Sunday, 2 February 2014

Weights and Measures

Are your sins metric, troy or avoirdupois?
Many younger players know little of the imperial system of weights and measures even in Britain. Foreigners tend to know nothing useful while Americans have the additional confusion of a similar system with the same names but different details. On top of that, Gygax did not specifically say whether he was using British or American versions.

Here's a guide for the bewildered based on the use of British (more specifically, English, since Britain was not yet a united kingdom in mediaeval times).

Firstly, some names and abbreviations:

gr = grain (of wheat), a weight
oz = ounce
lb = pound (from libra, the Latin equivalent)
bu = bushel, a volume
ac = acre, an area
yd = yard, a length
ft = foot or feet, ⅓yd
in = inch, 1/12in
tr = troy, a system
av = avoirdupois, another system

Troy and Avoirdupois

Once upon a time there was a very clever person who decided to design a system of weights and measures. He (the chances that a woman would have been allowed to even assist at the time is remote) decided that a cubic foot of water should be defined as 1000oz. That would weigh 62½ lbs.

But, he thought, merchants clearly use two different systems of measurements - dry and liquid. He didn't really want to have to have two systems of barrels and boxes so he struck on an ingenious idea: have two types of pound instead which weigh different amounts but take up the same space. The denser would be for liquids like water, beer, and wine and called "Avoirdupois" and the less dense pound, for wheat and bread, would be the "Troy" pound possibly from Troyes, a town in France. The concept of the troy pound seems to have come over with the Normans and slowly replaced the old Saxon pound which was called the "Tower pound".

Both pounds would be based on the nominal weight of a grain of wheat. A troy pound would be made of 12 ounces of 480gr each, for a total of 5670, but the avoirdupois pound would be divided into 16 ounces of 437½gr each for a round 7000gr total. This set the ratio of troy to avoirdupois pound to 144:175, the same as the ratio of the density of wheat to water.

This meant that a barrel which was stamped "320 lbs" would hold 320 lbs avoirdupois of water or 320lbs troy of wheat.

Unfortunately, because the troy pound was already in wide-spread use, our inventor could not make a cubic foot of wheat weigh 1000 tr.oz, so although the cubic foot of wheat weighs 62½lbs in either system, in the avoirdupois system it is a nice neat 1000oz, in the troy system it is 750oz which is nice, but not as nice and the ratio of troy ounce to avoirdupois ounce is 192:175, different from the pounds' ratio and notice also that although the troy pound is lighter than the avoirdupois pound, the troy ounce is heavier than its counterpoint.

While avoirdupois has survived to the modern day and is what we normally talk about in terms of weight, the troy system was abolished some time ago and survives only in the area of precious metal. So, if you look up the price of gold and find that it is "$1251/oz" that "oz" is a troy ounce, not a normal kitchen-scale ounce.

Sticking to liquid for now, the definition of a cubic foot of water is 1000oz gives us the next fixed point, as an English pint has 20 fluid ounces (fl.oz.) which means:

1cu.ft. water = 50 pints exactly (users of purify food and water, note!)

and since 8 pints make a gallon,

1cu.ft water = 6 gallons and 2 pints.

and since a pint is 20 ounces (1¼lb),

1 gallon water = 10lbs avoirdupois = 160av.oz.


1cu.ft water = 62½lbs of water.

and so,

1 gallon wheat = 10lbs troy = 120tr.oz = 8lb 3oz 287½gr avoirdupois

Working backwards,

4½lbs of water (enough to fill a wineskin in the DMG) 0.072cu.ft and so a cubic foot of water represents just under 14 DMG wineskins (13 and 8/9ths)

1.3lbs of water (enough to fill a flask in the DMG) is 0.0208cu.ft and so a cubic foot of water represents just over 48 flasks (48 and 1/13th).

100lbs of water is 10 gallons, which is 1.6cu.ft.

Art: David Wyatt
A 320lb-capacity barrel contains 5.12 cu.ft of water. If it were a cylinder 18" across, it would be 2' 10¾" tall. Too small for a human, but a hobbit or a dwarf might just squeeze in.

Standard rations for a week for one person weigh 20lbs. Technically, that should be troy and if it was, then that represents one peck-sized container and a standard barrel would hold a week's supplies for 16 people (see table below). Iron rations would be much more space-efficient at 42⅔ man-weeks per barrel, although more water would be needed if there is no supply en-route.

Personally, I wouldn't dream of enforcing the difference between avoirdupois and troy in a game, even if the 21% difference is quite substantial. But, it could be done.

The old system generally worked on a binary pattern, so that each named unit is equal to two of the unit below. This obviously made calculations easier but over time some units - e.g., the gallon - proved to be so much more useful than the others that the underlying pattern was forgotten along with many of the under-used units like pottles and chopins.

So the theory is:

2 gills=1 chopin (chiefly in Scotland & France) = 5/8 lb
2 chopin=1 pint (20oz of water) = 1¼lb
2 pints=1 quart = 2½lb
2 quarts=1 pottle = 5lb
2 pottles=1 gallon = 10lbs
2 gallons=1 peck = 20lbs
2 pecks=1 demi-bushel = 40lbs
2 demi-bushels=1 bushel (or firkin of liquid) = 80lbs
2 bushels=1 strike (or kilderkin of liquid) =160lbs
2 strikes=1 barrel or coomb (coomb is technically dry but very rarely used) = 320lbs
2 barrels=1 quarter (or hogshead of liquid) =640lbs
2 quarters=1 pipe (again rarely encountered in dry measure) or butt =1280lbs
2 pipes/butt=1 ton (tun is mostly used for liquid) = 2560lbs

A problem arises here, which is that our unknown systematizer was largely just that - unknown. The simple system he devised was more or less forgotten and certainly not transmitted across the country. As a result, in real life, these units were rarely used so systematically and the derivation of the ton that we have today (in Britain and, by what the French call coincidence, in the metric system) is:

1 ton=20 cwt ("hundred weight")
1cwt=8 stone or 112lbs
1 stone=14lbs
1 ton = 2240lbs

In addition, all of the big above list were based off the gallon and that also varied across the country, each variation taking the other units with it. This version of the system made allowances for crating and packing. So a hundred-weight (cwt) supposedly included 12lbs of packing allowance and a ton 240lbs, leaving 2000lbs for the actual goods. In America this allowance was discarded and weights simply given in terms of delivered goods, and so their ton is this "short" ton of 2000lbs.

Anyway, the practical upshot of all this is that the weight of any of these units depends greatly on the contents. Clearly, if one piles grain into a bushel measure and levels it off there is a great deal less air in the resulting container than if one did the same thing with apples, let alone the issue of the different densities of an individual grain or apple. Meanwhile, the local definition of the bushel varied frequently.

Thus bushels vary in weight:
Wheat or rye: 56lbs is the most common size encountered, followed by 64lbs
Barley: 48lbs
Oats: 38lbs

Modern bushels are mostly encountered in the US where the wheat bushel has been rounded to 60lbs.

Notice that none of these bushel weights is very close to the theoretical weight of 65 and 29/35 lbs that the avoirdupois:troy ratio would suggest. Which tells you all you need to know about how successful the would-be systematizer was.

Since bread was made from wheat, old sources tend to talk about a 1lb loaf meaning one troy pound. This means that a pound of bread provided somewhere in the region of 920 kcals, not the 1120 that one might expect if using avoirdupois weights.

Small Weights
The pound avoirdupois was sub-divided:

1lb= 16oz = 256 drams
1oz=16drams = 32 quarters
1dram=4 quarters
1 quarter = 1/1024 lb

The pound troy was sub-divided:

1lb = 12oz
1oz = 8 drams
1 dram = 3 scruples
1 scruple = 20 grains
1 grain = 1/5760 lb

However, since the troy pound came to be the pound of silver and silver was the coinage of the realm, it could also be divided so:

1oz = 1 shilling
1 shilling/oz = 12 pennyweight
1 pennyweight = 24 grains
£1 = 20 shillings = 240 pennyweights

and this is the origin of the slogan on all English banknotes "I promise to pay the bearer on demand the sum of ..." followed by the face value of the note. It used to be that a £50 note was literally worth fifty troy pounds of silver and one could exchange it at the Bank of England. This ended in the late 1700's but the text remains essentially as a hollow endorsement of the government's non-existent commitment to financial prudence.

A foot is 12" and an inch is now defined as being exactly 127/5000th of a metre, for what that's worth.

3 feet are a yard, so a tank with a capacity of one cubic yard holds 1350 pints weighing 1687½lbs.

2yds is a fathom.

5½yds is a pole or perch.

22yds is a chain.

220 yards (40 poles) is a furlong. Dividing the furlong into 200 units gives you a metre.

8 furlongs is a mile.

3 miles is a league.

1 furlong by a chain is an acre of 4840sq.yds. or 43560 sq.ft

One inch of rain on an acre thus represents 3630cu.ft of water, which is 226,875lbs of water, or 2,2687½ gallons, or 709 barrels (minus half a gallon).

1 furlong by a furlong is 10 acres

640 acres is a square mile.

30 acres is a virgate.

4 virgates (120ac) is a hide.

100 hides is a "hundred". However, the word "hundred" actually originally mean 120 and in some places this held in the definition of the hundred of land while in other places the hundred was chopped up without changing the name. Consequently, references to "hundreds" of land in old sources can refer to quite widely differing amounts of actual land. In any case, the original concept seems to have been that each hide would be responsible for providing a warrior to the king's warband.

I think this has been abolished except in parts of Lincolnshire.


  1. I doubt the fifty pound note was ever worth fifty pounds of troy silver. The English pound was significantly debased from around about the fourteenth century, and in any case had long been using the tower pound (5,400 grains).

    1. I agree about the £50 note; by then the relationships were very nominal. The Tower pound seems to have played an important role in giving moneychangers a profit margin but that role and the consequent ratios changed frequently from the conquest onwards.

      So, up to 1279 there were 240 pennies to the Tower pound, but then the ratio changed to 243 (or 245) until 1335 when it changed to more than 250 etc.

      As far as I know, at least shortly after a recoinage, local usage was at face value, so 240=£1 while foreign merchants were more prone to going by weight. After a few decades of wear and tear, the face value would start to be doubted by so many people that new currency had to be re-minted on a large scale.

      Anyway, the difference between Tower and Troy seems to have been used, or perhaps even designed, to allow a profit margin for the mints.

      Probably. The topic of coinage is a complicated one and, like everything else, gets harder to follow once you go back beyond about 1250.

    2. It is also worth looking into the "groat", which was worth four pence, but by the fifteenth or sixteenth century down to about 2.1 grams. That is a pretty good map for the nominal versus the real value of the silver pound.