How many copper coins fit inside a cubic foot?

Question

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?

Answer 1

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.

What if you melt the coins together?

You could try some scheme that involves melting the copper coins into a single solid piece of copper and then transmuting that into silver, or even just starting with a solid block of some other mundane substance. This would indeed allow you to transmute the entire mass into a single piece of silver, but you've defeated the purpose of using coins in the first place. You want to have the silver in the form of coins because merchants tend to accept coins without inspecting them too closely, under the assumption that coins are relatively difficult to counterfeit. Not to mention that coins are convenient and easy to carry. If you lug a single several-hundred-pound bar of silver around and try to pay a merchant with it, you're going to get a lot more raised eyebrows, and more importantly, a lot more questions you can't answer without rolling a deception check. It's certainly not impossible to pull off, especially since you can afford to take a "loss" on the value of the silver and still make a profit, but it's a different sort of problem than counterfeiting silver coins.

Answer 2

• 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.

Answer 3

27,950 coins

A quick google "weight of a cubic foot of copper" showed 559 lbs.

If 50 coins = 1 lb, then 559lbs = 27,950 coins

"But what about shape/gaps???"

You don't want silver coins with copper coin markings. You also don't want to try transmuting ~28,000 separate objects. You'll need to find a way to melt it down into a solid block, and sell it as raw material.

Ironically, you could sell the block for legitimate silver coins, which you don't need to hold a transmutation spell on.

Final note—you will probably never reach an inventory of 28,000 coins, nor will you be able to easily sell 650 lbs of silver (which is what a cubic foot of silver weighs), so you don't need to worry about weight and size for this strategy. The problems are more:

1. How do we melt the copper coins?
2. How do we sell the silver, get back on ship, set sail, and get out of the harbor before the transmutation runs out?
3. How do we keep ahead of news of a transmutation scam?

Answer 4

It depends what "a cubic foot of coins" means.

• If it means that the volume of the coins alone is one cubic foot – i.e., the quantity of coins you'd get by making one cubic foot of copper into coins – then a cubic foot of copper is 559lbs and that times fifty coins per pound is 27 950 coins.

• If it means "as many coins as you can fit in this one-cubic-foot box", then we should fill the box with stacks of coins arranged in hexagons, like this,
  
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  which is optimal if we ignore effects around the edge of the box. That covers about 91% of the base, so the volume of the coins is about 91% of a cubic foot, giving about 25 400 coins.