# So what units should i use with E=mc^2?

## Main Question or Discussion Point

I guess this is a question about what units to use in any equation. Which ones pair together. If you use 300,000,000 m/s and 1 gram in e=mc^2, you will get 300,000,000, but what unit? Joules? How do you know which to use and which ones pair together?

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First, you didn't square $c$. You would get $9\times 10^{16} \text{ g m}^2/\text{s}^2$. Which isn't joules. You pair units up the same way you would for $E = mv^2/2$. You use kilograms and meters per second and you get joules for energy.

You know what quantities to use when using SI units, right?

Oh crap your right, forgot to square. By quantities do you mean the proper prefixes? I know liters, meters, seconds, grams, joules and so on are all associated with metric. If you mean prefixes, then no, i guess that is my question.

jtbell
Mentor
Meters, kilograms, seconds, and joules go together. These are MKS or SI units.

So do centimeters, grams, seconds, and ergs. These are CGS or Gaussian units.

Even though it has a prefix, all quantities calculated with SI use kilograms as the base unit of mass. So a joule is defined as being measured equivalent to kilograms x meters^2/seconds^2.

In real life, you can use any valid units of mass and velocity in $E=mc^2$ and get a meaningful result. Just keep track of what units you used and don't throw them away. You can measure mass in terms of pounds and velocity in terms of feet per second, and you'd say the energy is measured in terms of pounds feet^2/second^2. As it happens, this combination of units does have a name: it's called a foot-pound. (Why is it called a foot-pound? Because imperial units use "pound" for both mass and force. Sometimes the latter is abbreviated lbf. to say pounds of force. A pound of force applied through one foot is a measure of energy, the foot-pound.)

But really, in order to talk about quantities like energy in terms of nice units (like joules or ergs), you need to have some understanding of what those mean in terms of a small base of units like meters, kilograms, seconds, and so on.