Coin Weights Using Math!!!!

[aaronpark]

so I decided to figure out the size and value of various coins in the Pathfinder world. I used the base copper, silver, gold and platinum coins where 10 copper = 10 silver = 100 gold = 1000 platinum. I used modern day values (I couldn't find a source for medieval or renaissance values of these metals) and the densities of the metals to find how big each coin is. I did this twice with once being a standard 1 oz gold coin and the other with 50 gold per pound.

If anyone has any idea how to put a chart in to here, let me know as I have no idea

Copper Silver Gold Platinum
$/Oz 0.1875 20.87 1315.1 1,428
Relative value 1/100 1/10 1 10
Dollars/coin 13.151 131.51 1315.1 13151
Oz/Coin 70.13866667 6.301389554 1 9.209383754

I made a picture to see easier

So by this scale the most efficient coin is indeed the platinum coin as it has 10 times the value of a gold coin but only 9 times the weight and copper coins would have to be over 4 pounds each.

Copper Silver Gold Platinum
$/Oz 0.1875 20.87 1315.1 1,428
Relative value 0.0032 0.032 0.32 3.2
Dollars/coin 4.20832 42.0832 420.832 4208.32
Oz/Coin 22.44437333 2.016444657 0.32 2.947002801

Same relative scale but the copper coin would still be able to substitute a bludgeoning weapon.

If anyone knows a relative value scale from the middle ages or renaissance, I will try to update this

[Lucio]

You might want to correct your relation expression, you've used the correct fractions on the chart, by expressing them as fractions (or multiple) of a GP.

1000cp = 100sp = 10gp = 1pp

You're also missing a rather key point on money, even in the real world, a penny coin costs MORE than 1p to produce, and may even be worth more than 1 penny if you were to buy the base metals. The same applies to other coins, they can be worth more or less than the actual metal they're made from. Their value stems from the fact that they're a coin, marked in a special way, that people agree has a "fixed" value within their society.

So no, a copper piece in the game doesn't have to weigh 4lbs, it has to simply be the correct size, weight and marked in a way that people recognise it to be a copper piece.

[Sissyl]

.... Except there was no fixed exchange between the coin types back then. That is a far more recent development. In at least afew cases, the different types of coin were used by different classes of people. Demand varied by what types of job were paid for by what type of coin. Supply varied depending on the currently active mines in the country, all factors that made coins a severe headache back in the day.

[Ashiel]

In Pathfinder, 50 coins = 1 lb., regardless of type. This is why I've always explained that you can't just use prestidigitation to make copper look like platinum and rip people off. They're differently sized coins with different weights, minted in such a way that 50 of them always equals 1 lb. of material (which also means shaving them will show dubious results).

[Chemlak]

I did the maths on this a little while ago (I'll have to look up the results) assuming that all coins are approx 5mm in diameter (about the size of a UK 5p), which means that only the thickness varies. A pp is about 1.5mm thick, and a copper piece somewhere about 3.6, IIRC. It's quite an interesting exercise: I'll pull out my full final results later and post them.

[pachristian]

Relative value scale from medieval or renaissance:

Values are hard to estimate, due to the fact that values of the base metal varied over time and location. We're talking about a thousand years of history here! So, we'll oversimplify.

The roman denarius was a 'standard value'. It was initially 4.5 grams of nearly purse silver (~100 lb). It became the English silver penny (which varied in size, but by the medieval period you could say ~1.7 grams ~260/lb), as well as the Byzantine Miliaresion, and Arabic Dirham (both of which were about 3 grams ~150/lb). Although these medieval prices really don't correspond to modern prices, you could say that one of any these coins was worth about U.S.$20 to $30 in buying power.

Note that there was just more silver and gold in the east than the west.

A gold piece - English shilling, French sou, Roman (and Byzantine) solidus, and Arabic Dinar, was worth 20 silver. So, about $500 to $600. It was a slightly heavier coin - about 2 grams in the west (~200+ per lb), and about 4.3 grams in the east (~110/lb.).

Copper coins did not really exist. A simplified historic ratio of the value of copper to silver is 100 copper = 1 silver. Romans (and Byzantines produced coins that were described as "bronze" but were actually copper with a small amount of silver added. 25 Byzantine Follis made up a miliaresion. This gives a follis a buying value of about ~$1. The follis ranged in size, but ~9 grams is reasonable for the 9th century.

In fact, this tendency to alloy makes game coinage possible. Instead of being pure copper, silver, or gold, you have alloy coins.

Platinum coinage simply did not exist. Platinum is a very hard to work metal, and platinum-working capability did not come into existance until after the medieval period. In fact, Spanish Conquistadores abandoned two gold mines in Central America because of their high platinum content! I hate to say “we use magic” because that puts so much reliance on magic as technology.

So in game terms:
Coin value Size
Copper ~ $0.25 150/lb.
Alloy (Cu/Ag) ~ $2.5 150/lb.
Silver ~ $25 150/lb.
Gold ~$250 200/lb.
Platinum?

Here's the website where I got my primary information: http://www.luminarium.org/medlit/medprice.htm

Also check out:
http://web.mit.edu/21h.416/www/

[pachristian]

Of course, to be fair about all this.

When I'm running Pathfinder in Golarion, I use 50 coins/lb., and tell the players that a copper piece is roughly $.5, a silver piece $5, a gold piece $50, and a platinum piece $500.

While I like using historic settings, with appropriate details, it's often more trouble than it's worth.

[Googleshng]

Ashiel wrote:

In Pathfinder, 50 coins = 1 lb., regardless of type. This is why I've always explained that you can't just use prestidigitation to make copper look like platinum and rip people off. They're differently sized coins with different weights, minted in such a way that 50 of them always equals 1 lb. of material (which also means shaving them will show dubious results).

Well no, they'd all be the same weight. If 50 coins stacked up weigh 1 lb. each individual coin has to weight 0.02 lbs. Different volume, sure, some might be noticeably bigger than others. Different styling, absolutely, some maybe octagonal, some maybe with various sized and shaped holes. The weight's a fixed standard though. It's the whole pound of feathers vs. a pound of bricks thing.

[Torchlyte]

Googleshng wrote:

Ashiel wrote:

In Pathfinder, 50 coins = 1 lb., regardless of type. This is why I've always explained that you can't just use prestidigitation to make copper look like platinum and rip people off. They're differently sized coins with different weights, minted in such a way that 50 of them always equals 1 lb. of material (which also means shaving them will show dubious results).

Well no, they'd all be the same weight. If 50 coins stacked up weigh 1 lb. each individual coin has to weight 0.02 lbs. Different volume, sure, some might be noticeably bigger than others. Different styling, absolutely, some maybe octagonal, some maybe with various sized and shaped holes. The weight's a fixed standard though. It's the whole pound of feathers vs. a pound of bricks thing.

I wonder if he meant the weight/volume ratio of the metals were different, since he seemed to get that sizes were different and total weights were the same.

[Kazaan]

If you have mass and density, you can derive volume at least.

Copper: 8.96 g/cc
Silver: 10.49
Gold: 19.30
Plat: 21.45

1 g ~ 0.0022 lbs

So one coin, of any metal, weighs about 9.091 grams.

Volumes
Copper: 1.01 cc
Silver: 0.8666 cc
Gold: 0.4710 cc
Plat: 0.4238 cc

This means that the coins get progressively smaller with greater value with a gold coin being less than half the size of a copper piece. But value is typically directly associated with size (people see a bigger coin and automatically think greater value) so it makes sense that thickness was used to modulate the surface area such that coppers and silvers were probably pretty close to the same size with gold and plat being progressively thinner but also larger on the face. A US penny is about 1 mm thick while a quarter is about 1.5mm so lets say a Pathfinder copper piece is about 1 mm thick.

Copper: 10.1 mm^3; 1 mm thick x 3.59 mm across... even at only 1 millimeter thick (the thickness of a real-life US penny), a Pathfinder copper piece would only be three and a half millimeters across. Even a Euro penny has a diameter of 16.25 mm and is thicker to boot. So a Euro penny is 4.5 times the diameter and 50% thicker than a pathfinder penny. If you wanted to make a pathfinder penny 16 mm across, the thickness would drop to 0.0502 mm or half a freakin micrometer. That's not a coin, it's a piece of copper foil. So, even from the very get-go, while you could theoretically calculate the size of a pathfinder coin, the results you get are totally ridiculous because, remember, if a copper coin either has to be a quarter the diameter of a Euro 1 cent or foil-thin, a platinum coin is less than half the volume!!! A Platinum piece the same with as a Euro penny would be a quarter of a micrometer thick or, if 1 mm thick, you could fit about 10 across the face of a Euro penny.

[Distant Scholar]

1.01 cubic centimeters is 1010 cubic millimeters, not 10.1 cubic millimeters. A US quarter is less than 1.01 cc in volume.

[DungeonmasterCal]

In an ancient article in Dragon Magazine, Gary Gygax declared gold pieces weigh 1.6 ounces. I don't recall what the others weighed.

[Orfamay Quest]

Kazaan wrote:

If you have mass and density, you can derive volume at least.

Copper: 8.96 g/cc
Silver: 10.49
Gold: 19.30
Plat: 21.45

You are again making the classic mistake of assuming that a gold coin is 1.0 fine.

[Orfamay Quest]

DungeonmasterCal wrote:

In an ancient article in Dragon Magazine, Gary Gygax declared gold pieces weigh 1.6 ounces. I don't recall what the others weighed.

That was in D&D, where there were ten coins to the pound. All coins weight 1/10 of 16 oz, hence 1.6 oz.

[Bellona]

Was this the version of D&D where the science/maths indicated that - if taken to logical extremes based on what the rules claimed - gold could float on water?

(Some of my older players claim that any worlds where gold floated on water must have had Gygaxium in the air.)

[Kazaan]

Distant Scholar wrote:

1.01 cubic centimeters is 1010 cubic millimeters, not 10.1 cubic millimeters. A US quarter is less than 1.01 cc in volume.

Well that's what I get for doing math before coffee in the morning.

Copper: 1010 mm^3
Silver: 866.6
Gold: 471.0
Plat: 423.8

So a Platinum coin, if made 1 mm thick, would be 23mm across so just shy of a Quarter but as thin as a Penny. If you made a Copper 2 mm thick, it'd be about 2.5 cm across, the size of a quarter but as thick as 2 pennies put together. You can modulate the thickness from there to get in-between sizes, maybe going for 24mm across for a silver and 25mm for a gold. You'd probably want to make the Silver piece distinctly different from the Plat so as not to confuse the two due to similar color so either drastically different size or maybe one is octagonal in shape.

[j b 200]

You can also add things like holes in the coin or less precious metal inserts. This idea is foreign to many Americans, but even in Europe they aren't uncommon.

[Kazaan]

j b 200 wrote:

You can also add things like holes in the coin or less precious metal inserts. This idea is foreign to many Americans, but even in Europe they aren't uncommon.

Not realized doesn't mean foreign. Our penny is about 95% zinc with just a copper shell and it still costs 1.6 cents to make a 1 cent piece. We should do away with it like we did with our half-cent, but it's not a polarizing "left-right" issue so it never sees the light of day in Congress.

[Orfamay Quest]

j b 200 wrote:

You can also add things like holes in the coin or less precious metal inserts.

Bimetallic coins may not be practical at Golarion technology. Other than special purpose commemorative medallions, they first appeared in the 17th century here on Earth. Even milled edges are relatively new (16th century). (In fact, Isaac Newton is generally considered to have introduced them to English currency.)

[Atarlost]

Googleshng wrote:

Well no, they'd all be the same weight. If 50 coins stacked up weigh 1 lb. each individual coin has to weight 0.02 lbs. Different volume, sure, some might be noticeably bigger than others. Different styling, absolutely, some maybe octagonal, some maybe with various sized and shaped holes. The weight's a fixed standard though. It's the whole pound of feathers vs. a pound of bricks thing.

Except a pound of copper is not equal to a pound of silver.

Spoiler:

because base metals like copper are measured in pounds avoirdupois while precious metals are measured in pounds troy

[Kazaan]

Avoirdupois is French and there is no France in Golarion so your point is invalid. Seriously, though, it's a classic Equivocation Fallacy, but in reverse. You call out the distinction between differing units of weight sharing the name "pound", but fail to recognize that those different types are neither iron-clad rules nor are they pertinent to the Pathfinder game. I won't spontaneously combust if I measure copper in pounds troy and it's just as valid of a measurement as any using any other unit of weight so long as I keep conversion ratio in mind. In Pathfinder, there's only one kind of pound so the distinction between the two kinds of pounds in real life is moot. Furthermore, the distinction may be valid in the present time, but before globalization, different cultures would each have their own units of measurement. Ancient China or Egypt wouldn't care how the western world chooses to weigh their metals; all they care about is how much that weight translates to in their own measurements in the case of trade.

So, in short, while the difference between French inches and British inches may have made Napolean seem shorter than he really was (he was slightly above average for a Frenchman of his time), the difference between base and precious metal units of weight is a non-issue in Pathfinder.

[Ashiel]

Torchlyte wrote:

Googleshng wrote:

Ashiel wrote:

In Pathfinder, 50 coins = 1 lb., regardless of type. This is why I've always explained that you can't just use prestidigitation to make copper look like platinum and rip people off. They're differently sized coins with different weights, minted in such a way that 50 of them always equals 1 lb. of material (which also means shaving them will show dubious results).

Well no, they'd all be the same weight. If 50 coins stacked up weigh 1 lb. each individual coin has to weight 0.02 lbs. Different volume, sure, some might be noticeably bigger than others. Different styling, absolutely, some maybe octagonal, some maybe with various sized and shaped holes. The weight's a fixed standard though. It's the whole pound of feathers vs. a pound of bricks thing.

I wonder if he meant the weight/volume ratio of the metals were different, since he seemed to get that sizes were different and total weights were the same.

Yeah, that's right. Thanks for figuring out my ill-explained post. I was getting at the fact their size/thickness, not weight (-.-'), would have to be different specifically because 1 copper weighs the same as 1 platinum, but platinum and copper do not weigh the same, so we can deduce from this that they are different sized coins that are weighted to a certain scale.

Kind of the ol' ton of cotton vs ton of lead idea. >_>

[pachristian]

Orfamay Quest wrote:

j b 200 wrote:

You can also add things like holes in the coin or less precious metal inserts.

Bimetallic coins may not be practical at Golarion technology. Other than special purpose commemorative medallions, they first appeared in the 17th century here on Earth. Even milled edges are relatively new (16th century). (In fact, Isaac Newton is generally considered to have introduced them to English currency.)

Uh - no.

The first official coins, Croseus's Lydian coins, were electrum: an alloy of gold and silver.

[aaronpark]

I was more basing my measurements off of the fact that they simply referred to by their metal names and not a denomination of currency. This is why I assumed for my calculations that they were pure metal.

Also, if someone has a more "period appropriate" source for comparative values of the metals, I'd be interested in fixing my math.

[Orfamay Quest]

pachristian wrote:

Orfamay Quest wrote:

j b 200 wrote:

You can also add things like holes in the coin or less precious metal inserts.

Bimetallic coins may not be practical at Golarion technology. Other than special purpose commemorative medallions, they first appeared in the 17th century here on Earth. Even milled edges are relatively new (16th century). (In fact, Isaac Newton is generally considered to have introduced them to English currency.)

Uh - no.

The first official coins, Croseus's Lydian coins, were electrum: an alloy of gold and silver.

That's different -- that's not a "less precious metal insert."

For an example of what j b and I are talking about, look at the British two pound coin. It's literally two separate alloys -- a goldish alloy (actually nickel-brass) ring around a silverish (actually cupro-nickel) center.

[Weirdo]

Orfamay Quest wrote:

pachristian wrote:

Orfamay Quest wrote:

j b 200 wrote:

You can also add things like holes in the coin or less precious metal inserts.

Bimetallic coins may not be practical at Golarion technology. Other than special purpose commemorative medallions, they first appeared in the 17th century here on Earth. Even milled edges are relatively new (16th century). (In fact, Isaac Newton is generally considered to have introduced them to English currency.)

Uh - no.

The first official coins, Croseus's Lydian coins, were electrum: an alloy of gold and silver.

That's different -- that's not a "less precious metal insert."

For an example of what j b and I are talking about, look at the British two pound coin. It's literally two separate alloys -- a goldish alloy (actually nickel-brass) ring around a silverish (actually cupro-nickel) center.

As seen here