Relativistic energy ($E=\gamma m{c}^2$)

For a massive free particle with invariant rest mass $m$, speed $v<c$, and Lorentz factor $\gamma =(1-v^2/c^2{)}^{-1/2}$, its total energy is $E=\gamma m{c}^2$. It includes the rest energy $m{c}^2$ and the relativistic kinetic energy $(\gamma -1)m{c}^2$. Here $c$ is the speed of light. At fixed total energy, a larger speed requires a smaller rest mass.

For an isolated decay of a parent of rest mass $M$ into products of rest masses $m_i$, the difference between total final and initial kinetic energies is $(M-{\sum }_i{m}_i)c^2$ in every inertial frame. Conservation of total energy and inclusion of all products are essential.