It’s time for another “measuring things” themed post! Where we go revel in a topic somewhat adjacent to data, usually data collection or measurement units, and see what we find.
[For similar posts, here’s one about measuring rulers, and why rice cookers have a 180g measuring cup for rice.]
This time, the motivation is wondering getting confused and frustrated when looking at physical paper goods. Measuring paper within the US is an absolute head-spinning mess. We’re going to go into this rabbit hole, lose a bit of our minds, then come out at the end with a new respect for an ISO standard, as well as learning all sorts of things about paper. We’re dealing with paper here, an artifact that humans have been using for thousands of years — “legacy quirks” does not begin to describe it.
Paper in the US is very odd
To us common everyday folk, we don’t think about paper much even though we’re surrounded by it. We know that paper comes in thick and thin forms, there’s the stuff that goes in the printer, there’s cheap notebook paper and fancier notebook paper. There’s the thin stuff used for newspaper, thicker stuff used paperback books, and even thicker stuff used in hardcover books. Then there’s stiff stuff used for cards.
When I go buy some paper for my printer, I know the box reads “20 pound bond paper” and always wondered what it meant. As befit a legacy system that’s based off old conventions built up over time, it’s complicated.
Things you need to describe a single piece of paper
It’s length and width, 8.5”x11”, A4, B2, etc
It’s thickness, called “caliper”, expressed as 0.001” (mils, or thous) or micrometers
It’s weight, because paper density varies, knowing just the volume isn’t enough
Details about it’s material composition and properties - lots of details like what its made of, the processing done, etc. Which I can’t get into because it’s way too much
So, AHA! that “20 pounds” on my pack of 500 sheets of paper, that’s the weight and I know the dimensions, 8.5x11”! It says “Bond” which probably says something about what type of stuff it’s made of. I know what my paper is! Right?
Except… nope! Because if things were this simple, you wouldn’t be getting a post about the topic in your email. In fact, NONE of the stuff in the previous paragraph is correct.
What all that stuff written on your pack of paper is referring to a “basis ream” of paper. It’s the original big sheet of paper that came out of the paper mill, stacked into a canonical ream (often 500 sheets, sometimes 1000, sometimes 480).
The word “Bond” describes the type of paper, originally used for fancypants uses like government bonds. We now use it as our everyday printer/writing paper. It was standardized to be made into 17x22 inch sheets, stacked into 500-sheet reams. It’s THAT basis ream is what weighs 20 pounds. Our little pack of 8.5x111 is one quarter of that basis ream, so it’s only 5 pounds of weight.
See the table below for a bunch of paper types and their basis ream parameters.
Chaos. It means that a 20lb piece of bond paper might be more or less denser than a 20lb piece of another type of paper. The only saving grace to this mess is that WITHIN a paper type, higher weight is correlated with higher density.
The most frustrating thing about this system is that you need to know about this theoretical basis ream in order to make any comparison. There’s no way to just compare any number between paper types and come to guaranteed conclusions. 100 pound text paper is thinner than 80 pound card stock.
Oh, also, higher weight is correlated but not exactly proportional to the paper’s caliper, its actual thickness. Paper fibers can be compressed more or less for a given weight. This happens when you do things like put glossy finish coatings on paper. There’s no escaping needing to know that parameter.
Enter ISO 216, aka, the way everyone else does paper
By now, I’m sure readers from outside of North America are sitting here, horrified, at the system we’ve got in place.
“Today the [ISO 216] standard has been adopted by all countries in the world except the United States and Canada. In Mexico, Costa Rica, Colombia, Venezuela, Chile, and the Philippines, the US letter format is still in common use, despite their official adoption of the ISO standard.”
Outside of North America, the world uses one paper standard, because it makes significantly more sense than the American one, or any local national standard prior to that.
While the concept of being scientific about paper sizes had been bouncing around since at least the late 1700s (according to the Wikipedia anyways), Germany was the first to codify into into an actual national standards, DIN 476, in 1922. It then got quickly adopted by other countries during and after World War II, before finally just becoming the ISO standard.
It’s divided into 3 series, A, B, and C. The most important part of the standard is that the aspect ratio between the length and width is defined to be 1:√2 , ~1.4142. This gives the paper the very useful property where if you fold one piece in half across the length, you get two exact sheets the next size down. Since each size of sheet is just half of the previous size, they’re referred to as a “series” with an initial base size being defined.
The start of the A-series of paper, A0, is defined as a square meter of paper with the aspect ratio of √2. A1, A2, A3, etc. would simply derive from that. A4 being the size used most often in daily office life.
The less common B-series is similar but defined at a different start point. Wikipedia claims it was defined as the geometric mean of the areas between A series sizes, so for areas: B1 = geomean(A0,A1). It seems really convoluted. It’s MUCH easier to remember that the short side of B0 is 1 meter long, and that length halves as you go down to B2, B4, etc…
The C-series (which got dropped as an ISO standard but exists in various national standards) exists as the geometric mean of the A and B areas, so areas C1 = geomean(A1, B1). The primarily motivation for the size is to create paper containers, envelopes, with the intention that A-series stuff can be placed in an envelope made of C-series paper with little waste, and C can fit inside B.
Thickness of paper is quoted in microns, aka micrometers. It of course varies with the density and processing of the paper, but common printer paper hovers around 0.1mm.
Weight is simply grams/square meter, often seem abbreviated with the improper unit of gsm in English contexts. Since the A-series starts off as a square meter of paper, it’s just the weight of the A0 sheet. There’s no nonsense about basis reams and basis weights. More gsm means heavier paper. Done!
In fact, the metric weight of paper is so useful and convenient, it’s very often quoted right alongside the customary units for paper specifications.
Okay, but WHY is US paper this way?
Apparently, no one fully knows exactly why things wound up where it is.
The American Forest & Paper Association seems to think that it traces its roots to Dutch paper making frames in the 1600s. A typical worker can only hold a certain size of frame to make paper (supposedly 44 inches, double the 22inch length of bond basis length), and when you fold it a few times you arrive at something close to 8.5x11”. It’s not clear if this origin story is actually true or not.
Like with many traditional units, a couple of forces comes into play in these situations. The manufacturing process wants to make paper as large as possible, because it’s more efficient to. Humans find certain sizes convenient to use in everyday life. which is why US Letter, A4, and hardcover books are all within a pretty narrow range of sizes. Throw in a desire to not waste too much paper cutting things to size, and the system will gravitate towards certain solutions. In fact, the famous Quarto size that was common in the Elizabethan era and where much of Shakespeare’s work was printed on, is also of similar dimensions.
The problem is that these traditional measurements reach a local optima balancing these concerns on the supply and demand size. They’re rarely global optima, because no individual or group sat down and tried to figure out what the optimal solution is.
So was historical paper just as wonky, and ISO had fixed it later with math and science?
Actually, from what I can find, paper size evolution wasn’t a steady march of progress.
Here’s a copy of a block put on a public building in the public square of Bologna, Italy. They showed what the official sizes of paper (technically, the moulds that make the paper), for the city. That way if there’s a disagreement about whether something is to spec, you can just walk up and compare it. It’s said to have been in marble from the 1300s, but the version that exists today is what appears to be a limestone reproduction from the 1700s.
Luckily, scholars have gone to the trouble of measuring the frames and sizes for us:
Notice that the aspect ratios are all hovering around 1.4. Recall that the basis of ISO paper sizes, √2 ~= 1.4142. Could this have been mere coincidence? There’s tons of paper sizes throughout history that don’t have ratios of 1.4. Since paper tended to require a final cut to size anyway, it probably wasn’t necessary to be accurate beyond one or two decimal places.
Digging more into the history of paper, it seems hat scholars have argued that this convergence of ratios is NOT a coincidence. Papermaking is a massively labor intensive process. Take a read of this page here describing Medieval and Renaissance paper making techniques. To get the finest white paper, rags had to first be carefully sorted by color and grade. Then, the rags needed to be soaked in mixtures of alkaline solutions (potash, lye, etc), then fermented (“retted”, I’m convinced the word is a cognate of “rotted”), literally composted down for weeks, months, even years in what sounds like a horrifyingly pungent process involving fungus and other things. This is done to break down the cellulose fibers, as well as break down the lignin which makes paper yellow and weak. Afterwards it is mechanically beat into pulp, and eventually formed on moulds into sheets of paper that are trimmed to size.
With so much time and energy placed into making sheets of paper, the incentive to minimize waste is high when cutting down to smaller sheets. So sticking close to the aspect ratio of 1.4 meant you could fold sheets down into smaller ones without much waste, if any.
There’s also evidence that paper dimensions actually looked to parchment, the previous writing medium of the era, for ideas on what dimensions to make paper. Paper from Arabic regions from the Medieval period and earlier show some rough agreement in dimensions to the Italian dimensions.
There have also been arguments that the size of the largest sheets of paper are roughly in line with the size of animal hides from which parchment was made. Since goats, sheep and calves were used (according to this Cornell University Library Conservation post), things never got super large. As with most technological advances, people thought about new technologies very much in context of the ones they were used to using.
So there’s SOME evidence that certain people in certain places long ago created paper with aspect ratios of 1.4. HOWEVER, plenty of other people did not. A quick gander at the traditional sizes of various countries on Wikipedia shows aspect ratios all over the map between often 1.2 and 1.7.
A table by John Lane, from this source about 2/3rds down, shows how a sample of historic paper dimensions were between the ~1.2361 (1 / 2*phi, the golden ratio) and √2 (~1.4142). People of the time seemed to either preferred the ability to form two golden rectangles when folding sheets in half, or the self-similar properties of √2. The US ratio of 1:2941 sorta sits vaguely in between middle, which doesn’t really accomplish anything useful.
Under the circumstances, everyday people did the completely reasonable thing — they used what they had access to. People would fold and books books and other goods in somewhat irregular sizes. they’d demand certain sizes for high demand items like books and writing paper.
Then, industrial papermaking probably made it worse. The gov’t didn’t help much either
In 1799, the Fourdrinier machine was patented. It could create paper in a continuous process instead of individual sheets and continues to be the primary basis of modern industrial papermaking. This meant that aspect ratios weren’t necessarily restricted to the dimensions of moulds since you could slice sheets off the rolls at whatever ratio you wanted. Even the final roll widths are sliced from giant rolls at the end, (YouTube video showing the process), so paper can be made to the specifications of the customers now.
About 45 years later, the process of pulping wood to make paper was invented, meaning paper didn’t have to use expensive processed rags as input. The price of paper dropped dramatically, and paper became ubiquitous in the world.
I can’t find any decent sources that detail what the effect of machine-made paper had on the paper world, but I suspect the massive investment in capital in paper mills, commercial printers, consumer printers, etc. added a ton of inertia to the paper industry. Just like how the US can’t really get away from customary units for building materials because there’s so many existing buildings that create demand for materials in customary sizes, the paper industry probably stuck in the same way. Just like adopting the metric system, conversion would be possible, but individual actors aren’t incentivized to take up the cost unless everyone else does it.
Normally, it would take a government to overcome this structural barrier, and they don’t seem interested in that either.
If anything, the latest update to paper size standardization happened in the 1980s when President Reagan made the 8.5”x11” Letter size the government standard. That was a change from the “Government Letter” size of 8”x10.5” which had been set by Herbert Hoover in 1921 while he was U.S. Secretary of Commerce. Why that was chosen wasn’t clear, but some speculate that might have been for cost savings, or just because 8.5x11 was easily available, and you could bleed print on that sheet and trim things down to 8x10.5. Either way, in the 1980s having two similar-ish sizes became too cumbersome and they just picked the one used by more people.
¯\_(ツ)_/¯
Next week we’ll have a more pedestrian data topic. I promise.
Extra Reading!
So much stuff I found along the way. All very fascinating reads
Historical data about various properties and composition fo paper through time
A discussion about the shape of paper over time
Magnolia Edition’s Paper Studio has amazing, detailed resources on making various styles of paper by hand. Including their discussion of the Bologna stone [pdf]
There’s a full on academic journal about paper history =O Their journals up to 2016 are open to read. I haven’t had the time to sift through them.
About this newsletter
I’m Randy Au, currently a quantitative UX researcher, former data analyst, and general-purpose data and tech nerd. The Counting Stuff newsletter is a weekly data/tech blog about the less-than-sexy aspects about data science, UX research and tech. With occasional excursions into other fun topics.
All photos/drawings used are taken/created by Randy unless otherwise noted.
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