How do you actually use Einstein's famous equation E = mc-squared?

This equation is perhaps one of the most iconic equations in all of physics. It appears on T-shirts, on TV series such as the 1960's program Twilight Zone, and god known how many other advertising venues. I do not want to get into a lengthy mathematical discussion to describe where this equation comes from, but I can tell you in this limited space how to use it.

Quantitatively, in metric units, energy is measured in joules. In one second, a 100 watt light bulb emits 100 Joules of energy. One watt is equal to 1 Joule per second.

Ok...Einstein's equation states that the amount of energy you have is equal to the mass involved times the square of the speed of light. If 1 kilogram of mass is converted into energy, then to determine how much energy is involved in joules, you just multiply 1 kilogram by the speed of light squared, with the speed of light in units of meters per second.

Energy in Joules = 1 kilogram x (300,000,000 m/sec) x (300,000,000 m/sec).

This equals 90,000,000,000,000,000 Joules of energy.

Now, to convert this into other physical units is a bit awkward but doable. For instance, this is equal to the energy emitted by a 100 watt bulb (producing 100 Joules/sec) for:

90,000,000,000,000,000/(100) = 900,000,000,000,000 seconds. Since there are about 30,000,000 seconds in a year, this means that a 100 watt bulb running for 30,000,000 years produces as much energy as 1 kilogram of matter converted into energy. Or you can think of it as 30,000,000 hundred-watt bulbs burning for one year - the output from a small country's town lighting system.As another reference point, 90,000,000,000,000,000 Joules of energy is equal to about a 20 megaton hydrogen bomb explosion.

Return to Dr. Odenwald's FAQ page at the Astronomy Cafe Blog.