter Z, N, and neutral atomic mass, then click Calculate.

Summary

Enter proton count, neutron count, and isotope atomic mass to get the mass defect in atomic mass units and binding energy in MeV.

How it works

Enter Z (number of protons) and N (number of neutrons) for the nucleus.
Enter M_atom, the measured neutral atomic mass in atomic mass units (u).
The calculator sums Z × 1.00782503223 u (hydrogen-atom mass) and N × 1.00866491595 u (neutron mass).
Mass defect Δm = (Z × mH + N × mn) − M_atom is computed.
Binding energy E = Δm × 931.494 MeV/u converts the defect to energy.
Results show Δm to 6 decimal places and E to 3 decimal places.

Use cases

Verify nuclear physics homework involving mass defect and binding energy.
Compare binding energies across isotopes to assess nuclear stability.
Understand why fusion of light nuclei and fission of heavy nuclei release energy.
Cross-check published nuclear data tables against calculated values.
Teach or learn the connection between special relativity and nuclear structure.
Explore why iron-56 has the highest binding energy per nucleon.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu