#### Coin Size & Mass: Results & Recommendations From An Investigation

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, May 18th, 2016 at 11:17 (8260 Views)
I posted this into the Forums in August 2015, but thought it'd be better off as a Blog Post, so I've re-posted in here - enjoy!

Preface

This article isn't for everyone; some RPG groups aren't that concerned with highly accurate or realistic world or social systems, being more concerned with simply having fun playing. On the other-hand, some groups find a highly detailed, realistic and accurate "system" helps in their enjoyment and "suspension of disbelief". This article is aimed at the later groups, and deals with the physical aspects of coins in an attempt to marry up the historically and physically accurate with our RPGs.

Introduction

Those that know me and the way I like to set up my game worlds know that, while I am quite willing to fudge a value and/or round a number off to make it "more pleasing", I look at the reasons behind why a given system was set up the way it was and then use that as the basis for the model to base all of a world's "stuff" on. This then is the underlying principle I have used in my recent investigations and determinations on the size and mass of the various coins we use in our (primarily fantasy) RPGs. During my investigations I have delved into different weight systems and also the historical basis of ancient currencies and coins, and also the value of beer, all in attempt to determine "proper" sizes and weights for coinage, in particular the coinage of the DnD RPG. This information I've presented here to assist anyone else who is interested in providing their games with realistic RPG coinage.

Be aware that this article delves into a number of seemingly unrelated topics - hang in there, it'll all come together in the end.

Pounds Troy

The Troy weight system consists of Pounds Troy (lbt), Ounces Troy (ozt), Carats (k, not to be confused with Carats for measuring gemstones), Pennyweights (dwt) and Grains (gr) - 1 lbt = 12 ozt = 24 k = 240 dwt = 5760 gr. Troy weight isn't used much any more, except in the measurement of precious metal, particularly gold and silver.

Pounds Avoirdupois

The "common" Imperial weight system most familiar to us today is the Avoirdupois system. It consists of Pounds (lb), Ounces (oz), Drams (dr, also known as drachms) and Grains (gr) - 1 lb = 16 oz = 256 dr = 7000 gr. The only common measurement between the Troy and Avoirdupois weight systems is the Grain, which allows us to determine that 1 lbt = 0.82 lb (approx).

Volume of Coins

The volume of a coin is simply the volume of a cylinder, which is given by: thickness times pi times radius squared - v=t*PI*r^{2}. If we take the measurements in centimeters the resulting volume is in milliliters (ml), which is convenient because 1 ml of water weighs 1 gram (g).

While coins are not smooth disks (they are stamped on both sides and so have hollows and ridges) they start out as smooth disk and no volume is lost or added during the stamping process, so we can safely ignore any stampings and treat them as smooth disks.

It is interesting to note that if you halve the diameter of a disk (halve the radius) you need to increase the thickness by a factor of 4 to retain the same volume: an interesting fact to remember if you want to modify the recommendations below.

Ancient English Coinage

The English coinage of the 16th Century was based on the Silver Standard and consisted of Sovereigns (li, pounds), Shillings (s) and Pennies (d) - 1 li = 20 s = 240 d. This system was based on the older Roman system of coins. Note that Pennies were made of silver and not the more common (nowadays) copper. The Troy weight system was in widespread use in England during this time and it was here when the English coinage system was standardised with respect to weight of silver content. Silver for coinage was refined to 222 parts in 240 parts pure (22.2K) while gold was refined to 22 parts in 24 (22K) - hence 22 carat gold. This obviously ties back to the Carat Troy and therefore the Pound Troy, such that a (silver) Penny weighed 1 pennyweight (1 dwt).

RPG Coins

We now have a model we can use to determine the size of our coins. We know the volume of a disk (in ml, from above) and we can look up the relative density of the five main metals used in coins (platinum, gold, electrum, silver and copper) relative to water, and then multiply the coin volume by the density to give the weight - w=d*t*pi*r^{2}

If we take 1/8 oz (3.54g) as a good weight for our RPG coins (based on the historical range of weights for real coins) and allowing only plus or minus 1/80 oz (0.35g) we end up with the the following recommended coin sizes:

A quick cross-check with historical coins shows these values are all in the same general area. Any of the above figures would be acceptable and can be justified due to imperfections in the casting process, clipping, etc.

CoinBest2nd BestCopper (cp)1" * 1/32" (25.4mm * 0.8mm)

5/8" * 5/64" (15.9mm * 2.0mm)

1/2" * 1/8" (12.7mm * 3.2mm)Silver (sp)3/4" * 3/64" (19.1mm * 1.2mm)

1/2" * 7/64" (12.7mm * 2.8mm)7/8" * 1/32" (22.2mm * 0.8mm)

5/8" * 1/16" (15.9mm * 1.6mm)Electrum (ep)1" * 1/32" (25.4mm * 0.8mm)

5/8" * 5/64" (15.9mm * 2.0mm)

1/2" * 1/8" (12.7mm * 3.2mm)Gold (gp)3/8" * 3/32" (9.5mm * 2.4mm) 1/2" * 1/16" (12.7mm * 1.6mm)

3/8" * 7/64" (9.5mm * 2.8mm)Platinum (pp)3/8" * 3/32" (9.5mm * 2.4mm) 1/2" * 1/16" (12.7mm * 1.6mm)

3/8" * 7/64" (9.5mm * 2.8mm)

1/8 oz is also a good weight to choose as that then means there are 128 coins in a pound. Setting a pound (of gold or silver) to be 120 coins (120gp or 120sp) means that our coins would be 15 parts in 16 pure (22.5K) - a good approximation for the actual purity of coins.

Justification (in Beer)

(Trust an Ozzie... )

The Beer Standard is a way of measuring the various values of commodities across countries and across time. The idea is that a pint of beer cost the same in relative terms no matter where or when you are, and thus by converting something into the equivalent value of beer it makes comparing different things in different places and/or times easier. It has proven to be surprisingly accurate and thus we can use it as a second, independent method to see if our coinage (values) are "close".

A mug of ale in 3.5E cost 4cp or 0.04gp. Assuming a mug of ale contains a pint (a not unreasonable assumption), that means we can buy 3000 mugs of ale for our 120gp pound of gold.

Based on the average beer price in New York, NY in 2015, a pint of beer is about US$6 (from Google) and so 3000 pints of beer would cost US$18,000.

There are 14.58 ozt in a lb, and Gold is selling for about US$1250 per ozt (gold fluctuates widely day-to-day, but its not unreasonable on average to use US$1250), so a pound of gold is worth around US$18,230, which is pretty close to our (beer) calculation of US$18,000 (about 1.28% greater).

So our choice of 120gp per pound of gold and 128 coins to a pound of metal is pretty good.

Summary

So, in conclusion, for 3.5E DnD (and thus similarly in other RPGs):

1 lb OfHas a Value OfMakesCopper 120 cp 128 cpSilver 120 sp 128 spElectrum 120 ep 128 epGold 120 gp 128 gpPlatinum 120 pp 128 pp