# How many types of coins are necessary in an economy?

I am creating a universe based on medieval Europe and I was wondering how many types of currency would be needed for a medieval economy to work. Example:

• The US dollar uses cent, nickel, dime, quarter, half-dollar, and dollar.
• The euro coin uses 1, 2, 5, 10, 20, and 50 cents, €1, and €2.

I have been reviewing the use of coins in different historical medieval and pre-medieval periods, but the currency changed so much in short periods of time or coexisted with different types of coins that I have not been able to understand it. Thank you very much for your time.

• That totally depends. Stable empire? Mix of irregular states? Economic leagues? Global trade system with ships? Ready supply of pure gold? You don't NEED coins, you can have barter on a local level. It's just really not great for trade. Coins were often a stable way to assure a weight and quality of metal. Metal allows trade between multiple rival states, but coins co-mingle and require multiple denominations, weights, systems, etc. – DWKraus Oct 26 '20 at 12:59
• Just copy an existing system; for example the Roman system (from about 50 BCE to about 250 CE) was [half as] - as - dupondius (2 as) - [sesterce (4 as)] - [victoriatus = quinary (8 as)] - denary (16 as) - aureus (25 denaries = 400 as). (Coins in [brackets] were more often not issued.) (And depending on what specific medieval period you have in mind, money may be very much less important than this question assumes.) – AlexP Oct 26 '20 at 13:33
• What about this question is "opinion based"? Economics is a science, and the question is clearly worded with an implied "minimum necessary". – John O Oct 26 '20 at 20:27
• This is a well defined mathematical problem with algorithmic solutions -- see change-making problem on Wikipedia – EDL Oct 26 '20 at 21:41
• A plus to the "totally depends": There is an Austrian 10000 Euro Gold Coin, where the value of the Gold is more than 10000 Euro. This is, because it is legal to bring up to 10000 Euro in cash to other european countries - like Germany. So there is a legal way to bring more than 10000 Euros (I think it worth about 20000 Euros) from Austria to Germany. Btw. this is a coin because in the Eurozone, the countries still have the right to mint coins, but not banknotes. – Julian Egner Oct 27 '20 at 11:01

You're putting the cart before the horse

Coins reflect the economy — the economy does not reflect coins.

Well into the medieval period (and not completely without merit today) is the most basic form of economic exchange: bartering. I need bread and have chickens. You, my neighbor, need chickens and have bread. We negotiate how many chickens are worth a specified amount of bread. We know this today as the "rate of exchange" and it's an important term.

As economies, political ideologies, and political boundaries (e.g. "nations") grow the need to standardize the rate of exchange increases. This is what brings coinage into play. Paper and/or cloth is certainly more convenient when it comes to hauling around an object that represents a great deal of value — but back then it didn't last. Coins and/or other hard-object markers of value (like the Rai stones of Micronesia's Yap island) allow for a controllable rate of exchange using something that will last more than a short period of time.

So, in the beginning is a basic unit of money people can use to negotiate the purchase of anything and, more importantly to the Crown, pay taxes. Because it's hard to prosecute a war when your warehouses are filled with only chickens and bread.

It's early in our economic history, so we'll call this first coin a Seren and by Royal Decree a Seren is worth one chicken or seven loaves of bread.

But nothing lasts forever

The problem is that as your economy grows, so does the need for greater precision and larger denominations. Eventually, some smart aleck notices that your chickens are smaller than your neighbor's chickens so your chickens are only worth half the decreed amount: 3.5 loaves. Now what?

Our ancestors solved the problem by shaving and clipping coins. This is where the idea of "pieces of eight" came from: people cutting coins into eight pie-shapped pieces because they needed more precision than the coinage of the realm had. The rate of exchange was too high.

It's also one of the many reasons why early Europe had such cool coinage: because it's a lot easier to cut a coin into eighths than it is into tenths. The decimal system makes a lot of sense after the development of inexpensive minting and printing.

So, now we have two coins: the Seren and the Eighth Seren lovingly known as a Marie.

My point is that by trying to create the monetary system before developing even the basic history of your region (putting the cart before the horse) you're creating an artificial system that won't feel natural or will feel too much like today's monetary systems crowbarred into yesteryear.

How many coins do you need? As many as wanting. You therefore should first develop a feel for how many coins are wanting. If your history started with an arrogant leader who wanted the coin to reflect his/her enormous ego, you'll develop a "unit" coin (the Seren) that has far too low a rate of exchange and this will lead to the development of a lot of smaller coins (increments below one Seren). If it starts with too high a ratio, you'll end up with more coins of integer increments above the Seren.

"Just right" is the number of coins you, the author, believes reflects the complexity of your economy and the complexity of your world's history. It can be anything you want. There is no one "right" answer. Frankly, you really do want an organic in-universe feel, but you can do that with two coins just as easily as twenty as they both represent benefits and complications that you can interweave into your world and/or story.

I didn't directly answer your question. I think it's a mistake to do so. What I've done is pointed out (a) why so many authors simply say "the adventurer gave some coins to the barkeep," (b) why so many RPGs use a hugely simplified system like copper, silver, and gold pieces, and (c) why knowing the history of your world is so important. Which is a long and wordy way of saying I taught you how to fish, because I'm pretty sure the fish I have to give you are inadequate for your needs.

• 12 was also a good calculatable fraction for large amounts, as 12 is divisible by 2, 3, 4, and itself is a fraction of 60, which is divisible by 2, 3, 4, 5, 6, 10 and 12. – Trish Oct 27 '20 at 10:29

We can probably look to historical examples for a plausible answer. So your reference to US coinage isn't too far off the mark. However, you're a little biased... within your own lifetime, it's certainly only that list. But in the last few centuries there have been additional denominations:

• The half-penny
• The two-cent

Also, there are bullion coins (made of gold, silver, and recently, of platinum!)

• The \$5 • \$10
• \$25 • \$20
• \$50 • \$100

Historically, I'm only aware of \$10 and \$20 coins though. So, we're probably talking about ten denominations that saw actual use. And not all were available simultaneously either, with as many as 7 or 8 at any given moment maybe being minted (though with circulation times being what they were in the 19th century, no doubt all ten were being used somewhere).

As a counter-example, let's use pre-decimal British coinage, because they were a little bit crazy with their stuff.

• 1/4 farthing
• 1/3 farthing
• 1/2 farthing
• Full farthing
• Half penny
• 3 farthing
• Full penny
• 3 Half-pence (1.5 pennies)
• Half-groat (don't even know what this is, but wikipedia lists it)
• 2 penny
• 3 penny
• Groat
• 6 penny
• Shilling
• Quarter angel (gold?)
• 2 shilling
• Half crown
• Half angel
• Crown
• Angel
• Half sovereign
• Half pound
• Double crown
• Half guinea
• Sovereign
• 2 pounds
• 2 guineas
• 5 pounds
• 5 guineas

Again, not all of these were being minted simultaneously. But I've also left out quite a few that were minted only for a few years at a time... these are the list that were minted for about a century at minimum. This is approximately 30 denominations.

Part of the reason there are so many is because this lists includes denoms that are pre-paper-money. (If we included paper money, we'd easily double the denoms for the US and most other currencies.) That's how it has amounts like the 5-pound coin (a minor fortune, especially if you're a Dickensian orphan asking for more soup).

So, anything from about 8 denominations on up to 30-40 isn't without precedent, and maybe even with most of those circulating or being minted simultaneously.

Now that we've covered that, we should really discuss just what is needed. Because if an economy needs another denomination, and if the country's planners are even slightly competent they will see the need and try to respond, no?

Coins will serve (in a medieval environment) the same purpose as paper money does for us today (or more properly, did serve us until the late 1990s). So on the high end, denominations need to be large enough for the largest transactions commonly occurring without using too many of them. In modern times, it'd be "can we fit enough $100s in the briefcase to buy our cocaine shipment", but in medieval times it would be "can this purse fit enough currency to let me smuggle in my sailing ship's worth of brandy" or something like that. Coins are small, and large denominations are going to be precious metal. Exceptions: For the very largest transactions, like kings buying and selling their kingdoms to the Medicis to finance wars, transactions will occur in the same manner that these things occur today. A bank will put the amounts in a ledger, and keep track of the interest to the fraction of the smallest coin amount. You didn't pay for your house with a suitcase full of cash, and neither did I. So there's no need for the$10 billion florin coin.

On the low end, how granular are your transactions? The British had fractional farthings because the poor wouldn't be found with pound-coins (if they were, they were likely about to be shipped off to Australia), but the poor still tend to buy bread and what-not. They might be paid just a few farthings per month, but needed to make more than a few transactions per month (this is pre-refrigerator, pre-preservative food).

Between these two extremes, we can postulate that increments only occur every so often. If the two extremes are close, then there might only be a few intermediate values, but if they are extreme (as was the case in the British Empire), then there will be many intermediate values. And with less competent economic management, not all of these values will have available denominations, but the more competent it becomes, the more of those values will see actual coins. I really do like the Brits as an example of the most extreme you'll likely see.

• This is an interesting, alternate take; where I tried to answer "what is the bare minimum", you're looking at "what is likely". It's not clear which answer the OP wants. That said, it's worth noting we both came up with the same criteria for the range of values to be covered. – Matthew Oct 26 '20 at 14:26

### None?

Economies can be built using currencies other than coinage. Even assuming (as you imply) we are not talking about a time when digital currency is practical, there have been times when exchange was based on weights. And before you argue that just changes the problem into how many weights you need, I'll note that sliding-countermass scales and spring scales don't have this issue.

Also, as per comments, this is assuming you even have currency as such. While it's true that something which served as "currency" has been pretty common throughout history, its use depends on at what level of the global economy you are looking. States, or well-traveled individuals might use currency, but individuals within a small community might operate entirely on barter, and may not even accept currency. (What good is a coin, after all, if no one accepts it as payment?)

### But more practically...

There is no good fixed answer. Rather, coinage tends to develop into whatever denominations are "convenient". The reason we have denominations is because it's awkward to pay for a car using a million pennies, both in terms of carrying them around, and in terms of counting them out in order to complete a sale. You want your smallest coin to be about the value of a very inexpensive item, but more importantly, to be a value that most people won't care about an item's cost differing being more or less by that value. Many would argue that the US penny is too small.

Once you have your smallest coin established, you want coinage in larger denominations up to an amount you would expect someone to pay cash rather than using a bank note of some sort (think "check", not paper money; for our purposes, paper money and coins are roughly interchangeable). These denominations should strike a balance between making sense in your counting system (e.g. why coins tend to divide larger decimal numbers nearly) and minimizing the number of coins. For example, if we had coins strictly in powers of two, it would minimize the number of coins in any transaction, but humans don't like dealing with powers of two and it would actually maximize the number of different coins.

In this respect, having a base-ten number system is a disadvantage. A species/culture with a base-16 system would almost surely have only coinage at powers-of-four values, since this is a pretty good "sweet spot" between not needing more than a few of any specific coin for a given sale, and denominations that neatly round up to "whole" increments of larger values (that is, values consisting of a single non-zero digit followed by some number of zeros). Five would also work well, but most humans don't think in powers of five, which is why we wind up with tens (and twos, like the \$20 and \$2 bills; the latter is real, if almost never seen in practice). But using only powers of ten would mean needing up to nine of a smaller coin, and that's getting to be a bit much.

A more practical system — assuming your culture uses base-10 — might be to alternate fives and fours (with twice as many fives as fours). We sort of have this with nickels and quarters, and with \$5 and \$20 bills. It's not hard to imagine eliminating dimes and \$10 bills, in which case... ### Seven ...pennies (1¢), nickels (5¢), quarters (25¢), dollars (\$1), \$5, \$20 and \$100 are probably sufficient. (For values above that, people will probably want to involve accountants rather than paying out of cash-on-hand. Keep in mind this also assumes that a penny is actually worth something. Also, don't think of these as directly relating to real currencies, or as literal "coins"; I'm trying to address your question which was about types of currency. "1¢" might be a chunk of a coin that has been cut into bits, where doing so is common enough to be an accepted way of "making change".$100 might be a brick of silver or gold; not something you'll see every day, and indeed something many people will never see in their life, but not so large that no one wants to ever deal in them directly.)

• Medieval means coins with intrinsic value. A hundred dollar coin (dollar as defined by the US Coinage Act of 1792) would be two and a half kilograms (five pounds avoirdupois) of silver: rather impractical. – AlexP Oct 26 '20 at 13:38
• @AlexP, you're making an assumption about the value of a "penny". Don't think of my suggestion in terms of actual currencies, but rather as describing the range of values which people might want to deal in. The point is there is no smaller unit than a "penny", which might actually be the equivalent of an eighth shilling. (If you instead allow splitting coins — which, in fairness, was typical in those eras — then replace the lowest denomination or two with partial coins.) (Con't...) – Matthew Oct 26 '20 at 13:45
• (...con't) Also, only rich people are likely to deal in the top 1-2 denominations anyway; we're likely talking about values that only come up when buying something like a horse, a carriage, or a hovel. I was trying to think of at what point it would still be practical to deal in individual currency tokens. Anyway, it wouldn't be a 5kg silver "coin", it would be a gold bar. (IOW, I'm treating "coin" as "distinct token of currency".) – Matthew Oct 26 '20 at 13:48
• Actually, I'll grant that your value of "penny" might be reasonable, but you're taking "coin" too literally. The OP asked about "currency", not about "coins" specifically, which I am (ab)using to mean "tangible denominations of currency". So, yeah, $100 is probably a gold brick and not a literal coin. Even$20 is probably a bar/ingot. I would expect there to be some dealings in those, but not every day. – Matthew Oct 26 '20 at 13:57

"Medieval" means that coins have intrinsic value, except possibly very small denominations which may be tokens.

A direct consequence of coins having intrinsic value is that all coins of all states are accepted, their value being given by the amount of precious metal in them. Basically, in the Middle Ages coins were little more than standardized pieces of silver (and sometimes, rarely, gold) with a known fineness and weight. Nobody cared much in what specific coins a payment was made, provided that they totalled up at the agreed amount of silver.

Excursus: Originall a "pound sterling" was exactly that: one pound (pound Troy of 373 grams, or Tower pound of 350 grams) of sterling (= 92.5% fine) silver. Of course there was no such thing as a one pound coin, which would have been impractically large; the common coin in circulation was the penny, which was actually one pennyweight (1/240 of a pound Troy, 1.55 grams) of sterling silver.

Small denomination coins, such a a farthing (= 1/4 penny) were made of copper or bronze and were in the nature of tokens; they were good only up to a certain (small) limit.

Since coins had intrinsic value, they circulated and were imitated all over the world. Specialized traders, called money changers, exchanged exotic foreign coins (of which local people didn't know the weight or the fineness) into local (better known) coins.

So that in the end the best course is to take one historical set of coins and use it as such, or maybe tweak it a little. For example:

• In the Roman system, the basic coin was the denary, about 4 grams (1/84 or a Roman pound) of silver. It was soon arranged (1/96 of a Roman pound, 3.5 grams, 93.5% fine) to be almost equal to the well-known (at that time) Attic drachma, and in this form circulated all over the Old World for some three centuries. 1/4 of a denary was a sesterce (silver); 1/16 of a denary was an as (copper token). 25 denaries were reckoned to be equal to an aureus (1/45 Roman pound, gold).

As an indication of value, one denary was considered to be the pay for one day of (semi-) skilled work; at the current price of labor in developed countries, that would be about 100 US dollars or euros. (Excursus: How has the dollar fallen. The original definition of the US dollar was 25 grams of silver, about 7 Roman denaries.)

• In the system of Charlemagne, the basic coin was the penny (= denier, denarius) of 1/240 (1.8 grams) of a pound of 94% fine silver. (Theoretically 1/240, but in practice more like 1/260.) 12 pennies made a sol (not a real coin, just a name of the weight of 12 pennies), 20 sols made a pound. The smallest silver coin was the half-penny.

# You don't need your own coin system

Let's look at a historic example of a society that ran entirely on various foreign coins. They started to use foreign coins around 800 and we know nobody there minted any own coins before 995, and the massive import of foreign coins that were valued just like the local ones only ended around 1100. How did this society operate if they pretty much didn't mint their own coinage and how did it evolve?

# Of Svear and Rus, Danes and Norveigers

Well, starting around the year 800, vast amounts of silver (and golden artifacts) started to flood into the coffers of the various lords and then trickled down via trader of goods and slaves. To the Danes and Norveigers in the west and north, this influx came mainly from the west via the north sea, to the Svear in the middle, it came from the southern Baltic coast and via trade with their neighbors in either direction and the Rus in the east via the Wolga and even down from Byzantium, where some served as an elite mercenary group called Varänger.

## 793-1066

The cultures I mention there were mainly a set of farmer communities that didn't use a lot of money in itself. It was a bartering and service society: My comb for your hoe, my labor of the next three days for you shingles.

However, once they started to go on larger scale trade and looting missions (that is a Viking, a member of such a mission is a Vikingr), there was the influx of mainly silver coins as loot and trade rewards flowed into the modern Skandinavia.

This "golden age" commonly is dated to end in 1066. In that year, a descendent of the mycel hæþen here with the nickname "William the Bastard", after inheriting and consolidating the French area known as Normandie (given to his great, great-great-grandfather Hrólfr Ragnvaldsson aka Rollo in 911), did re-invade the British islands (where Rollo had come from), beat down the king Harold with the weakened army after he had just defended against another invasion from the Norveigers under Harald Hardrada. In the same year, Hedeby burned down, and many of the people there resettled to Schleswig, just a little down the river.

## The effect of foreign coins

The inherent value of the foreign coins in Scandinavia was the benefit, that it could be turned into something the Scandinavian people cared for much more than the coin itself - it was decorative and held a value for trade with other countries, where they imported blades and steels from the west and silk and slaves from the east, stone from the north and wheat from the south. Scandinavia had quickly become both military power and the extension of the silk-road in a trade network. Some of the large exchange ports were the following:

• Hedeby - Somewhat inland, this port's main feature was the short track over to Hollingstedt, and so it exchanged wares from the Baltic to the North Sea and vice versa. It took at times less than 3 days from the moment a ship entered from the Baltic into the Schlei to unload in Hedeby, cart the cargo to Hollingstedt and then load a different ship that went down the Treene and get to the North Sea. The track via the Skagerak in comparison took weeks.
• Ribe - protected by large islands north and south, it was a good anchoring spot for traders going southwards to the Frankian coast and was a perfect spot to sail west towards York.
• Roskilde - Well protected, this was a booming trade city that dealt with many of the wares coming into Scandinavia through the Skagerrak in the north, out of the Baltic in the south, as well as the wares that came from Jutland and Skane on both sides.

## Weight is Value

But the coins were inhomogenous: Frankian coins weighed 1.8 grams, eastern, Islamic dirham (which flowed into Scandinavia en masse in the 900s to 1000s) weighed 1.2 grams and were purer as times went on. How to solve that gap or pay for something that is worth only a fraction of a coin? It's rather simple: the money is not worth its minted value. It's worth its weight in silver. And as a result, coins were cut up to create what is commonly known as "Hackgeld". The parts then were weighed against a set of weights. In the eastern half of Scandinavia, these weights had often the shape of cubooctahedrons and seem to have used multiples of 1.2 grams pretty much.

## Distributing large amounts

But how was it feasible to evaluate the loot from for example Wessex, who paid 30000 pennies to be spared? Simple: those vast amounts were not weighed or counted, they were taken in large chests and only dispersed to the warriors surviving as spoils of war later, using - in one source - volume measure to ensure somewhat even distribution.

## Excursus: Multinational trade around 1200-1400

The Hanseatic League in the high middle ages still weighed (and assessed) coins to calculate local exchange rates based on what they asserted the pure metal in the coins to be worth. But at times the whole exchange of money was on paper in the trade depot's ledgers.

From personal experience:

My home currency (BGN) experienced rather significant inflation in my lifetime, so limiting the diversity of denominations had to happen by itself. It was BGL before the 1000-to-1 denomination in 1999.

The traditional order of BGL/BGN denominations is profoundly decimal, just like modern EUR and manu others: 1/100, 2/100, 5/100, 10/100, 20/100, 50/100, 1,2,5,10,20,50,100 and so on.

As the value of the currency decreased, bigger and bigger denominations (200,500,1000, etc) were printed and the smaller ones were converted to coins or fell out of use because they were too small for trading anything of worth.

But in any single moment, only 6-7 of them, corresponding to ~3 orders of magnitude (1:1000), were in actual, widespread, use. Right now, we have 1,2,5,10,20,50 and not much used 100. We also do have 1/100, 2/100 and 5/100, but they are virtually never used and generally disregarded. Prices of most retail goods are rounded to 0.1 or even 0.5 BGN. 0.5 BGN is a cheap coffee from a vending machine.

Transactions of more than 5000 are forbidden in cash so in theory you never need more than a pocket full of money.

A more math-backed currency (see here, but a currency is probably better E2) could have an order of denominations like 1,3,10,30,100

7 of them (up to 1000 value) can probably cover all the social inequality present in the economy for everyday transactions. For bigger things you needs accountants and cashiers anyway, even in a medieval context (and banks are always here to help).

• "1 2 5" is used because it allows us to make any amount up to the next decimal with at most 3 coins (and usually <2), allowing super-fast calculation of intermediate amounts: 3=2+1, 4=2+2; 6=5+1; 7=5+2; 8=5+2+1; 9=8+2+2; 10=5+5. The "1 3" needs on average 3 coins to make the next and 4 to make the next decimal. Its only benefit is fewer denominations. – Trish Oct 27 '20 at 10:47
• 1-2-5 is just the E3 series of the "preferred numbers" in the link above (the link is electronics-centric, but the preferred numbers are not necessarily so). One can choose between E2 and E3 series depending on the technology available. Simplicity vs diversity. – fraxinus Oct 27 '20 at 11:01
• true, the E2 series hoever is more cumbersome and leads to on average more coins needed while the E3 needs more denominations but leads to effectively less coins actually used. – Trish Oct 27 '20 at 11:04