E = mc2: What Does Einstein's Famous Equation Really Mean?

By: Robert Lamb & Yara Simón  | 
Energy and matter are one.
Philip and Karen Smith/Iconica/Getty Images

Einstein's famous equation, E=mc², pops up on everything from baseball caps to bumper stickers. It's even the title of a 2008 Mariah Carey album. But what does Albert Einstein's famous equation really mean?

Read on to learn more about the meaning and origins of this well-known equation.


Origins of E=mc²

Albert Einstein formulated E=mc² in 1905 as part of his special theory of relativity. He first published a paper in June of that year about the properties of light and time. A few months later, he had reached a new conclusion, which gave us the equation.

This marked a groundbreaking and revolutionary concept in physics, reshaping our understanding of the fundamental relationship between energy and mass.


It also had profound implications in the realm of nuclear energy, explaining how nuclear reactions, such as nuclear fission and nuclear fusion, release enormous amounts of energy by converting a tiny fraction of mass into usable energy.

Before the equation, scientists treated mass and energy as separate and distinct properties. The equation revolves around the theory of mass-energy equivalence — though it's important to note that Einstein was not the first to make this observation.

But E=mc² asserts that mass and energy are interchangeable. In practical terms, this means that a small amount of mass can be converted into a vast amount of energy and vice versa.

Reportedly, Einstein felt disappointed that his theory didn't have as big a response at the beginning. However, by 1906, European physicists traveled to Switzerland to discuss the equation with him.

E=mc² Experiments

Einstein might not have proved his theory, but other scientists have attempted to do so in the years since. In 2005, for example, scientists at the Massachusetts Institute of Technology created GAMS4 to back up the theory.


Breaking Down Einstein's Formula

For starters, the E stands for energy and the m stands for mass, a measurement of the quantity of matter. Energy and matter are interchangeable. Furthermore, it's essential to remember that there's a set amount of energy/matter in the universe.

If you've ever read Dr. Seuss's children's book "The Sneetches," you probably remember how the yellow, birdlike characters in the story go through a machine to change back and forth between "star-bellied sneetches" and "plain-bellied sneetches."


The number of sneetches remains constant throughout the story, but the ratio between plain- and star-bellied ones changes. It's the same way with energy and matter. The grand total remains constant, but energy regularly changes form into matter and matter into energy.

Now we're getting to the c² part of the equation, which serves the same purpose as the star-on and star-off machines in "The Sneetches." The c stands for the speed of light, a universal constant, so the whole equation breaks down to this: Energy is equal to matter multiplied by the speed of light squared.

Why would you need to multiply matter by the speed of light to produce energy? The reason is that energy, be it light waves or radiation, travels at the speed of light. That breaks down to 186,000 miles per second (300,000 kilometers per second). When we split an atom inside a nuclear power plant or an atomic bomb, the resulting energy released is moving at the speed of light.

But why is the speed of light squared? The reason is that kinetic energy, or the energy of motion, is proportional to mass. When you accelerate an object, the kinetic energy increases to the tune of the speed squared.

You'll find an excellent example of this in any driver's education manual: If you double your speed, the braking distance is four times longer, so the braking distance is equal to the speed squared [source: UNSW Physics: Einsteinlight].

The speed of light squared is a colossal number, illustrating just how much energy there is in even tiny amounts of matter.

A common example of this is that 1 gram of water — if its whole mass were converted into pure energy via E=mc² — contains energy equivalent to 20,000 tons (18,143 metric tons) of TNT exploding. That's why such a small amount of uranium or plutonium can produce such a massive atomic explosion.

Einstein's equation opened the door for numerous technological advances, from nuclear power and nuclear medicine to the inner workings of the sun. It shows us that matter and energy are one.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.


Einstein's Formula

What does Einstein’s equation actually mean?
It shows that matter and energy are the same thing — as long as the matter travels at the speed of light squared. The latter is an enormous number and shows just how much energy there is in even tiny amounts of matter. That's why a small amount of uranium or plutonium can produce such a massive atomic explosion. Einstein's equation opened the door for numerous technological advances, from nuclear power and nuclear medicine to understanding the inner workings of the sun.
Why can't we travel at the speed of light?
Einstein's theory predicts that when a mass of matter is multiplied by a square of light's speed, it gives off huge energy. However, for us to move at such high speeds, we'd require an infinite amount of energy, which is not possible.
Is E=mc2 dimensionally correct?
Yes. When mass and speed of light squared are multiplied, they give the same unit as that of energy – Joules. Thus, E=mc2 is dimensionally correct.

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  • "E = mc²: What does it mean, and where did the equation come from?" UNSW Physics: Einsteinlight. (Sept. 3, 2010)http://www.phys.unsw.edu.au/einsteinlight/jw/module5_equations.htm
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