Pick up a ream of copy paper in the United States and read the wrapper. It says 8.5 × 11 in, and it says 20 lb. Neither number describes the paper inside.
An A4 ream has no such problem. It says 210 × 297 mm and 80 g/m². Both of those are properties of the sheet you are holding: its dimensions, and its mass divided by its area. Check them with a ruler and a kitchen scale and they come out right.
The American numbers are properties of something else. The 8.5 × 11 is one quarter of a sheet 17 by 22 inches, cut and trimmed twice. The 20 lb is the weight of five hundred of those 17 by 22 sheets. Both describe a piece of paper you have never seen, and which the wrapper does not name. Every ream sold in the country is labeled with the specifications of a parent sheet, and the buyer is expected to infer it.
That is the whole difference between the two systems, and it has nothing to do with which sheet is handsomer. One measures the page. The other measures the page’s ancestry.
The ratio that folds
A4 belongs to a family with one rule: halve a sheet on its long side and the halves keep the shape of the parent. That requires a ratio of 1 to √2, about 1.414. Georg Christoph Lichtenberg, a physicist at Göttingen, worked out the algebra in a letter to Johann Beckmann dated 25 October 1786, and closed with a question that nobody has quite answered since. Were the papermakers following the rule, he asked, or had the rule been read off their paper?
Germany turned it into a standard. Walter Porstmann’s system replaced a confusion of German formats as DIN 476 in 1922, and the same shapes became ISO 216 in 1975. A0 is one square metre. A1 is half of A0, A2 half of A1, and A4 is A0 halved four times: 210 by 297 millimetres, one sixteenth of a square metre.
The consequences only announce themselves when you need them. Two A4 pages set side by side are exactly one A3 page, so a copier enlarges from A4 to A3 at 141 percent and leaves no margin white. One hundred sheets of 80 g/m² A4 paper weigh 500 grams, because 80 grams per square metre times one sixteenth of a square metre is exactly five grams a sheet. The arithmetic is not a convenience added afterward. It is the definition, and everything else follows.
The sheet that was already there
The American size arrived the other way round. It was not designed. It was found.
In 1921 the Department of Commerce, under Herbert Hoover, set out to reduce industrial waste by standardizing the things Americans made in dozens of sizes. A Committee on the Simplification of Paper Sizes, appointed on 30 August 1921 to work with the Bureau of Standards, recommended a short list of basic sheets. The first was 17 by 22 inches.
8.5 × 11 is that sheet folded twice. So is 11 × 17, the tabloid, which is the same sheet folded once. The series alternates between two shapes, 22/17 and 17/11, because a 17 × 22 rectangle is not a 1:√2 rectangle and folding cannot make it one. Half of 17 × 22 is 11 × 17, a different shape; half of that is 8.5 × 11, the original shape again. An American copier therefore cannot enlarge a page onto the next size up without changing the margins, and most machines sold in North America do not offer the function at all.
Whether 17 × 22 was chosen for any reason beyond availability is genuinely unclear, and the careful sources say so. Markus Kuhn’s International standard paper sizes records the standing hypothesis that the size descends from a mould used in hand papermaking, and then quotes the paper historian J. C. Dunn: “It does not appear, even in the selection of 8 1/2 × 11 inch size paper, that any special analysis was made to prove that this provided an optimum size for a commercial letterhead.” Kuhn’s own conclusion is plainer still. “It appears that this standard was just a commercial compromise at the time to reduce inventory requirements without requiring significant changes to existing production equipment.”
A standard that costs nothing to adopt and asks nobody to buy new machinery is a standard that survives. That is most of the explanation for why the United States still prints on it. Hoover’s personal preference, as it happens, ran smaller: 8 by 10.5 inches, which he declared the standard for his own department in March 1921 and which the Permanent Conference on Printing adopted that September as the general government letterhead. Federal offices used that sheet until January 1980, when 216 by 279 millimetres took its place.
What “20 lb” is the weight of
The second number is worse than the first.
American paper is sold by basis weight: the weight in pounds of five hundred sheets of the grade’s basic size. The basic size is not the same for every grade, and it never appears on the package. Writing and bond paper use 17 × 22 inches, the very sheet from which the letter size is cut. Text and offset paper use 25 × 38. Cover stock uses 20 × 26, and newsprint 24 × 36. (USPS Publication 25, §2-1.2) Index stock uses 25.5 × 30.5. (Ricoh, paper weight conversion table)
So “20 lb” means that five hundred 17 × 22 inch sheets of this paper weigh twenty pounds. That converts to 75 grams per square metre, which is a real density. The conversion is exact, and the industry publishes tables of it, because the alternative is chaos. Ricoh’s table puts 75 g/m² at 20 lb bond, 50 lb text, 28 lb cover and 42 lb index, and 90 g/m² at 24 lb bond, 60 lb text, 33 lb cover and 50 lb index.
Read that again. A sheet of 50 lb text paper and a sheet of 20 lb bond paper are the same paper. The number is two and a half times larger and the paper is identical. Neither label is wrong. They answer two different questions, and each answer depends on knowing a grade of paper that the label never names.
The confusion is not hypothetical. Ask for 80 lb stock and you may be handed text paper at 118 g/m² or cover paper at 216 g/m². The second is nearly twice as heavy as the first and carries the same number on the box. The only defense is to order by grade and weight together, which is to say to supply the half of the specification that the label left out.
Metric has no such gap, and the reason is worth stating precisely. Grammage is mass divided by area, so it is a property of the sheet in your hand whatever its dimensions. A4 at 80 g/m² and a poster at 80 g/m² are the same paper. Weigh a single sheet on a kitchen scale and it comes out at five grams, and that is the number printed on the wrapper. Weigh a single sheet of 20 lb Letter paper and you get 4.5 grams, a figure that appears nowhere and cannot be derived from the label without also knowing the basis size and the cut.
The bill for the inheritance
None of this makes Letter a bad piece of paper. It is 0.0603 square metres against A4’s 0.0625, within four percent, and A4 is only six millimetres narrower and eighteen millimetres taller. Every printer sold in the United States handles both. The two sizes are close enough that the mismatch is survivable, which is exactly why nobody has ever paid to correct it.
What the American system costs is not paper. It is the ability to reason about paper without a lookup table. A4 declares its own area and its own weight. Letter declares the dimensions of its parent and the weight of five hundred of them. The information is all present, in the sense that a deed is present in a registry, provided you know which registry to open.
The bill has been paid downstream, wherever paper meets a machine or a scale. Copiers without an enlargement key. Envelopes that fit one system’s fold and not the other’s. A postal calculation that needs a conversion rather than a division. Fifty years of Canadian printers stocking two grades because Ottawa kept both.
Metrication reached the United States several times as an idea and never once as a decision about machinery. That is the difference between a standard that was designed and one that was inherited: the designed one can be explained from first principles, and the inherited one can only be explained by its history. The history here is not embarrassing. It is merely expensive to carry, and it is carried by anyone who has ever stood in an office supply aisle wondering what the twenty in “20 lb” weighs.
PRH | huffmanwrites.org | © Philip Huffman