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Alchemy, in Full Metal Alchemist, is based on the concept of 'one needs to provide materials of equal value compared to the thing one want to create' (equivalent exchange).

But, how does it exactly work. Can this amount of required materials be calculated by the alchemist? If so, how? Are there some sort of lookup-tables?

Or does one need to guess and provides something of more value to be on the safe side? If so, can one become a more skilled alchemist by experience of successful guesses?

Also, different alchemists might have different specialized skills. How does that work? For the guessing part, I can imagine that one have a preference for certain kinds of alchemy and thus gain experience with a specialized skill.

Edit: Madara Uchiha's answer suggests that there are always materials required. I was also wondering about the situation where this is not the case and the alchemist was successful none the less.

For example:

In the end Edward trades his alchemy skill in exchange for returning Alphonse's body to him.

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Alchemy has three stages: Understanding, Break down, Rebuild.

Different alchemists have different specializations because of the Understanding part, learning chemistry in general isn't easy, and digging into a specific subject (For instance, the study of the atmosphere and oxygen in Roy Mustang's case), is even harder, hence specialization.

Matter of "equal value" means of equal "type" (Mineral to mineral, organism to organism, you can't turn stone into a flower), and of equal Mass.

This works well in accordance to the physical laws of matter and energy conservation. You cannot make matter disappear, nor you can make it appear out of nothing. You can't input more matter to be on the safe side, that matter won't be used for the alchemic transmutation (at best), or result in a rebound (at worse).

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    How about non-material to material type of alchemy (or the other way around)? For example, when Edward and Alphonse try to bring their mother back using alchemy. It is hard but it seems to be possible (although not in that situation) – Veger Dec 11 '12 at 23:48
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    @Veger: A soul is priceless in alchemy standard. That's why you cannot create one from nothing (A passed soul is considered "lost", it cannot be "retrieved"). They thought that by gathering the materials required to construct a human body, plus giving "Soul Information" in the form of a drop of blood, it would be enough. In reality, Alphonse's soul was placed in the created vessal, and because they didn't have the required knowledge to perfectly construct a human body (no one has), the process failed entirely. Also, as an unrelated note, it's considered a Taboo, and Truth doesn't like it. – Madara Uchiha Dec 11 '12 at 23:52
  • It was an example that does not spoil anything, as it is about the first thing that happened, but there are other examples where non-materials are involved that did (somehow) work... Or is it not explained and left in the dark how those work? – Veger Dec 11 '12 at 23:57
  • @Veger: Like what? I already gave Roy's example, which amplifies the oxygen levels in the air, and igniting with his gloves (Which is why he's useless on rainy days). What other example is there? Edit your question with a >!Spoiler block if you'd like. – Madara Uchiha Dec 12 '12 at 0:00
  • I did, good idea – Veger Dec 12 '12 at 0:08
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That's why alchemists study so long, and National Alchemist even more. There are lots of books explaining how to do It properly, how to calculate the amounts, the type of materials, the decomjposition of things and so on.

They aim to use exactly what they need, not more, not less, so they work to fine-tune, to understand how things are made, how things work, and then replicate them as they wish.

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