Tutorial:Applied power math

In this tutorial we'll be answering the question: how much coal is needed to power our factory?

First off, we need to know: how much power does our factory use? That's easy &emdash; you can check the electricity tab by clicking on a power pole.

Here we see one radar using 300kW (the 299kW is a rounding error). Factorio uses real science here. A Watt (W) is a measure of energy transfer. A kilowatt (kW) is 1000 W, a megawatt (MW) is 1000 kW, and if you're lucky enough to ever make a factory big enough, a gigawatt (GW) is 1000 MW.

So that answers the question of how much power our factory uses. To keep our factory running at full speed we need to maintain 300 kW. For ease of comparison, we'll convert that to 0.3 MW

Next question! How much power is stored in coal? That's also easy, because it tells us when we hover over it: 8 MJ.

A Joule is another standard measure of stored energy. As with Watts a kilojoule (kJ) is 1000 J, and so on. There is a fixed relationship between Joules and Watts. 1 Joule can provide 1 Watt of energy for 1 second. As a formula:

   J = W × s

So to run our factory at 0.3 MW, we need to consume 0.3 MJ every second.

Quiz

Assuming perfect efficiency, how long could one piece of coal (8 MJ) run our factory?

Expand to reveal answer

   8 MJ = 0.3 MW * s
      s = 8 MJ / 0.3 MW
      s = 26.67

Nearly 27 seconds.

Assuming perfect efficiency, what is the maximum size factory (in watts) a single piece of coal could run for 5 seconds?

Expand to reveal answer

   8 MJ = MW * 5
     MW = 8 MJ / 5
     MW = 1.6

1.6 megawatts.

BONUS! A ton of real world coal about 21 GJ. How much does a piece of factorio coal weigh?

Expand to reveal answer

The energy ratios will match the weight ratios, so:

   8 MJ / 21000 MJ = weight / 1000 kG
            weight = (8 MJ / 21000 MJ) * 1000 kG
            weight = 0.38 kG

About 400g! Still doesn't explain how our character can carry so much of it...

Efficiency

Let's test it! We should be able to run a radar for 27 seconds, right? By dropping a single piece of coal in the burner, we should get our 27 seconds.

We barely got 20s! What's wrong? We are getting less energy than expected. Let's measure using an accumulator.

We started with 8 MJ in the coal, but only 4 MJ ended up in the accumulator. This is because, like in the real world, some energy is lost along the way as waste. In this case, only 50% is making it into our accumulator. In Factorio, this loss happens in the boiler, and it actually tells us this in the item details! You can think of the waste 50% as going into the pollution it generates...

Now we have everything we need to answer our initial question: how much coal do we need to power our factory? Well, the question actually needs to be a bit more precise: how much coal do we need per second_' to power our factory.

Quiz

How much coal per second is needed to power a 20 MW factory?

Expand to reveal answer

Since J = W × s, a 20 MW factory will consume 20 MJ/s. We'll need 40 MJ/s input due to the 50% boiler efficiency loss. Since coal contains 8 MJ, we'll need 5 coal per second (5 × 8 MJ = 40 MJ).

BONUS! How many mining drills are needed to produce that much coal?

Expand to reveal answer

Per the linked page, an electric mining drill produces ~0.5/s, so we'll need 10 electric mining drills (10 × 0.5 = 5).