Mass Defect Calculator

Mass defect (Δm) is the difference between the total mass of a nucleus's individual nucleons (protons and neutrons measured separately) and the actual measured mass of the assembled nucleus. The assembled nucleus is always lighter because some mass has been converted into binding energy that holds the nucleus together, as described by Einstein's E = mc².

The calculator uses Δm = Z·mp + (A−Z)·mn − M, where Z is the atomic number (proton count), A is the mass number, mp is the proton mass (~1.007276 u), mn is the neutron mass (~1.008665 u), and M is the actual nuclear mass in atomic mass units. Binding energy is then Eb = Δm·c².

Mass defect and binding energy are two sides of the same phenomenon. The 'missing' mass Δm is converted entirely into energy that holds the nucleus together. Using E = mc², the binding energy equals Δm multiplied by the speed of light squared. A larger mass defect means more energy is released when nucleons combine — and more energy is needed to pull them apart.

Mass defect is most commonly expressed in atomic mass units (u), where 1 u = 1.66054 × 10⁻²⁷ kg. The corresponding binding energy is expressed in joules (J) for SI calculations or more conveniently in mega-electronvolts (MeV), using the conversion 1 u = 931.494 MeV/c².

Yes — you can calculate mass defect for any nuclide from hydrogen (Z=1, A=1) up to the heaviest known elements, as long as you supply a reliable nuclear mass value. Standard proton and neutron masses are pre-filled, but you can override them for advanced precision work.

Binding energy per nucleon (BE/A) divides the total binding energy by the mass number A, giving the average energy holding each nucleon in place. It's the most useful indicator of nuclear stability — iron-56 has the highest BE/A (~8.8 MeV) and is therefore the most stable nucleus. Nuclei lighter than iron can release energy through fusion; heavier ones through fission.

Actual atomic masses are tabulated in the Atomic Mass Evaluation (AME) published by the International Atomic Energy Agency (IAEA) and appear in standard periodic tables, nuclear data sheets, and physics reference textbooks. Values are typically given in atomic mass units (u) for specific isotopes.

A zero or negative result usually means the nuclear mass you entered is equal to or greater than the sum of the individual nucleon masses — which is physically impossible for a stable bound nucleus. Double-check that you're using the correct isotope mass, the right atomic number Z, and the correct mass number A. Ensure your masses are all in the same units (atomic mass units).