For an energy to mass calculator in which m = E ÷ c², click here

Unless you have lived in a cave your entire life, the above formula must be very familiar to you. It was formulated in the Special Theory of Relativity by the German-born American physicist Albert Einstein (1879-1955).

E=mc² has to be the most famous equation of all time. Authors David Bodanis, Pete Moore (and no doubt many more) have each written entire books concerning just this one equation.
It is the name of an Internet website.
It was shown at the beginning of Twilight Zone television episodes (“A dimension of mind” – remember ?) and at the beginning of “Twilight Zone: The Movie” (1983).
E=mc² was the name of a 1996 film.
E=mc² is the title of a Mariah Carey album.
Many corporations (computers, graphics, management, etc) use this equation as part of their name.

You may have wondered what this mysterious equation is all about. It seems that knowing how to use this equation conveys intelligence.

Basically, the equation states that matter and energy are identical. If you could convert a small amount of matter completely, it would yield a
tremendous amount of energy. Let’s use gasoline as an example. If we burned 3 kilograms of gasoline (about 1.05 US Gallons or 3.97 liters), it would yield
140,000,000 Joules, which is a tremendous amount of energy. However, the burning of gasoline only produces a chemical change.
Now let’s calculate converting those 3 kilograms of gasoline completely into energy. Finally, we will use the legendary

E=mc²

And the meaning of this equation?
The energy (e) of a mass to energy conversion equals the mass (m) that was converted multiplied by the speed of light (c) squared.
If we choose mass in kilograms and the speed of light in meters per second, then the answer will be in Joules.

The mass (from the above example) would be 3 kilograms and the speed of light (c) is 299,792,458 meter per second.
So c² = 89,875,517,800,000,000 mtr²/sec² which rounds (for purposes of this discussion) to 9 x 10¹⁶ mtr²/sec².
So, the energy equals
3 kg (mass) x 9 x 10¹⁶ mtr²/sec² (c²),
which equals 27 x 10¹⁶kg • mtr²/sec²
which equals 2.7 x 10¹⁷Joules.
This is almost 2 billion times the
energy we obtained from the “ordinary” burning of 1 gallon of gasoline. (And we all know that is a huge amount of energy).

It is fascinating and quite intimidating to learn that a matter to energy conversion of just one gram yields the equivalent of 21.5 kilotons of tnt – the energy of the Hiroshima atomic bomb. Yes, all that power is generated from one gram of matter transmuted into energy – the mass of one paper clip!

Every second, the Sun converts 4.29 x 10⁶ metric tonnes (9.47 x 10⁹ pounds) of matter into 3.86 x 10²⁶ joules of energy. That is a phenomenal amount of energy! Trying to harness all that energy would be a task far beyond our current level of technoogy. Basically, in order to harness all that energy we would have to build a sphere of “solar collectors” completely surrounding the Sun at a radius of the Earth’s orbit. (called a Dyson Sphere).
In order to make those numbers a little easier to visualize, we’ll introduce another power unit – the quad. Basically, if we were to express the Sun’s total energy output in this unit, it would be about 636,000 quads! In 2015, the total energy used by everyone on Earth, was 575 quads, so it might be a while before we need to harness all of the Sun’s energy.

The calculator below is very easy to use. Input a number, click on the units this represents and you will be shown the amount of energy when that quantity of matter is completely converted to energy.

Numbers are displayed in scientific notation in the amount of significant figures you specify. For easier readability, numbers between 1,000 and -1,000 will not be in scientific notation but will still have the same precision.
You may change the number of significant figures displayed by changing the number in the box above.
Most browsers, will display the answers properly but if you are seeing no answers at all, enter a zero in the box above, which will eliminate all formatting but at least you will see the answers.