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Physical coins are fun.
Advanced Dungeons & Dragons, in its first edition, is famous for its heavy coins. Each has a weight of a full tenth of a pound, or 1.6 ounces for each coin! In the second edition, this was changed to 50 coins to the pound, which is better. Though still pretty heavy compared to average historical coinage, it is within the typical coin weight range.
For most purposes, either one of these is fine. The heavy coins make figuring weight carried easier (so easy, in fact, that all weights were scaled to the coin, with each "gold piece weight" being equal to a tenth of a pound*; simply divide the number of "gold piece weight" units carried by ten to get the weight in pounds), while the later coins made for a reasonable compromise.
In Dragon magazine issue #80, an author named David F. Godwin provided an article titled "How Many Coins in that Coffer?", which proposed to work out volumes taken up by coins so that chests and other boxes of coins (not to mention magic items that were given volumes but not weight limits) could be appropriately evaluated. The article details the math and physics, but the upshot is that, if you don't want to go into detail, the large coins can be assumed to take up 0.25 cubic inches each, loosely arranged, or put another way a box can hold up to 4 loosely packed coins per cubic inch. Also, coins are about an inch and a half across, and about 1.5mm thick. The author makes the assumption that all of the metals are alloyed to have a similar specific gravity for simplicity. The article was written long before the arrival of the second edition, so it didn't include the math for the lighter coins, but it works out simply to divide the volume of the coins by 5 (0.05 cubic inches per coin) or multiply the number of coins per volume by 5, so 20 of those coins per cubic inch. That is certainly the easiest way to handle the matter.
For those who aren't interested in an array of artificial alloys that make everything easier, I have worked out more detailed numbers for the AD&D coins, but trust me that you probably don't really want to use them. Still, here they are. The assumptions are that loosely stacked coins take up 10% more volume on average than neatly stacked ones, which is based on the article referred above, and that neatly stacked coins take up a number of cubic inches equal to their diameter squared times their thickness. Note that coins are given diameter and thickness in millimeters, but volumes are converted to cubic inches. I'll be using the normal abbreviations for the coin types, which are: PP for Platinum Pieces, GP for Gold Pieces, EP for Electrum Pieces, SP for Silver Pieces, and CP for Copper Pieces. The metals were worked out as 90% pure, with the alloys being: Platinum 90%/Silver 10%, Gold 90%/Copper 10%, Gold 45%/Silver 45%/Copper 10% (Electrum), Silver 90%/Copper 10%, Copper 90%/Zinc 10%. The difference of using Copper 90%/Tin 10% (or Bronze) is so small as to make effectvely no difference, about 0.2% greater specific gravity, so you could do that if you preferred.
Given those assumptions, the heavy coins are as follows:
PP: 37.73mm diameter x 2mm thick
GP: 40.87mm diameter x 2mm thick
EP: 44.94mm diameter x 2mm thick
SP: 52.92mm diameter x 2mm thick
CP: 57.58mm diameter x 2mm thick
Note that the silver and copper coins have gotten very large in diameter, over 2", so it is possible to make them 3mm thick instead, which makes the SP 43.21mm in diameter and the CP 47.01mm in diameter. This has no appreciable effect on the volume of the coins.
Loose coins per cubic inch/Cubic inches per loose coin
If instead you prefer the lighter coins that weigh 1 pound per 50 coins, those sizes and numbers are:
PP: 19.49mm diameter x 1.5mm thick
GP: 21.10mm diameter x 1.5mm thick
EP: 23.21mm diameter x 1.5mm thick
SP: 27.33mm diameter x 1.5mm thick
CP: 29.73mm diameter x 1.5mm thick
Cubic inches per loose coin/Loose coins per cubic inch
But again, it would be much simpler to simply assume that each coin has an equivalent weight and volume due to the array of alloys used, and allow exactly 4 or 20 coins per cubic inch of storage space. If your coins have another ratio to pounds, then simply multiply the volume appropriately. For example, if you have 100 coins per pound, then allow twice as many as the 50 coins per pound number, or 40 coins per cubic inch. My historical £sd coins, of which the pennies are approximately 300 per pound, would have 60 coins to the cubic inch (yes, they are tiny, just as the historical Tower pound pennies were, at 240 pence to the Tower pound; as you can see at the original article on my blog**, the silver pennies are 14.73mm in diameter and 1.28mm thick, while the larger Gold Crowns measure 17.55mm diameter by 1.5mm thick), which seems odd, but is because the specific gravity of silver is not the same as the specific gravity of the "Universal Alloy" used in the referenced article.
*In fact, in the "basic" D&D line (B/X, BECMI, Cyclopedia), weights were simply called "coins", keeping the same tenth of a pound per coin ratio.
**I am going to have to re-figure a lot of that article, as I never accounted for impure metal and all of those sizes and weights are based on pure silver, copper, and gold. I can get away with simply multiplying the diameters by the square root of the ratios of the specific gravities of the pure metals to the impure alloys (I think; right now figuring the math in my head is giving me a headache so I'll work it out in detail later). I never did figure the volume of the coins, either, but I was figuring on abstracting specific volumes to the stone/item weight categories, which was a feature of the encumbrance system I was planning.