The masses of atoms and nuclei are measured in "atomic mass units", symbol U, where U is defined as exactly 1/12 the mass of a C-12 atom. Note that "atomic mass" is not to be confused with atomic mass unit: atomic mass is the mass of an atom given in atomic mass units.
The mass of a nucleus is always less than the sum of the masses of its nucleons. The difference of mass, or "mass defect", arises because energy is released when nucleons combine to form a nucleus.
The energy released, per unit of mass, in the formation of nuclei is enormous. It is so large that it has a significant mass-equivalent, given by Einstein's equation: E = [C squared]M, where E is energy in Joules, C is the velocity of light in meters (m) per second squared and M is mass in kilograms (kg).
This equation is used to convert a given mass to an equivalent amount of energy; or to convert a given amount of energy to an equivalent mass.
Consider the formation of an Iron (Fe) nucleus from protons and neutrons: Fe has atomic mass 56, therefore the nucleus contains 30 neutrons and 26 protons; the mass of an Fe nucleus is 55.90638 U; the mass of a proton is 1.00728 U and the mass of a neutron is 1.00866 U.
The mass difference (M diff) between an Fe nucleus and its constituent nucleons is therefore: M diff = (26 x 1.00728 U) + (30 x 1.00866 U) -- 55. 90638 U = 56.4491 U -- 55.90638 U = 0.5427 U.
Noting that a mass of 1 gram (g) equals 6.022 x (10 raised to the power 23) U, which is "Avogadro's number" of U, Einstein's equation is then used to determine the energy difference (E diff), or the binding energy of the Fe nucleus, as follows:
E diff = [2.998 x (10 raised to the power 8) m / second)] squared x [0.5427 U] x [1 g / 6.022 x (10 raised to the power 23) U] x [1 kg / 1000 g] = 8.100 x (10 raised to the power -11) kg x (m squared) / second squared = 8.100 x (10 raised to the power -11) Joules.
The binding energy per nucleon is therefore: 8.100 x (10 raised to the power -11) / 56 nucleons = 1.446 x [10 raised to the power -12] Joules / nucleon.