Does the Inertia of a Body Depend on its Energy Content?
Which means that the most accurate formulation of the famous equation may be:
m = E/c^2
Not the more familiar algebraic equivalent:
E = mc^2
These apply only to a body at rest.
Nobel laureate Frank Wilczek puts it this way:
can some of a body's mass arise from the energy of the stuff it contains? Right from the start Einstein was thinking about the conceptual foundations of physics, not about the possibility of making bombs or reactors.
The concept of energy is much more central to modern physics than the concept of mass. This shows up in many ways. It is energy, not mass, that is truly conserved. It is energy that appears in our fundamental equations, such as Boltzmann's equation for statistical mechanics, Schrödinger's equation for quantum mechanics, and Einstein's equation for gravity.
(From Wilczek's book,
The Lightness of Being: Mass, Ether, and the Unification of Forces, a good read if one has interest in such cutting edge things.)
Concerning units, conventionally one uses SI units in science (traditionally, meters, kilograms, seconds). Particle physicists use a more convenient system of units for them, where c = 1 light-second/sec and E = m, both measured in electron-volts.
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