These days pretty much everyone knows that mass and energy are two sides of the same coin, as discovered by Einstein. In fact this is so well known that the average man on the street – knowing nothing at all of physics – would still recognize the expression even if he didn’t know what it meant or how to use it:

E is energy, m is mass, c is the speed of light. As with all such formulas, you need to have properly matching units. You can’t just use mass in pounds, e in British thermal units, and speed in furlongs per fortnight. But any properly consistent set of units will work; for macroscopic purposes we usually use joules, kilograms, and meters per second.

Since the speed of light c = 299,792,458 m/s, the speed of light squared is about 8.99×10^{16} m^2/s^2. As such one kilogram of mass is the equivalent of a ridiculously huge amount of energy, as we see in nuclear reactors and weapons. It’s a little less commonly understood that this isn’t just true for nuclear reactions, it’s true for everything. Burn some logs in your fireplace and the total mass of the wood and oxygen will have been just microscopically higher than the final mass of the combustion products. The remainder has gone into the energy released to warm your house. It’s the very same equation on a much smaller scale.

To get a specific number for this, we need to know how much energy is released by wood. Some googling seems to indicate a figure around 15 million joules per kilogram, so if we assume the burning of 10 kilograms of wood, we get 150 million joules total. Divide that by the speed of light squared and you’ll get a mass of about 1.7 micrograms. Very tiny, much smaller than your average sand grain.

In fact the total solar power output absorbed by the earth is about 1.8 ^{17} watts. Over the course of a year, this comes out to a staggering 5.68^{24} joules. It’s a huge amount of energy, which you might expect since it’s responsible for warming the earth, driving the weather, and powering essentially the entire biosphere. Dividing that by c^2 and you’ll see that a total of about 63 million kilograms of solar mass is converted into sunlight each year in order to illuminate the earth. It sounds like a lot, but the same mass of water would fit in a cube 40 meters on a side.

The sun is quite a bit bigger than that, and though it doesn’t come close to achieving perfect conversion efficiency, it probably won’t be running out of nuclear fuel any time soon.