Gfyuki

I have a Wizard who is level 5, currently running in a pirate campaign (homebrew), and I thought about some scams I could pull to earn the ship some extra coinage whenever we touched port to resupply or whatever. I have the School of Transmutation, and I was thinking of turning copper coins into silver ones using Minor Alchemy.
In the Player's Handbook it states that I can take a cubic foot of non-magical material and transform it into a different listed substance (wood, stone, iron, copper, silver).

Now, I talked to the DM and he said that that would be acceptable, as long as I do not abuse it. At later levels, I might (if this works, and assuming the DM approves) take it up a notch, like copper coins to gold coins.

However, we got to talking: just how many copper coins would it take to make a cubic foot? We know that 50 coins equal a pound, but... That is about it.

Is there any official rulings that I am missing or something really obvious I am overlooking?

You can only transmute one coin at a time

Other answers have given you good estimates of the number of coins that will fit in a cubic foot, but that doesn't matter for your purposes, because you're missing an important limitation of the Minor Alchemy feature: you can only transmute one object at a time:

Starting at 2nd level when you select this school, you can temporarily alter the physical properties of one nonmagical object, [...] After 1 hour, or until you lose your concentration (as if you were concentrating on a spell), the material reverts to its original substance.

So you can't transmute a pile of coins all at once. You can spend 10 minutes transmuting a single coin, but as soon as you transmute a second one, you will lose concentration on the first one, causing it to revert.

• Copper is 8.96 g per cm^3. That means a copper ingot with one cubic feet volume is 559 lbs.


• A heap of copper coins is no solid ingot. As a first approximation, imagine there are stacks of cylinders. A cylinder 1" high and 1" in diameter has a volume of 0.78 cubic inches. (A coin is flatter, but think of it as stacks of a dozen or so.) That means the heap is 436 lbs.


• 436 lbs. of coins are 21,800 copper pieces. Call it 20,000 because they won't be stacked and aligned perfectly.

But there is a problem. This scheme will yield silver coins with the image of a copper coin. Everybody would suspect that it is a copper coin coated with a thin silver layer. Much smarter to take a mixed heap of copper goods and to transform them. This could include a few ingots, but also copper kettles and the like. Well, perhaps not copper roof slates, because nobody has silver roof slates.

We can solve this with MATH.

The density of copper is about 9 g/ml, so a cubic foot of solid copper is about 550 pounds, or 27,500 coins.

If the coins are a uniform size and you stack them, then push the stacks tightly together, the packing factor is the same as for circles in a plane, about 90%. This gives you about 25,000 coins.

If you have a giant sack of loose change, the packing factor is somewhere in the vicinity of 0.6, for about 16,000 coins.