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In the anime/manga Fullmetal Alchemist, the Philosopher's Stone (賢者の石 Kenja no Ishi lit. 'Wise man's stone') is the central element that drives the plot, and the object of the Elric Brothers' (the story's protagonists) search.

It is based on the legend of the philosopher's stone, able to transmute inexpensive materials into gold and grant immortality to its user. In Fullmetal Alchemist, it is a likewise legendary item said to allow the holder to completely bypass the law of Equivalent Exchange. It's rumored that the Stone could give its owner the ability to perform a flawless "human transmutation", thus the Elric Brothers search for the Stone, in order to gain back what they lost during the failed transmutation to bring back their mother from the dead.

In the adapted anime version, there are incomplete Philosopher's Stones called "Red Stones" or "incomplete Philosopher's Stones" which can be transmuted from a toxic liquid known as Red Water. Because it is incomplete, this stone will usually use up its power after just a few uses, sometimes backfiring on its holder. Much less expensive, and much easier to obtain than the real Stone, it can amplify the power of its holder to various extents, bypassing the law of Equivalent Exchange to a minor degree, acceptable for many practical uses.

Given its toxicity, appearance and alchemic significance in the plot, the "red water" material of the stone is probably cinnabar.

A crystallized Red Stone

The raw material of Philosopher's Stone is a very large amount of human lives, ranging from dozens to millions. The first stone in history was transmuted by "Father", using the souls of the people of Xerxes. This event inspired the legend of a country which was destroyed in a single night. The later Philosopher's Stones were transmuted by Doctor Tim Marcoh and his fellow alchemists who were instructed to make the Stones by Lust and the other Homunculi, using the lives of Ishval prisoners, and later the makers themselves to cover it up. This series of Philosopher's Stones wasn't complete - they were made from only about 13 prisoners (based on the count shown in chapter 59). The stone that Father Cornello used was also one of this series.

• A "Red Stone" can be obtained by crystallizing the highly toxic "Red Water." As the water emits highly toxic vapor that can kill over a wide area, the easiest method to crystallize it is to insert the substance into the womb of a pregnant woman, and leave it to became solid, killing the woman and the unborn fetus. Then it can be surgically removed. A slow and expensive chemical process is also possible, but the Stones created are usually very small, and not very useful.

• The real Stone takes a high toll. Only a master alchemist could transmute it, using as raw material a very large amount of human lives, ranging from thousands to millions. In the series it appears that Hohenheim used Red Water to begin the process and provide the power to generate a Stone.
  

  

  The array used in Lior to transmute a true Philosopher's Stone
  The lives of plague victims and those sentenced to death for witchcraft were transmuted by Hohenheim, and later the sacrificed lives from the Ishval and Lior Massacres were harvested by Scar and his brother to create a Philosopher's Stone. In the Fullmetal Alchemist anime history, only Hohenheim and Scar were able to perform such a terrible feat. Though Dante possessed the knowledge, she feared to do it herself as the transmutation can be fatal to the one who creates the stone. Hence the saying "those who seek the Philosopher's Stone are destined to die".

The obtained Stone is not bound to a fixed form. The first Philosopher's Stone stone transmuted by Hohenheim was shown as a glowing diamond-like stone not much larger than a tennis ball; a sort of "perfect red stone". However, Scar's arm (and before, his brother's entire body) was an Imperfect Philosopher's Stone, able to perfect itself in the armored body of Alphonse Elric, who retained his metallic appearance, only with a red glow in his inside, and glowing red marks, reminiscent of the tattoos on Scar's arm, that appeared whenever he was touched by an Alchemist or a Transmutation Circle. Even this form, due to the metal impurity that was Alphonse's body, was not a truly perfect Stone - only after Gluttony consumed Alphonse would it be perfected.

The backfiring of a Red Stone

The Philosopher's Stone has many potential uses for an alchemist. The State Alchemist Tim Marcoh researched it for the military, and was forced to turn over his research, including several vials of liquified Red Stones, to Basque Grand in order to improve the already incredible military efficiency of the State Alchemists involved in the Ishval Massacre. The stones rendered the alchemists nearly invincible, and contributed in large part to the Ishval genocide. After deserting from the military, Marcoh became a medical doctor, using the imperfect Philosopher's Stones only as a way to help the sick. It was hinted that even for those relatively unskilled in alchemy, like Father Cornello, could perform amazing feats like the transmutation of chimeras and temporary reanimation of dead animals. Scar's arm, an imperfect Stone, gave him the ability to decompose matter by alchemy and an instinctive understanding of a material's makeup.

A genuine Philosopher's Stone is capable of amazing feats, among them complete human transmutation and allowing a soul to be transferred into a new body. Such transference comes at the cost of a fraction of the alchemist's soul, and runs the risk of the new host body decomposing into a living corpse. In the manga, the Philosopher's Stone is the main ingredient in the creation of a Homunculus, while in the anime the Homunculi seek it to obtain humanity. Even a true Philosopher's Stone is not immune to Equivalent Exchange: every time it is used, a bit of it vanishes, and its power is likewise reduced.

The two types of Stone operate in the same manner. When a transmutation is performed, the matter is usually supplied by the alchemist himself. A broken radio can be reshaped into a fully functional radio, some scrap iron can build a sword, a spear, a gun, etc., but the source of the energy necessary to the process is only revealed in the final episodes. This energy is supplied by the mysterious Gate, a passage present in every human soul, linked to a second world (which is in fact our world). In the movie, the Fullmetal Alchemist world was thought to be the mystical Shamballa by the Thule Society. Every death in the second world generates energy, meaning the souls of the dead became the energy harnessed by alchemists to perform their transmutations. The Philosopher's Stone supplies an additional energy source, utilizing not the souls from the other side of the Gate, but souls collected in the alchemy world which are transmuted into the Stone. This allows amazing feats, such as human transmutation and incredible alchemic augmentation, to be performed as the souls from the stone are sacrificed as Equivalent Exchange for the desired power, effectively meaning giving up more than what one initially had. But as one uses the stone the souls used in making it are sent through the gate as energy, so over time the stone "rots" by using it.

The primary reason for seeking a stone is to ignore the principle of Equivalent Exchange. The stone supposedly bypasses this law and allows the alchemist to gain without sacrifice, but this is not the case. The Philosopher's Stone is made up of thousands if not millions of lives, and after each usage its power diminishes. The equivalent exchange for ignoring the law would be thousands of lives as represented by the stone. Minor human transmutations, such as Shou Tucker using the stone to resurrect his daughter's body, use up a percentage of the stone. Complete human transmutations, such as Alphonse bringing Edward back to life, require the consumption of the stone entirely (although it may have used all of Alphonse's body because he was an incomplete philosopher's and/or the fact that Gluttony had recently eaten a large part of his body). Therefore it can be said that (in accordance with equivalent exchange) to bring a single human back to life, the sacrifice needed is thousands/millions of lives. Conquering the ultimate truth of life (death) requires an ultimate sacrifice.

It is never explained in the anime or manga why the "equivalent exchange" of human transmutation is not one life sacrificed for one human brought back to life. One obvious theory explaining this is that one life is never equal to another, that is, a person holding a loved ones life above those a multitude of strangers. Factors that may come into play with the human transmutation is the potential of all humans,and the cost of revivifying this is unimaginable. In real science, as well, no reaction has 100% efficiency, with most 'energy' from a single human soul being wasted. The logic could be reversed so that one sacrificed human made into a stone could bring back to life thousands/millions of humans. However, given the story's anti-war perspective, it is likely that this version of "equivalent exchange" was used in order to put the sacrifice of large numbers of people in warfare in a more negative light.