Result

Mass-energy equivalence

E = γ m c^{2}, E_{0} = m c^{2}

Statement

An object's total relativistic energy; at rest (γ = 1) this reduces to the rest energy E₀ = mc².

Symbols and units

$E$	total relativistic energy	J
$E_{0}$	rest energy	J
$m$	rest mass	kg
$γ$	Lorentz factor	—
$c$	speed of light	2.998×10⁸ m/s

When it applies

Special relativity, any speed from rest up to (but not including) c.

Don't use when

E = mc² specifically gives rest energy (v = 0) — a moving object's total energy is γmc², always greater; using the rest-energy form for a moving object underestimates its energy.

Derivation

Total energy generalizes rest energy by the same factor γ that appears in time dilation; kinetic energy is the difference between total and rest energy:

K = (γ - 1) m c^{2}

Watch out for

E = mc² is specifically the REST energy (v = 0); a moving object's total energy is γmc², always greater. A tiny mass corresponds to an enormous energy because c² is such a large conversion factor — why nuclear reactions release far more energy per kilogram of fuel than any chemical reaction.