The Art of Mathematical Transmutative Alchemy

Foreward: Tramsutation is the art and science of mathematical potential energy transference. The underlying principle is that potential energy exists in every element regardless of the form, and a series of mathematical principles can be used to create a formulaic expression which transmutes the potential energy of one substance into another. While this transmutation does not require a magical focus, it does require a symbol drawn on the element which is an expression of a mathematical equation resolving the potential energy transference.

The Transmutation Process

Alchemy is accomplished with the Craft (Alchemy) skill with a base DC of 30.

The Focus Symbol

While understanding the potential energy exchange is important, a focus must be used to express the mathematical principles by which the alchemist transmutes his substance. This is done by drawing a Focus Symbol on the substance. The Focus Symbol is typically a circle that represents the mathematical process of reconfiguring potential energy into another substance. These symbols are almost always circles since the equation itself is usually circular. The Focus Symbol can be drawn in any mundane material, from chalk to ink. The alchemist may also use his own blood to draw the Focus Symbol which enhances the alchemical process since the alchemist is introducing even more increased potential energy into the equation, contained within his own blood. A Focus Symbol drawn in blood also helps the alchemist transmute the substance by virtue of the sympathetic connection he has with his own life force and the leniency of converting potential energy since his blood introduces more of it into the equation. For every 5 points of the DC, the Alchemist bleeds 1 hit point to draw the appropriate Focus Symbol. For every hit point used to draw the Focus Symbol, the alchemist receives a +1 circumstantial modifier to his Craft (Alchemy) check. Drawing the Focus Symbol requires 1 minute per 5 points of the DC.

The Alchemist may attempt to transmute up to 10 times the DC of the Transmutation check in pounds.

Transmutation Variables

A few different variables factor into the equation and augment the DC of the Craft (Alchemy) check accordingly.

Value: Determine the value of the item being transmuted per pound to the nearest whole coins divisible by 5. For example, something that costs 15 copper per pound would be rounded to 10 copper which is then converted to 1 silver. 35 copper would be rounded to 50 copper which is then converted to 5 silver. (So our increments are 1 or 5 coins for every tier [cp, sp, gp, etc]). Typically prices per pound are more agreeable, such as 5pp / pound for Gold or 5cp / pound for wheat, but the instructions above should help with any abnormalities.

Base DC: To determine the base DC of the Craft Alchemy roll, start with the base difficulty for each tier which is 10 per step increase in coinage. The following prices represent the average value per pound of a substance. Therefore, 1cp is DC 30, 1sp is DC 40, 1gp is DC 50, and 1pp is DC 60. If the coin value is in 5s, add 5 to this number. For example, 5cp is DC 35, 5sp is DC 45, 5gp is DC 55, and 5pp is DC 65. Values exist above these DCs and are limited only by the skill of the Alchemist.

Target DC: After figuring the base DC, the Alchemist can choose a more dangerous transmutation formula to attempt to create more of one substance from another. This process involves drawing on the potential energy that makes up the cosmic universe and is extremely difficult. The Alchemist may raise the difficulty in increments of 5 for various effects:

• Increase the weight of substance transmuted

As an added bonus, attempting a more difficult transmutation typically results in a more profitable transmutation.

Constant: In order to determine the total amount made from the transmutation, there is a Constant that needs to be determined. In order to determine the Constant, take the DC of the roll and divide it by the number of coins in the price per pound. For example, 5gp has a constant of 11 (DC 55 / 5) while 1sp has a constant of 40 (DC 40 / 1). We’ll use this number later to determine the final value of the transmutation.

Final Value

To determine the final value of the alchemy check, the character rolls a Craft (Alchemy). If the check meets or exceeds the Target DC, the character successfully transmutes the substance. If the character fails, he is subject to backlash (described below). To determine the value of the successful transmutation, multiply the check result by the Target DC. Then, take this number and divide it by the (Base DC x constant). The formula looks like this:

Craft (Alchemy) Result x Target DC
Base DC x Constant

Finally, take this number and multiply it by the number of pounds originally transmuted to determine the total value of the new substance (rounded to the nearest coin). To determine how many pounds of the substance are created, simply divide the total value of the new substance by its price per pound.


Alchemy is, of course, a very dangerous process. Even a minor miscalculation in the transmutation equation can cause disastrous effects for the Alchemist since a miscalculation in the transmutation of energy results in the potential energy rebounding on the alchemist. If the alchemist fails to meet the determined Target DC, he suffers 1d6 points of damage per 5 points of the Target DC. Note that it doesn’t matter if the alchemist fails by 1 or 100, failure results in the complete rebound of the potential energy and destroys the substance the alchemist was attempting to transmute.

Putting It All Together

Example 1 : Basic Transmutation
Cainan wants to transmute 15 pounds of wheat into gold. His Base DC is 35 for the Craft (Alchemy) check since wheat is valued at 5cp per pound. He will not be increasing the weight or decreasing the time, meaning his Target DC is also 25. Cainan has a bonus of +21 and rolls a 14 for a total value of 35, the exact Target DC of the transmutation. He multiplies the check (35) by the Target DC (35) to get 1225, then divides this number by the Base DC (35) times the constant. The constant is 35 (the Base DC) divided by the number of coins in the per pound value (5), which is 7. The divisor then becomes the Base DC (35) times the constant (7), or 245. So, the net result (1225) divided by the divisor (245) is 5. Now we take the final result (5) and multiply it by the number of pounds transmuted (15) to determine the final value of the completed transmutation, 75 copper pieces. Since gold is worth 50gp per pound, or 5,000cp per pound, we discover Cainan creates 0.015 pounds of gold. The speck of gold is unfortunately not even enough to create a single coin with. Notice that since he hit the DC exactly, the wheat used up and the gold produced are the exact same net worth.

Helpful Tables

Common Densities:
Wood (Ash avg) : 46 lbs / ft3
Water : 62 lbs / ft3
Dirt : 120 lbs / ft3
Iron : 491 lbs / ft3
Copper : 559 lbs / ft3
Silver : 655 lbs / ft3
Gold : 1,206 lbs / ft3
Platinum : 1,340 lbs / ft3


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