# How much energy does the replicator consume?

I have been seeing in various comments references to replicators in Star Trek, occasionally arguing against various scenarios from the standpoint of energy usage - with arguments along the lines of "you might be able to replicate something that big, but the energy requirement would be astronomical."

We probably don't have any solid math explaining how this is done - however, are there any specific mentions that touch on the in-universe cost of this process?

• As far as I remember, only references to rationing of replicator use due to energy shortages on Voyager. Or, the wisenheimer answer: 12. They use 12 energy. – Politank-Z Feb 4 '18 at 17:26
• The replicator doesn't turn energy into matter. It turns one form of matter (referred to as feedstock) into other forms of matter by re-arranging its molecules. – Valorum Feb 4 '18 at 17:47
• @Valorum Fair enough. Deleted that part, since it doesn't change the question. – Misha R Feb 4 '18 at 18:39
• @Politank-Z Well, the practical difference between canon technobabble and a wisenheimer is pretty subtle. But, for the time being, canon is what I'm looking for. If that doesn't work out, I might revisit 12. – Misha R Feb 4 '18 at 19:05
• The "feedstock" thing isn't really common knowledge, IMO. (I don't think it ever appeared on-screen.) So anyone arguing about energy usage might (or might not) be assuming that the replicator is subject to the good old E=mc^2. – Harry Johnston Feb 4 '18 at 20:08

I'd be thrilled at a canon-based answer - but here's some reasoning out:

It would depend on the nature of the feedstock - the majority of food is Carbon, Hydrogen, Oxygen and Nitrogen - but we need a lot of other trace elements, too (iron, potassium, sodium, chlorine, calcium, and more). Plus, things like glasses and plates need to be made - so we need silicon, too.

We also don't simply take in atomaceous nutrients - we need it in the form of simple sugars and more complex carbon chains (carbohydrates and fats), and proteins.

There are three possible ways the replicators use the feedstock:

• all sugars, starches, fats, etc, are precomposed and simply assembled into a steak and potatoes. This means only transportation energy is required. Two problems: much like an inkjet printer can run out of one particular colour, too much ice cream can deplete sugar and fat before starches; and, things like glasses and plates rely on more crystalline or complex structures.

• the feedstock is elemental and carbon chains and crystalline structures are composed individually on demand. This adds the energy of creating bonds to the transportation. Could still run out of specific elements, though.

• the replicators can manipulate protons and neutrons into the specific atoms it needs to then create the molecules we need. Huge amounts of energy! But highly flexible.

Luckily, ships and bases have ridiculous amounts of energy on tap from warp cores and fusion reactors.

For food: 3-4 kiloWatthours per day per person. The energy requirement for each crew-member is about that of 2-4 desktop PCs.

For other objects: Far more power than the replicator was designed for.

As laid out by @Horuskol, we assume that the food is somehow assembled from simpler components. If say, carbon, hydrogen and oxygen are assembled into fat molecules, these molecules contain more energy than the original atoms and the replicator must have added that energy. This is equivalent to the "food energy" released when a human consumes it.

A human gets about 12 MegaJoules (MJ) worth of energy from her food every day. This is equivalent to ca 3.3 kWh or 2 desktop PCs running all day.

We don't know the energy requirements of teleporting the food into the replicator tray, but since we're not seeing much dissipation of energy at the receiving end (heat, radiation) it's fair to assume not much energy was expended at the sender either. This leaves the food energy as the main energy cost.

What we have not calculated is the energy cost of liberating individual atoms from the feedstock. For food, the required Hydrogen, Oxygen and carbon can be stored as gases (H, O2 and CO2). But if you are going to replicate something made of metal, your energy requirement is basically that of vaporizing the metal.

To vaporize 10kg of iron takes about 635 MJ or more than 50 days worth of replicator food. Assembling this in a second, as replicators do, means applying 0.6 GigaWatts of power. In today's terms, it is equivalent to the power from 300 windmills or roughly half a nuclear plant.

Assuming 4 meals a day, assembling something with 10kg of iron therefore taxes the replicator 200 times as much as assembling a single meal. This explains why food is easily replicated, but heavy gear and tools are out of the question.

• I would say that this makes several unsupported assumptions. A. That energy required in assembling basic elements into complex food structures is similar to the energy they release when eaten (this runs counter to the way manufacturing - especially micromanufacturing - works in real life). B. That apparent lack of energy dissipation in the user tray represents the actual lack of energy dissipation on the back end. C. That, with the availability of teleportation disassembly/reassembly process, you would need to vaporize iron before rendering it useful for reconstruction in a specific structure. – Misha R Feb 5 '18 at 18:30
• @MishaRosnach: I agree that A and B are valid counter-arguments. As for C, what I had in mind is that a free iron atom has a higher potential energy than one locked into bounds with other iron atoms or an oxidised atom. For the teleporter to abide by the conservation of energy, this potential energy must be added. When vaporized, each atom receive exactly enough energy to be completely liberated from the others. But looking up the actual binding energy would have been more correct. – Abulafia Feb 8 '18 at 12:40