E=mc² is a physical equation, first given by Albert Einstein in his 1905 paper "Does the Inertia of a Body Depend Upon Its Energy Content?" ("Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?"). The equation defines a relationship between energy and mass (matter). It is one of the best-known equations of all time — even those who may not explicitly know what it means may have some connotation of its meaning through culture.

According to Umberto Bartocci (University of Perugia historian of mathematics), the equation was first published two years earlier by Olinto De Pretto, an industrialist from Vicenza, Italy, though this is not generally regarded as true or important by mainstream historians. Even if De Pretto introduced the formula, it was Einstein who connected it with the theory of relativity.

E=mc² is, perhaps, one of the most famous and, perhaps, most misunderstood laws in physics. The equation resulted from Albert Einstein's inquiry into the dependence of mass on its energy content. The famous result of this inquiry is that the mass of a body is actually a measure of its energy content. To understand the significance of this relationship, compare the electromagnetic force with the gravitational force. In electromagnetism, energy is contained in the fields (electric and magnetic) associated with the force and not in the charges. In gravitation, the energy is contained in the matter itself. It is not a coincidence that mass bends spacetime, while the charges of the other three fundamental forces do not.

[itex]\mbox{Energy} = \mbox{mass}\,\times\,\mbox{(speed of light)}^2[itex]

According to the equation, the total amount of energy obtainable from an object is equivalent to the mass of the object multiplied by the square of the speed of light.

This equation was crucial in the development of the atomic bomb. By measuring the mass of different atomic nuclei and comparing that number with the mass of the individual protons and neutrons, one can obtain an estimate of the binding energy available within an atomic nuclei. This not only showed that it was possible to release energy by fusion of light nuclei or fission of heavy nuclei, but also to estimate the amount of energy which can be released.

It is a little known piece of trivia that Einstein originally wrote the equation in the form m = L/c² (with an "L", instead of an "E", representing energy). Albert Einstein’s Sep. 27, 1905 paper is available in the external links section.

A kilogram of mass completely converts into

It is important to note that practical conversions of mass to energy are seldom 100 percent efficient. One theoretically perfect conversion would result from a collision of matter and antimatter; for most cases, byproducts are produced instead of energy, and therefore very little mass is actually converted. In the equation, mass is energy, but for the sake of clarity, the word converted is used.

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