Can you create mass with $E=mc^2$?

If you use the equation $E=mc^2$ could you make matter by dividing the $c^2$? I'm sorry if this is a really stupid sounding question or if it shouldn't be asked here.

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If you're asking "can matter be created from energy" the answer is yes; this is done all the time in particle accelerators, though only in extremely tiny quantities. Consider the production of antimatter for instance. – Nathan Reed Mar 21 '13 at 3:19
It's not a stupid question, that's exactly the kind of "what if" question that should always be asked when discovering a new formula. Indeed, if very energetic light (gamma rays) hits atoms, the light particle can be converted into an electron and a positron pair. – Lagerbaer Mar 21 '13 at 3:22
You can't create anything with a formula. I'm kind of confused about what you're asking here... – David Z Mar 21 '13 at 6:14

As noted by someone else, energy can be "converted" into mass e.g. via pair production. However, there is another example of this that you may be interested in:

The mass of the matter you come into contact with on an everyday basis is almost entirely from protons and neutrons, which are roughly 2000x more massive than electrons. The proton, for example, is comprised of two up quarks and one down quark. The combined rest mass of these quarks is about 10 MeV/c$^2$. However, the proton mass is about 100x larger, i.e. roughly 1000 MeV/c$^2$.

Thus about 99 percent of the mass of a proton (and indeed, the mass of everything you interact with) does not arise from the rest mass of elementary particles (e.g. quarks) but rather from their binding energy. Note that this does not come from the rest mass of e.g. gluons, which are massless. Details here.

So is it possible for energy to be converted into "matter"? In the above sense, not only is it possible, but almost all the mass you interact with is due to binding energy. To put it cutely: It's the glue.

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Yes. Matter (assuming it has mass) can be created from energy using the mass-energy equivalence. And, hence this principle got its name. For instance, take pair production where an energetic photon can create an electron-positron pair.

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The two existing answers are both great, but I thought it worth adding that every collision in the LHC converts energy to mass.

The LHC collides two high energy protons, so two protons go in and several hundred assorted particles come out, and the total mass of the particles coming out is much greater than the mass of the original two protons. If you add up the mass + kinetic energy of the particles coming out you'll find it's the same as the mass + kinetic energy of the protons going in. Some of the kinetic energy of the two protons is converted to mass.

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here we go again confusing matter mass and energy. Mass is a*property*of energy. Energy does not "convert" to mass nor vice versa. When two protons collide of course the resultant mass is greater than the two separate protons - it includes the energy of the collision and energy is always accompanied by mass (which is a property of resistance/ reaction to any force that is applied to a material body in uniform motion.

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Could you please provide some links for the layman? I'm not even sure what to google for. – dotancohen Jul 8 '14 at 10:49