How many coins in a coffer?
“How many coins in a coffer?” by David F. Godwin, Dragon #80 (Dec. 1983) & Best of Dragon, Vol. V (May 1986)
The values and weights of the various coins in the AD&D® game system are reasonably well defined, A coin of any type weighs approximately a tenth of a pound, or 1.6 ounces. But many DMs are continually faced with the problem of the volume of a large number of coins. How many coins will fit into a coffer? A chest? If a 20′-square room is filled with piles of copper pieces to an average depth of 1 foot, how much does that amount to? How big is a gold ingot weighing (or worth) 200 gp? (In the official modules, ingots crop up all the time.) Finally, the ultimate question: How many coins can you cram into a portable hole?
To solve these problems, we need to know the size of the coins. Nothing is said about the actual size in the AD&D rule books, although the Players Handbook says all the coins are “relatively” the same size and weight, (It’s a fine point, but does “relatively” mean equal with respect to one another, or approximately equal?) Having all coins of the same size and weight is very convenient, even necessary, for game purposes, but it is fundamentally an absurd idea. Platinum weighs almost 2¹⁄₂ times as much as copper, so how can coins of equal size weigh the same? And if they weigh the same, how can they be the same size?
The easiest way out is to reiterate that it’s only a game and isn’t supposed to be totally realistic. What’s realistic about fire-breathing dragons or alignment languages? How does that accord with the laws of biology and physics? There are quite a few of us out here in the boondocks who feel perfectly comfortable with basilisks, fireballs, illusions, the fact that a spell called “continual light” produces continuous light with nothing intermittent about it, and even the rule that clerics can’t use edged weapons, but who balk at the idea of a world where platinum, gold, electrum, silver, and copper all weigh precisely the same for a given volume. But even if we do arbitrarily say that all coin metals weigh the same, we are still faced with the volume question.
It would certainly be too complicated to have a different weight for each one of five coin types. Not only would that be playing “house rules poker” and give the DM a nervous breakdown, but the volume problem doesn’t come up often enough to make that the easiest solution.
One possible, halfway realistic solution is to say that all coins weigh 0.1 (¹⁄₁₀) lb. each and have a diameter of about 1¹⁄₂ inches (that of a silver dollar), but that the thickness varies according to the relative weight of the metal used.
The problem here is that having a different thickness for each coin involves computing the volume occupied by each different type of coin and applying it in each individual case. I have actually done this myself, as described further on in this article, but you would still have some fairly hairy—and unnecessary—calculations to make in order to apply the figures. The different-thickness solution summons the shunned Demon of Needless Complication.
(In the D&D® game, all coins are supposed to be about the size of a half dollar, but even a platinum piece that small would have to be ³⁄₈ inch thick to weigh a tenth of a pound.)
Another easy way out would be to say that the laws of nature as we know them don’t apply in the world(s) of AD&D gaming (for example, magic works) and all metals weigh the same. If you’re sold on the dollar coin as a standard, including thickness (1.5 millimeters), you can even say that all coin metals weigh 25% more than platinum, one of the heaviest known substances on earth! (A new Eisenhower dollar weighs 24.59 grams; a tenth of a pound is 45.36 grams.)
One more possible and not altogether reasonable solution is this: In the world of reality, we are faced with the totally unreasonable fact that light always travels at the same speed regardless of how fast you’re moving with respect to the source. The light from a distant star strikes the earth with a velocity of about 186,282 miles per second. If the earth happens to be moving toward that star at 50,000 miles per second, the light from that star still has a velocity of 186,282 with respect to the earth, not 136,282.
So, in a hypothetical AD&D world, there may be a natural law to the effect that, although coins may be of different sizes or thicknesses, it takes the same number of coins to fill a given volume regardless of the type of coin or the volume of any individual coin. We already know that the volume held by a Leomund’s secret chest varies with the level of the magic-user, regardless of the size of the chest. We can simplify matters considerably by saying that, due to the weird laws of physics in an AD&D universe—which allow magic to work—any container will hold, say, four or five coins per cubic inch, period, regardless of the size, shape, thickness, or volume of any individual coins.
Ah, but the resources of “logic” and “science” are not exhausted yet! Who said that we are dealing with pure metals? A medieval technology, even with the help of dwarves and gnomes, can certainly not attain 100% purity in its refining processes. Therefore, we can easily say that all coin metals in the AD&D world weigh the same because of impurities. Even with modern methods, it’s possible for refined gold to weigh more than refined platinum, even though pure platinum weighs about 10% more than pure gold. Of course, the impurities would have to be different from those naturally occuring on this earth, but we can always postulate substances like adamantite, mithril, or “gygaxite” to account for the fact that all refined metals wind up weighing the same and to average out the 7-to-3 weight difference between pure platinum and pure copper. (I wonder what sort of metal adamantite would be, since diamond weighs only 3¹⁄₂ grams per cubic centimeter. Very light and very hard, obviously, which accounts for its desirability.)
For that matter, there is no particular reason to insist that what we call copper (or silver, gold, etc.) is the same thing as what the inhabitants of a fantasy world call copper. Maybe it’s just copper-colored gold. . . .
Okay, so, by whatever method you want to use to explain it, all coins are the same size (diameter and thickness) and weigh a tenth of a pound each.
But what size is this size, and how many coins will fit into a given volume? The original question.
Since we’re saying that all coins weigh the same, a good starting place would be to take the average of the specific gravities of the five pure metals. The specific gravity of a substance is how much it weighs compared to water. The specific gravity of water is 1. If something weighs twice as much as the same volume of water, its specific gravity is 2, and so on. (The specific gravity of diamond is 3.51.) The system is very handy if you use metrics, because a gram is defined as the mass of 1 cubic centimeter (cc) of water under normal conditions. Therefore, the specific gravity of anything is its weight in grams per cubic centimeter. (Mass equals weight for all practical purposes, under normal conditions of temperature, pressure, etc.) The weight in grams of 1 cc (that is, the specific gravity) of each of the five coin metals is: platinum, 21.4; gold, 19.3; electrum (average of gold and silver), 14.1; silver, 10.5; and copper, 8.9. So if a copper ingot weighed 8.9 lbs., a platinum ingot of the same size would weigh 21.4 lbs.—if you were dealing with pure metals.
The average of all of these, and therefore the working specific gravity of any coin metal in our hypothetical world, is about 15, Things will wind up being simpler in the end, however, if we add a little weight to our argument now and call it 15.66. A tenth of a pound (about 45.36 grams) of any coin metal, therefore, would have a volume of 2.9 cc or 0.177 cubic inch. If the coin has the same diameter as our dollar coin, then it is 1¹⁄₂ inches (3.81 cm) in diameter. With a volume of 0.177 cubic inch, a coin would be almost exactly ¹⁄₁₀ inch thick, and you could stack 10 coins to the inch. (Now you know why we used 15.66 for specific gravity instead of 15. The lower figure would give us a thickness of 2.63 millimeters, or about ⁷⁄₆₄ inch—a harder figure to work with on a per-inch basis.)
Of course, 15.66 is 176% of the specific gravity of pure copper, and the copper metal wouldn’t be as heavy as this even if it were half platinum, even though an alloy of half copper and half osmium (the heaviest matter on earth, with a specific gravity of 22.5) would be about right. We might note here that a copper piece, if made of pure copper and only as thick as an Eisenhower dollar, would have to be more than 4¹⁄₂ inches in diameter—a tad unwieldy, but that’s how much pure copper it takes to weigh 0.1 lb.
The specific gravities of the pure, or nearly pure, metals being what they are, we could more plausibly use the idea of impurities to produce a system where 1 gp or 1 pp would weigh 1 gp, a copper or silver piece would weigh ¹⁄₂ gp, and an electrum piece would weigh ³⁄₄ gp. But again, this seems like unnecessary complication.
We now have the following data for a standard, typical coin—regardless of metallic composition—in the AD&D game:
- Weight: 0.1 lb. = 1.6 ounces = 45.36 grams
- Diameter: 1¹⁄₂ inches = 3.81 cm
- Thickness: 0.1 inch = 0.254 cm = 2.54 mm
- Volume: 0.177 cubic inch = 2.9 cc
- Specific gravity: 15.66
Now we can theorize that, because the volume of a coin is 0.177 cubic inch, a box with a volume of 177 cubic inches would hold 1,000 coins. Well, it would hold that much volume of solid metal, but not that many coins. Round coins take up the minimum amount of room if they are neatly stacked. By experiment, loose coins seem to take up about 110% as much room as the same number of stacked coins.
Knowing this, we start by determining the volume of a single coin in a stack. Because of the necessary space between individual stacks, the volume effectively occupied by that coin is the same as for a rectangular solid 1¹⁄₂″ by 1¹⁄₂″ by 0.1″, which comes out to 0.225 cubic inch. With this figure, plus the number of stacks in the container and the height of each stack, you can determine how many coins are in this well-cared-for hoard.
Now let’s assume that the treasure is found in loose form; not too many monsters take the trouble to stack their money. Since the figure for a loose coin is 110% of the effective volume of a stacked coin, the effective occupied volume of a loose coin is 110% of 0.225, or 0.2475 cubic inch. There’s nothing hard and fast about the 110% figure, so let’s round up a bit and make that 0.25 (¹⁄₄) cubic inch, and there will very conveniently be four loose coins per cubic inch.
Before further considering coffers and other hard-walled containers, let’s dispose of backpacks and sacks. By virtue of its volume, a backpack or sack can theoretically contain a lot more coins than you can actually carry in it. A backpack, for instance, supposing it to be just the right size for a standard spell book, is 16″ × 12″ × 6″ (1,152 cubic inches), pretty close to the size of a modern camping backpack. Therefore it ought to hold 4,608 loose coins, right? So what happens if you put 460+ pounds of gold in a leather backpack and pick it up (assuming you have a strength of 19 or better)? The straps come off and it comes apart at the seams! The same thing applies to saddlebags, and even more so to sacks. So how many coins can you put in these containers without damaging them? The answers are nowhere to be found in the main AD&D rule books, although it is at least implied in the illustrative example on page 225, Appendix D, of the DMG that a large sack will hold 400 gp and a small sack 100 gp. These figures are confirmed by the data in the AD&D Character Folder, which also gives 300 gp for a backpack. Nowhere is anything said about saddlebags beyond price and encumbrance, but it’s probably safe to assume 300 gp on the average, like a backpack.
Now, back to the coffer: If the dimensions happen to be 5″ by 7″ by 1¹⁄₂″, or 52¹⁄₂″ cubic inches, the coffer will hold three coin stacks one way and four stacks the other way (assuming a coin diameter of 1¹⁄₂″). That’s 12 stacks 1¹⁄₂″ high at 15 coins per stack, or 180 coins. But, since the box is 1¹⁄₂″ deep, you’ve still got room to make short stacks of coins turned sideways around the edges—three stacks ¹⁄₂″ thick (five coins each) and four stacks 1″ thick (10 coins each)—so that’s another 55 coins for a total of 235 coins. There is still an unoccupied volume of 1¹⁄₂″ by 1″ by ¹⁄₂″ in the corner, but you can’t cram even one more coin in that. This space will be occupied if the coins are loose, however, but, at four coins per cubic inch, the coffer will only hold 210 coins if they are loose instead of stacked.
How many coins will fit into a chest 18″ by 30″ by 18″? This one’s a little easier: 12 × 20 = 240 stacks, each 18″ high, with no room left over. (If the dimensions are up to you, make the horizontal measurements multiples of 1¹⁄₂″ to avoid the “coffer problem.”) The volume is 9720 cubic inches. Right away we see that the chest will hold 43,200 stacked coins or 38,880 loose coins. (Each stack has 180 coins; 180 × 240 = 43,200.)
If a 20′-by-20′ room is filled with copper pieces to an average depth of 1′, how many cp are there? (A similar problem cropped up in a module published in DRAGON Magazine some time ago.) If loose, as they almost certainly will be, there will be 2,764,800 cp, the monetary equivalent of 13,824 gp, almost enough to cover living expenses of ten 7th-level characters for two whole months—and it only weighs a little over 138 tons!
Furthermore, since that’s a volume of 400 cubic feet, you can’t even get all those copper pieces in a portable hole, which has a volume of only about 283 cubic feet. (Of course, a 10th-level magic-user could teleport home with all of it by making only 1,106 round trips.)
Which brings us to the final question: How many coins can you put in a portable hole? Such an item is 10′ deep and 6′ in diameter, for a volume of 488,580 cubic inches. We’ll consider only loose coins in this case; who’s going to stack them? At four coins per cubic inch, the answer is: 1,954,320 coins.
Ingots are another problem altogether, and send us back to specific gravity. Take an ingot that weighs 200 gp. If it is pure gold, it will have a volume of about 28²⁄₃ cubic inches, which might be 2¹⁄₂″ by 2⁷⁄₈″ by 4″. But that’s pure gold. If all coin metals weigh alike, then, under the system developed here, an ingot weighing 200 gp (20 lbs.) would have a volume of about 35¹⁄₃ cubic inches, maybe 2⁵⁄₈″ by 2⁵⁄₈″ by 5¹⁄₈″. If the specific gravity of any coin metal is, as we figured, 15.66, then it weighs 15.66 grams per cubic centimeter, which works out to about 0.035 lb./cc or about 0.566 lb. per cubic inch. Dividing 20 lbs. by 0.566 lb./cu. in., we get 35¹⁄₃ cubic inches.
If you want to be exact, you use this method of dividing by 0.566, which is the same as multiplying by 1.767. It would seem to be a heck of a lot simpler, though, just to multiply by 1.75 (1³⁄₄) to get an approximate volume, which is all you need anyway. In the case of a 20-lb. ingot, this would result in a volume of 35 cubic inches, neglecting only ¹⁄₃ cubic inch—which ain’t much when you divide it up between three dimensions.
Just for information, here are some data I’ve compiled for the system of different coin thicknesses (all diameters are 1¹⁄₂″, all weights 0.1 lb.) for the pure metals. This system is much too complicated for game use, but might be of interest to somebody. The figures do show how the system of “all coin metals weigh the same due to impurities” as outlined here serves as a workable compromise among the actual pure metals involved.
| Metal | Specific gravity |
lbs. cu. in. |
Coin Volume | Thickness | ||
|---|---|---|---|---|---|---|
| cc | cu. in. | mm | in. | |||
| Platinum | 21.40 | 0.784 | 2.12 | 0.129 | 1.80 | 0.073 |
| Gold | 19.30 | 0.697 | 2.35 | 0.143 | 2.10 | 0.081 |
| Silver | 10.50 | 0.376 | 4.32 | 0.264 | 3.80 | 0.149 |
| Copper | 8.90 | 0.300 | 5.10 | 0.311 | 4.50 | 0.176 |
| Universal | 15.66 | 0.566 | 2.90 | 0.177 | 2.50 | 0.100 |
| Dollar | 14.40 | 0.520 | 1.71 | 0.104 | 1.50 | 0.059 |
“Universal” is the common coin metal we’ve worked out in this article, included for comparison. Also included for comparison is “Dollar”—the U.S. Eisenhower dollar coin. Its specific gravity looks pretty good; why not use it? Well, to begin with, it only weighs 24.59 grams (0.054 lbs.), about half as much as we need. Of course, it could be used as a base if you want to make it twice as thick, but then we don’t get nice, neat little figures like four coins per cubic inch, or 10 coins in a 1″ stack. (The Eisenhower dollar is, of course, a “clad” coin, not one homogeneous metal.)
Ambitious DMs who really get off on mathematical calculation might conceivably want to use the “different-thickness” method, but I’ll let them figure out how many coins in a 1″ stack and the effective occupied space of a loose coin for each different metal. I confess I have already figured it out and have the data, but I fear the editor would balk at including it. [You’re right, David. —Editor] Besides, it’s much easier to say all coins stack 10 to the inch, will occupy a given volume at four coins per cubic inch if loose, and measure 1¹⁄₂″ in diameter by ¹⁄₁₀″ thick, and that you multiply by 1.75 to get the volume in cubic inches of a certain number of pounds of solid metal.
But please don’t ask me about gems!
Notes
Pure gold and silver are too soft to make good circulating coins (they will loose weight and detail over time from rubbing or manipulation); thus gold and silver coin metals are usually alloyed with a small amount of copper to improve hardness.
The actual volume of a typical coin is ∼80% of its area × thickness due to the relief of the obverse and reverse designs.
| 2.42 5 Boron |
2.267 6 Carbon | |||
| 2.70 13 Aluminium |
2.329 14 Silicon | |||
| 8.908 28 Nickel |
8.96 29 Copper |
7.14 30 Zinc |
5.91 31 Gallium |
5.323 32 Germanium |
| 12.023 46 Palladium |
10.49 47 Silver |
8.65 48 Cadmium |
7.31 49 Indium |
7.265 50 Tin |
| 21.45 78 Platinum |
19.32 79 Gold |
13.53 80 Mercury |
11.85 81 Thallium |
11.34 82 Lead |
| Coin metal | g/cm³ | lb/in³ | Hrd. | Notes | |||
|---|---|---|---|---|---|---|---|
| platinum | 21.45 | 0.775 | 48 | ||||
| gold | 19.32 | 0.698 | 20 | ||||
| “crown gold” | 17.62 | 0.637 | ²²⁄₂₄ Au | ²⁄₂₄ Cu | UK (1526) | ||
| “standard gold” | 17.76 | 0.642 | ²²⁄₂₄ Au | ≤ ¹⁄₂₄ Ag | ≥ ¹⁄₂₄ Cu | US (1795) | |
| “standard gold” | 17.47 | 0.631 | .8992 Au | ≤ .0504 Ag | ≥ .0504 Cu | US (1834) | |
| “fine gold” | 17.32 | 0.626 | .900 Au | .100 Cu | US (1837) | ||
| electrum (AD&D) | 13.39 | 0.484 | ⁹⁄₁₉ Au | ¹⁰⁄₁₉ Ag | = ¹⁄₂ gold’s value | ||
| coin electrum | 12.87 | 0.465 | ⁹⁄₁₉ Au | ¹⁰⁄₁₉ Ag | (for 1 gp = 20 sp) | ||
| electrum (d20) | 13.16 | 0.476 | ⁴⁄₉ Au | ⁵⁄₉ Ag | = ¹⁄₂ gold’s value | ||
| coin electrum | 12.68 | 0.458 | ⁴⁄₉ Au | ⁵⁄₉ Ag | (for 1 gp = 10 sp) | ||
| palladium | 12.02 | 0.434 | 50 | (a natural numismatic “electrum”, if it wasn’t so rare) | |||
| silver | 10.49 | 0.379 | 25 | ||||
| sterling silver | 10.35 | 0.374 | 70 | 11 oz.t. 2¹⁄₄ dwt. Ag | 17³⁄₄ dwt. coin bronze | ||
| sterling silver | 10.36 | 0.374 | 70 | 11 oz.t. 2¹⁄₄ dwt. Ag | 17³⁄₄ dwt. cupronickel | ||
| copper | 8.96 | 0.324 | 35 | ||||
| coin bronze | 8.87 | 0.321 | 60 | ²³⁄₂₄ Cu | ¹⁄₂₄ tin | ||
| nickel | 8.91 | 0.322 | 65 | ||||
| cupronickel | 8.95 | 0.323 | 85 | ³⁄₄ Cu | ¹⁄₄ Ni | ||
D&D coins
1974–’88
- Weight
- oD&D: “Weight of a man - - 1,750”, “Weight: 1 Coin (Copper, Silver, or Gold) - - 1”(M&M-15)
- AD&D: “The conversion ratio of gold pieces to pounds of weight is 10 to 1.”(PHB-9) “…the size and weight of each coin is relatively equal to each other coin, regardless of type.”(PHB-35)
- BD&D: “All coins are about equal in size and weight. Each coin weighs about 1/10 of a pound.”(RC-226)
- ¹⁄₁₀ lb. = 700 gr. = 1.6 oz. = 1¹¹⁄₂₄ oz. troy ≈ 45359 mg
- Volume
- AD&D: “…assume 4,000 g.p. are equal to a cubic foot for purposes of this spell.” (fool’s gold)(PHB-70)
- Context implies a ft³ of metal yields 4000 coins (not that a ft³ hold’s 4,000 loose coins) and thus that coin gold is ≈0.23 lb/in³ (6.4 g/㎝³). This is ≈1⁄3 the density of real gold, and ≈72% of the density of real copper.
1989—
- 2nd: “…10 cubic inches…, equal to about 150 gold coins.” (fool’s gold)(PHB-141)(PHB-183)
- Context implies that standard coins have a 1⁄15-in³ metal volume. They would be ≈21.5 to the pound if pure gold, and ≈23.6 to the pound if crown gold.
- Allowing for typical design relief (∼80%), they could be ∼1⁄15″×⌀1.25″ or ∼1⁄10″×⌀1″ or ∼1⁄13.7″×⌀30.6㎜.
- 2nd: “Coins (regardless of metal) normally weigh in at 50 to the pound.”(DMG-134)(DMG-181)
- 3rd: “The standard coin weighs about a third of an ounce (fifty to the pound). It is the exact size of [a ⌀30.6㎜ half-dollar] the coin pictured in the illustration on page 146.”(PHB-96) “… page 168.”(PHB-112)
- 4th: “A coin is about an inch across, and weighs about a third of an ounce (50 coins to the pound).”(PHB-212)
- 5th: “A standard coin weighs about a third of an ounce, so fifty coins weight a pound.”(PHB-143)
- ¹⁄₅₀ lb. = 140 gr. = .32 oz. = ⁷⁄₂₄ oz. troy ≈ 9072 mg
- “A typical coin measures slightly more than an inch in diameter and is approximately one-tenth of an inch thick. A cubic foot (a volume 1 foot on each side) holds around 12,000 loosely stacked coins.”(Draconomicon-278)
- This puts D&D coin diameter between 1.1″ and 1.2″, and fits the 1.1284″ diameter of a one-square-inch area coin.
- For unstacked coins, assume a cubic foot holds around 10,500 coins (6/in³).
| in² | ㎜² | in | ㎜ | notes | |
|---|---|---|---|---|---|
| A = 1 in² | 1 | 645.2 | 1.128 | 28.66 | |
| ⌀ = 1.2″ | 1.131 | 729.7 | 1.2 | 30.48 | |
| ⌀ = 1⁄2$ | 1.140 | 735.9 | 1.205 | 30.61 | 2.15㎜ (∼1⁄12″) thick |
| gr. | dwt. | oz. | oz.t | №/lb.t | №/lb. | g | |
|---|---|---|---|---|---|---|---|
| dwt. | 24 | 1 | 0.055 | 1⁄20 | 240 | 291 2⁄3 | 1.555 173 84 |
| d20 coin | 140 | 5 5⁄6 | 0.32 | 7⁄24 | 41 1⁄7 | 50 | 9.071 847 4 |
| d20 coin | 144 | 6 | 0.329 | 0.3 | 40 | 48.61 | 9.331 043 04 |
| oz. | 437 1⁄2 | 18 11⁄48 | 1 | 0.911 | 13.17 | 16 | 28.349 523 125 |
| oz.t | 480 | 20 | 1.097 | 1 | 12 | 14.58 | 31.103 476 8 |
| AD&D coin | 700 | 29 1⁄6 | 1.6 | 1 11⁄24 | 8.23 | 10 | 45.359 237 |
| lb.t | 5760 | 240 | 13.166 | 12 | 1 | 7000⁄5760 | 373.241 721 6 |
| lb. | 7000 | 291 2⁄3 | 16 | 14 7⁄12 | 5760⁄7000 | 1 | 453.592 37 |
See also
- “Fantasy World Eeconomics 101: Introduction” by Dimitris Romeo Havlidis (2015 April 10)
- Gold Piece (Dungeons & Dragons Wiki)
- Currency (Forgotten Realms Wiki)
- Coinage
