A transmutation circle is an alchemical tool used to cause the transformation of materials into something else, such as mixing tin and copper to make bronze or turn lead into gold, using only drawings and material sources.  
All transmutation circles are based around a circle drawn or printed as perfectly as possible with overlaid lines, circles, and symbols to guide the reaction. Circles can be as small or big as the alchemist desires, depending on their purposes. Line thickness in a circle can indicate the strength of what the lines represent in relation to the other lines.
Area of Effect
Keeping all focal lines within the circle (touching the edges) will keep the reaction contained by the circle, though buffers may be needed to ensure this.
Allowing the focal lines to intersect the circle doesn't contain the reaction at all, which will cause it to go out to the edges of the surface on which it's drawn.
Adding extra unclosed focal lines intersecting the circle but not part of the primary elemental array will cause the reaction to go in the direction the lines point.
Some reactions require some form of extra energy or fuel, which can be provided in two ways: via consumption plexes or conduits.
Consumption plexes (pictured at right) are smaller circles which break the main circle, and are meant to be used to provide a reaction with material fuel if necessary. Materials used by these are often contained by the product but are irreversibly altered.
Conduits, also known as "external rings" or "power nodes", are smaller circles outside of the main circle connected via drawn "tubes" which are meant to convert matter into pure energy to fuel the reaction. Materials used by these are unrecoverable.
Transmutation circles have 12 basic crucible "circles", which act as instructions which drive the nature of the reaction. These are:
- Fire - Melting and fusing.
- Water - Any fluids.
- Air - Breathing and activation.
- Earth - Stone and metal.
- Creation - Making things out of raw materials.
- Terra - Soil, fertility, and life manipulation.
- Heva - Soul and spirit transmutation.
- Meta - Transmutations with multiple materials.
- Strucota - Precisely manipulating materials.
- Flame - Purification and destruction.
- Death - Decrease motion to "absolute zero" without freezing.
- Life - Increase or instill motion.
Bracing is the addition of extra circles or writing to produce better protection and stability for the circle. These can come in three forms:
Holding braces are additional circular lines around the main circle optionally with text inscribed between lines which are primarily for stabilizing the circle and its protection. Writing in holding braces can serve three purposes: telling someone else how to use the circle, act as a non-spoken incantation, or simply as a decoration and misdirection to keep others from using it.
Focusing braces are semicircles added to the inside of the main circle to bounce materials back into the center to focus the reaction.
Redirecting braces move the materials around in particular ways, which can help get the right result from a reaction.
Transmutation circles can be hand drawn or digitally printed, though there's extra nuance to hand drawn versions. They should be drawn in a clockwise direction starting from the rightmost point using organic or transorganic (inorganic but made from once-organic materials) drawing utensils, like squid's ink or chalk.
In Popular Media
Full Metal Alchemist is one of the most known well known popular depictions of using alchemy circles. They can also be found in some episodes of Supernatural.