Essays

Wizard Money

by Anton Generalov aka “XAHrOBEP” (pronounced “Hangover”)^[1]

The Exchange Rate on March 12, 2001

Introduction

Rebecca Boswell - What is the approximate value of a galleon?
JKR - About five pounds, though the exchange rate varies!

WEB LINK Comic Relief Live Chat, March 12, 2001

This interview that took place on March 12, 2001 became the historical point from which all theories and speculations about how much money would one need to go to Gringotts and to buy a Galleon started. Most researchers worked with the first JKR statement of “About five pounds,” while not addressing the more difficult second one, “though the exchange rate varies.” Who sets the exchange rate? Why should it vary? Is it falling or picking up?

In this essay I will try to estimate the exchange rate, how it varies through the time and explain why. Simultaneously I will try to determine the appearance of wizard money, because in my theory the appearance of wizards’ money is closely interrelated with its value. If there is not enough information from the Harry Potter Books I take the opportunity to make suggestions and assumptions as well as to use external data, common sense and wizard logic where applicable.

It is my belief that if you are a high school graduate or pre-graduate you will find no problem repeating my calculations, which use powers, roots and all that stuff, and find better solutions for coin sizes and more a exact exchange rate. You can find all necessary information on the last foot of this parchment, in footnotes. If you wish to avoid replicating my difficult way of trials and errors you may use my spreadsheets, to which links have been provided in the footnotes, or if you have difficulty downloading them from this site please write to me and they will be sent on your request.

If you are not yet a pre-graduate or on the contrary too-long-ago-graduate I trust you will give me the benefit of the doubt.

The Exchange Rate on March 12, 2001

In the Harry Potter Books there there are several descriptions of wizard money:

The Galleon is big enough to write several numbers on the edge that one can read without special optical devices. (OP19)
1000 Galleons are light enough to be carried by one person, and that person may forget that he or she is carrying them (GF36).
Wizards seem to be fond of prime numbers, numbers that cannot be divided without fractions, except by 1 and by the number itself, such as 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, and so on. 1 Galleon = 17 Sickles, 1 Sickle = 29 Knuts ( PS5)
A wizard coin may be as large as a hubcap (GF7), and a hubcap is big enough to write anything on its edge. However, the hubcap referred to by Mr. Roberts might simply be some foreign coin — we have never heard about any other wizards’ currencies but we cannot be sure that there are none.
There is some international trade between wizards. Britain imports thin-bottomed cauldrons from somewhere (GF5). No country was mentioned, but we know where “almost the same but cheaper” goods are coming from (GF5): Ali Bashir from some Middle Eastern country is eager to sell his flying carpets to Britain (GF7), Fred and George purchased some raw materials from Peru (HBP6), and Hagrid visits a bar in Minsk, Byelorussia (OP20).
The trade between Muggles and wizards does exist, although it is rather limited. Muggle-born Hogwarts students can exchange money (CS4), wizards can purchase clothes in Muggle shops and have to rent campgrounds with Muggle money (GF7).

In any case, the Wizard and Muggle worlds are not economically isolated, so the exchange rate of the currencies must be adapted to trade conditions. In other words — it is not constant.

The exchange rate is never mentioned directly in the saga. However, the prefaces of Fantastic Beasts and Where to Find Them (FB) and Quidditch Through the Ages (QA) give the sales of these books as 250,000,000 USD or 34,000,000 WZG. Henceforth, wizard Galleons will be abbreviated WZG. I will abbreviate Muggle currencies using the first two letters to identify the country and the third to identify the currency name. For example: United States Dollar – USD, Great Britain Pound – GBP, Russia Rouble – RUR, and so on. So, to determine the exchange rate according to the figures provided in the prefaces of FB and QA: 250,000,000 USD divided by 34,000,000 WZG equals 7.35 USD/WZG. On March 12, 2001, the date of the WEB LINK

JKR Comic Relief interview, the exchange rate between the U.S. dollar and the Great Britain pound was about 1.46 USD/GBP (see http://www.oanda.com/convert/classic). Using this rate to convert a Galleon’s worth of USD to a Galleon’s worth of GBP, we get 1 WZG = 5.03 GBP, which we arrive at by dividing 7.35 USD by the exchange rate of 1.46. The same day JKR said in her interview that the Galleon was approximately 5 GBP — perfect match!

As we know, wizard currency is based on precious metals, gold and silver (PS5), like all our Muggle currencies were only a bit more than 100 years ago. In those days exchange rates were fixed, and depended only on the precious metal content in the corresponding coin^[2]. There was no need to calculate the rate every day. In the nineteenth century the GBP (in the form of the “Sovereign” coin) contained 7.32 grams of gold and the French Franc contained 0.2903 grams ^[3], so the exchange rate was always 25.25 francs per pound. Banknotes in those days carried inscriptions like “this note is equivalent to this amount of gold or this amount of silver.” Most of our modern currencies are not fixed to the gold content, which is why rates vary due to economical and commercial conditions. Gold and silver nowadays are commodities and the price for them also varies.

So, to my mind, the goblins of Gringotts adapt the Galleon rate to the world gold and silver prices. If they don’t, then when prices for precious metals are high in the Muggle world nothing would prevent such crooks as Mundungus Fletcher from selling Galleons to Muggles at or a bit below the price of gold, using the proceeds of that sale to buy Galleons from wizards at the artificially low fixed exchange rate — and turning a nice profit from the arbitrage. For example, imagine Mundungus Fletcher opening a Muggle newspaper one morning and finding out that he can sell Galleons to Muggles at 10 GBP for 1 WZG, based on gold prices. At the same time, the currency exchange rate is fixed at 5 GBP per Galleon. He goes to some Muggle, and says — “I will sell you some gold for 90% of its real worth price, but I need the cash in advance.” The Muggle gives him 900 GBP for 100 Galleons. With this money Dung goes to Gringotts and buys 900/5=180 WZG. Then he immediately delivers 100 WZG to his Muggle customer and has 80 WZG as gross profit. In other words: criminals would spend Muggle money in periods of high gold prices. In periods of low gold prices, they would profitably purchase Muggle money from Wizards’ banks and then that Muggle money on Muggle gold. However, I suspect that the amount of Muggle money in Wizards’ banks is rather limited.

The Gold Galleon Coin

As we have cross-confirmed exchange rate of wizard Galleons (WZG) to U.S. dollars (USD) for March 12, 2001, we can take the price for pure gold (999 metric or 24 carat gold) for the same date (for example from WEB LINK http://www.kitco.com) to calculate the weight of the Galleon. On March 12, 2001, 24 carat gold cost 272.5 USD/oz, or 9.61 USD/gram (1 oz = 28.35 grams). Dividing the USD to WZG exchange rate on that date of 7.35 USD per Galleon, by the cost of a gram of pure gold in USD, a Galleon should weigh 7.35/9.61 = 0.7648 grams.

Using the well-known equations for mass and cylinder volume,^[4] we find that if the Galleon coin is about 2 centimetres in diameter it must a very thin 0.1-0.2 millimetres in thickness. This thickness is unacceptable for a coin used every day, being only a bit thicker than paper used in office printers and copy machines. Even if the Galleon is made of 14 carat gold (585 metric), as was the above-mentioned Sovereign, the Galleon must be only 0.2-0.3 millimetres thick. So the only logical conclusion is that the Galleon is made of 9 carat gold (the lowest possible gold grade, being an alloy of 37.5% gold and 62.5% some other metal, typically silver). This Galleon would have a diameter of 19 millimetres (3/4 inch) and a thickness of 0.5 millimetres, with a mass of 1.98 grams.

So the Triwizard Cup Prize of 1,000 Galleons weighs 1.98 kilograms, which seems rather heavy on one hand, but on the other hand it is a weight one can throw on a bedside table without the table collapsing (GF36).

We also have a description of another golden coin, size of a hubcap. Although he was likely exaggerating, for the sake of thoroughness before we move on to the silver Sickle we’ll consider possible sizes of a Galleon that match Mr. Roberts’s description. Sorree four mai Eenglish, but isn’t a hubcap the thingie in a middle of a car wheel, usually with an emblem of a brand? If so, the hubcap on my car is 50 millimetres in diameter.^[5] If for the purposes of our calculations we assume that the coin has diameter/thickness ratio similar to the 2 EURO coin, which is 25 mm/2 mm, or 13:1 (good magic number!), the coin Mr. Roberts was referring to is 3.8 millimetres thick.

In order to determine how much Mr. Roberts’s Galleon weighed we need to know what grade gold the coin was made of. Since we do not know this from the books, I offer three possibilities:

Carats (Grade)	Coin weight, grams	Value, WZG
24 (999)	145.903	191
14 (585)	118.261	92
9 (375)	104.273	53

Chart 1.

My initial estimations are rather rough, and as noted, Mr. Roberts perhaps exaggerated a little bit. Or a bigger bit. Let’s say he exaggerated the size of the coin by a factor or two, and that the real diameter of the coin he saw was 25 millimetres, with a thickness 1.9 millimetres. Recalculating the three possibilities for the weight of the coin, based on three different grades of gold:

Carats (Grade)	Coin weight, grams	Value, WZG
24 (999)	18.238	23
14 (585)	14.783	11
9 (375)	13.034	7

Chart 2.

None of these coins can be a Galleon. Harry’s Triwizard Cup Prize of one thousand of these coins would weigh in the range of 13-18 kilograms (approximately 26 - 40 pounds). And you know, no magic weightlessness would help the poor bedside table bear the brunt of having that weight tossed onto it. Mass is not only weight, mass first of all is inertia, something so basic to the physics of matter that it would be unlikely that one could change it with any kind of magic.

According to the second chart above, to purchase the three omnioculars for himself, Ron, and Hermione, Harry would have to pay one-half kilo of money (at 10 Galleons each, 30 Galleons would weigh from 390 - 540 grams), and have something left. Quite a weight in the pockets! Galleons of this weight thrown by leprechauns would results in serious injury — just imagine half an ounce falling from from a height of 50 feet! I would venture that if the coin Mr. Roberts saw was indeed this large, it was a 7-Galleon coin made of 9 carat gold or an 11-Galleon made of 14 carat gold. 23 Galleon is also not that bad. All these figures are in line with wizards’ (apparent) addiction to prime numbers. Or this could be some foreign coin, there were many guests from abroad at the Quidditch World Cup final match. In any event, Mr. Roberts’s description of the coin cannot be taken literally as a description of a one Galleon coin, and it is more likely that the Galleon is the more moderate size calculated earlier in this section.

The Silver Sickle Coin

Should the Sickle be worth the silver it is made of it could become an alternative currency itself. Which is not likely for wizards economy. The ratio of silver to gold prices is not constant, sometimes being as high as 1/50 and sometimes dropping to almost 1/100. So the value of the Sickle was based on silver prices there would be an unofficial separate variable Galleon to Sickle rate, from 1/17 to 1/34 (!), while banks would be obliged to accept money at its face value. Moreover, we never read in any of the Harry Potter Books anything like “This necklace is 15,000 Galleons, but you may have it for 14,500 if you pay in Sickles.” My conclusion is that Sickle value does not correspond to silver price.

There is another reason the size of a Sickle cannot be based on silver prices. If this were the case, given that the Sickle = 1/17 of Galleon and is made of silver we can calculate its mass. Silver has only one grade. For the last 16 years gold has been worth about 70 times more than silver, on average. Recalling we have speculated that the weight of a Galleon is 1.98 grams, we can multiply that weight times 70 to determine how many grams of silver a Galleon is worth: 138.60. Since there are 17 Sickles in one Galleon, if we divide 138.60 by 17 we’ll see how many grams of silver a Sickle would be worth in this scenario: 8.2 grams.

Once again using standard mass and dimensions formulas we can find possible dimensions of the Sickle. So if the Sickle has approximately the same diameter as we have speculated for a Galleon (19 millimetres) it would be around 5 times thicker.

I think that it is also not good to have a change coin (the Sickle) that is bigger and heavier than the main currency coin (the Galleon). Therefore I suppose that the Sickle is of approximately same thickness as the Galleon (0.5 millimetres) and a little bit smaller (less than 19 millimetres). It is worth much more than the silver it is made of and the reason for making it of silver is that this metal is good for making coins, it does not rust, and it is very plastic, so smaller graphic details could be cast or stamped.

Exchange Rates Through Time

Back to exchange rates. Gold and silver prices are also volatile through the time. For a Galleon made of 9 carat gold and with a mass of 1.98 grams we have the following “interbank” rates on various significant past dates, assuming the exchange of wizard currency exists. Goblins of course may set sell and buy rates slightly different from those listed below.

Date	Gold, $/oz.	Silver, $/oz.	GBP/USD	WZG/USD	WZG/GBP
July 31, 1991	362.85	4.060	1.6845	9.70	5.76
August 19, 1992	338.00	3.804	1.9292	9.04	4.69
July 3, 1995	384.50	5.083	2.683	10.31	3.84
March 12, 2001	272.50	4.510	1.467	7.35	5.01
July 25, 2006	618.75	11.010	1.8535	16.72	9.02

Everyone is probably familiar with the dates above except for the last one, which is the day I performed the calculations. But to review: July 31, 1991, is Harry’s 11-th birthday, when Hagrid took him to Diagon Alley to do his first wizard (and by the way, first ever) shopping; August 19, 1992, is the day when Hermione came to Diagon Alley with her parents and Arthur Weasley was so fascinated with Muggle paper money; July 3, 1995, is the day when Harry gave his Triwizard Cup Prize to Fred and George so that they could start their business; March 12, 2001, is the basic, cornerstone date, the release date of both QA and FB when JKR first stated the exchange rate of Galleon to pound.

I have also made available more detailed information about exchange rates for last 16 years, since Jan 1, 1991, including tables and charts, as well as a currency converter for US Dollars, UK Pounds and Russian Roubles (sorry, other folks).^[6] There we can see that the Galleon was more or less constant at around 10 USD from beginning of 1991 up to the second semester of Harry’s 6th year. After that it dropped below 7 USD in August 1999, and from March 2001, after the release of QA and FB, it started picking up again, to a historical maximum of almost 20 USD in May 2006. Since that time it has never dropped below 15 USD.

Conclusions

Assuming a GBP/Galleon exchange rate for March 12, 2001 as 5 to 1 (JKR’s statements in the interview of that date being canon), and taking into consideration existing prices for gold and silver we conclude that a Galleon is made of 9 carat (375) gold, is about 2 centimetres in diameter, 0.5 millimetres thick, and weighs 1.98 grams. Which is not much, but explains how Cornelius Fudge could carry 1000 Galleons in a small bag (GF36). Galleons of a “normal” size, or the same size as a 2 EURO coin (25 centimetres in diameter and 1.9 millimetres in width), would be comprised of gold worth several times more than one Galleon (see Chart 2 above), which is economical nonsense and could result in intensive smuggling of Galleons to Muggles, unless they have some special unmelting spell on them. However, the Galleon dimensions upon which we have settled are to a certain extent problematic for one aspect of canon on currency, and that is the use of fake Galleons by Dumbledore’s Army (DA). Hermione put the dates of DA meetings on the edge of fake Galleons (OP19), where presumably everyone was able to read them — which is rather difficult with letters smaller than 0.5 millimetres. But perhaps she meant the edge here:

Top coin edge

not there:

Side coin edge

where I think it is.

Sickles are made of silver not because they are worth the amount of silver they are made of, but to have better a appearance than would Sickles made from a copper alloy, like bronze. The face value of a Sickle is higher than the value of silver it contains. Sickles are smaller and lighter than Galleons.

The exchange rate of wizard Galleons to Muggle currencies varies depending on the precious metals prices. As of the date calculations were made for this essay, the Galleon is about 2 times more expensive than when Hermione’s parents came to Diagon Alley and almost 2.5 times more expensive than when Harry invested his Triwizard Cup Prize in the “Weasleys’ Wizard Wheezes” shop.

Most probably there are Galleon coins of larger denominations, perhaps 7, 11 maybe even 23 Galleons. These coins would be really thick, with inscriptions easy to read on their edges and and of a weight heavy enough to feel in one’s pocket.

A few questions are still not solved with my theory however:

How can wizards read letters small enough to fit on Galleons and Sickles without magnifiying glasses? (This relates to an oft-discussed question in the fandom: Why wizards do wear glasses, if they can cure everything with a single spell?)
Why do wizards call all golden coins Galleons, although there may very well exist gold coins with different values?
What do Sickles look like? With the lack of information on this subject in the canon, anything ventured in this area is pure speculation.

Anyway, these discrepancies do not much affect the other literary qualities of the Harry Potter Books. After all JKR writes novels, not research, and the absence of exhaustive technical detail does not detract from the drama of Harry’s fight against Voldemort.

Notes

^[1] St.- Petersburg, Russia, July 26, 2006. The author wishes to extend special thanks to the WEB LINK Magical Fellowship Forum and especially forum member creeping shade for fruitful discussion.

^[2] http://www.edinformatics.com/inventions_inventors/paper_money.htm; http://www.bankofengland.co.uk/banknotes/about/history.htm.

^[3]

http://en.wikipedia.org/wiki/British_Sovereign_coin;

http://en.wikipedia.org/wiki/Franc;

http://www.bis.org/press/p020708a.htm.

^[4] The volume of a cylinder is V = pr2h, and the formula for mass is M=DV. The density of gold is 19.3 grams per cubic centimetre.

^[5] Ed. Note: Most hubcaps are much larger than this, but many hubcaps do have the manufacturer’s logo on them and it is probably this to which the author means to refer.

^[6] See “Exchange Rate Historical.xls” and “Wizard Money.xls,” as well as explanatory notes at "About Galleon-Dollar Converter.doc." See also http://oanda.com/ for an up-to-date currency converter (not including a converter for Wizard money, of course!)

Wizard Money

Contents

Notes