Mass–Energy Equivalence

Often described as one of physics’ most influential equations, mass–energy equivalence connects an object’s rest mass with the energy associated with it.

Source code

E = mc^2

Rest energy equals rest mass multiplied by the square of the speed of light in vacuum.

Variables and constant

The equation has two variables and one physical constant. The squared constant is the conversion factor between mass and energy.

Definitions, meanings, and SI units of the symbols in the mass–energy equivalence equation
Symbol	Definition	SI unit or value
$E$	Rest energy	joule ( $\text{J}$ )
$m$	Invariant mass (rest mass) of the object	kilogram ( $\text{kg}$ )
$c$	Speed of light in vacuum	$299\,792\,458\ \text{m}\,\text{s}^{-1}\text{ (exact)}$

The speed of light’s SI value is exact by definition. The energy depends on the object’s rest mass.

A worked example

If one gram of rest mass were completely converted into energy, first express the mass in kilograms, then substitute the speed of light:

m = 1\,\text{g} = 1.00 \times 10^{-3}\,\text{kg}

E = (1.00 \times 10^{-3}\,\text{kg})(299\,792\,458\,\text{m/s})^2 \approx 8.99 \times 10^{13}\,\text{J}

That is about 90 trillion joules. This is a theoretical full conversion of the mass, not the energy released by an ordinary chemical reaction.

Why it matters—and what it does not say

The equation says that rest mass is a form of energy: changing the mass of a system changes its rest energy. This relationship is essential for accounting for the energy released in nuclear reactions, where the products can have slightly less total rest mass than the starting materials.

It does not mean that ordinary matter can readily release all of its rest energy. Chemical reactions convert only a tiny fraction of a system’s mass into other forms of energy, and even nuclear reactions release only the mass difference between their initial and final states. The displayed equation gives rest energy; a moving object’s total energy also includes its motion.

Check the units

The units on the right-hand side reduce to joules, the SI unit of energy:

\text{kg}\left(\frac{\text{m}}{\text{s}}\right)^2 = \frac{\text{kg}\,\text{m}^2}{\text{s}^2} = \text{J}