
International Standard Paper Sizes - polm23
https://www.cl.cam.ac.uk/~mgk25/iso-paper.html
======
mark-r
This is a very thorough explanation of what I consider a brilliant paper size
standard. What genius to make the aspect ratio identical for each size, and to
create smaller variants by cutting the larger one exactly in half.

There are two places where you can tell it's a bit dated though. The first is
in declaring the TV aspect ratio as 4:3; it's just about universally 16:9 now.
The second is the expectation that the U.S. would be converting to metric,
that becomes less likely with every passing year.

~~~
henrikschroder
The brilliance becomes obvious when you combine it with the envelope sizes.
Mailing things in the US always ends with you having to awkwardly tri-fold
papers and hope that you didn't botch it, so that the result will fit in your
envelope of a non-standard size.

Meanwhile, anyone can fold an A4 perfectly in half and it will always fit
perfectly in a C5 envelope. Paper can't be folded? Mail it in a C4 envelope
instead. Think a C5 is too big? Get a C6 envelope and fold it twice.

All the parts fit perfectly into each other, and it's obvious how they fit.
Any size paper can be mailed in any size envelope simply by folding it.

~~~
polm23
I live in Japan and the vast majority of mail is folded in thirds, just like
it is in the US... Is using envelopes for paper folded just in half actually
widespread in other countries?

~~~
tilt_error
After a vacation in, then, Czechoslovakia I received a letter from the police.
The letter was artfully folded so that the text would overlap at 90 degrees
(if viewed with a light source behind the folded letter). I always reckoned
that was done to scramble the letter from unintended reading.

Normally the C3 or C4 envelopes used by government would be printed on the
inside with a mass of letters, but in a way that matched with how the letter
paper inside would be folded.

------
alister
> _The Legal format itself is quite rarely used, the notion that it is for
> “legal” work is a popular myth; the vast majority of U.S. legal documents
> are actually using the “Letter” format._

Can anyone confirm that this is really the case in the U.S.? In Canada at
least, lawyers often use a paper size _even longer_ than legal format. It
makes photocopying a huge pain because the glass plate isn’t long enough on
ordinary copiers, and these extra long sheets don’t fit in standard file
cabinets without folding, and forget about using binders. Nobody uses these
ridiculous extra long sheets except (Canadian) lawyers.

~~~
polm23
So looking around more, this is interesting - historically US lawyers did use
legal size, but in 1983 the Supreme Court instituted a rule to move all
federal paperwork to letter size, and most states followed shortly thereafter
if they hadn't already transitioned.

[https://www.michbar.org/file/generalinfo/plainenglish/pdfs/8...](https://www.michbar.org/file/generalinfo/plainenglish/pdfs/89_july.pdf)

------
seven4
Digging around on the same page i stumbled into this which i think is a
fun/interesting look at the history..though sounds like the ratio was in use
even before its referenced here. Anyone know more about it?

 _" letter, written in 1786-10-25 by the physics professor Georg Christoph
Lichtenberg (University of Göttingen, Germany, 1742–1799) to Johann Beckmann,
seems to be the oldest preserved written reference to the idea of using the
square-root of two as an aspect ratio for paper formats"_

Excerpt of the English Translation -

 _" I once gave an exercise to a young Englishman, whom I taught in algebra,
to find a sheet of paper for which all formats forma patens, folio, 4to, 8,
16, are similar to each other. Having found that ratio, I wanted to apply it
to an available sheet of ordinary writing paper with scissors, but found with
pleasure, that it already had it. It is the paper on which I write this
letter, but to which, because since by cutting some of its original form may
have been lost, I also add an uncut original. The short side of the rectangle
must relate to the large one like 1 : √2, or like the side of a square to its
diagonal. This form has something pleasant and distinguished before the
ordinary [form]. Are these rules given to the paper makers or has this form
spread through tradition? Where does this form come from, which appears not to
have emerged by accident? Honoured wellborn forgive me this freedom."_

[https://www.cl.cam.ac.uk/~mgk25/lichtenberg-
letter.html](https://www.cl.cam.ac.uk/~mgk25/lichtenberg-letter.html)

------
hannibalhorn
> Based on the experience from the introduction of ISO paper formats in other
> industrialized countries at various points during the 20th century, it
> becomes clear that this process needs to be initiated by a political
> decision to move all government operation to the new paper format system.
> History shows that the commercial world then gradually and smoothly adopts
> the new government standard for office paper within about 10–15 years.

The article is obviously dated, but at this point that'd be such a waste of
time and resources. Government has to be focused on digitization and
paperless/electronic processes, ideally getting rid of photocopiers instead of
upgrading them.

Had never heard the logic behind the ISO paper sizes before though, very cool!

------
emj
From 1996, the one from 1999 is not that different though.
[https://web.archive.org/web/19990129003006/http://www.cl.cam...](https://web.archive.org/web/19990129003006/http://www.cl.cam.ac.uk/~mgk25/iso-
paper.html)

------
terakhirx
I feel there are something missing. B0, C0, A0, ..., B1, C1, A1, ..., B2, C2,
A2, ... . How about make "D series"? B0, C0, A0, "D0", B1, C1, A1, "D1", B2,
C2, A2, "D2", ... .

------
kkylin
[https://xkcd.com/2322/](https://xkcd.com/2322/)

~~~
mark-r
11/8.5 = pi/4?

------
systemvoltage
One of the things I keep hearing from non-Americans is how dumb Americans are
and then proceed to explaining the benefits of the metric system. I see this
from random internet forums to Youtube comments, from news paper articles to
talking to people in Europe. What people don't realize is that America is like
a giant ship that has a ton of inertia to change. It is the world's largest
economy with huge diversity of evolved shit that has piled up. It is difficult
to clean it despite of the will. The US gov tried to convert America to the
metric system unsuccessfully [1].

The US (NIST) in collaboration with international bodies lead the redefinition
of SI units based on fundamental constants [2]. Furthermore, semiconductor
industry, university labs, medical industry, etc. all use ISO standards and
the metric system. The US semiconductor industry alone is larger than the GDP
of Switzerland. I studied engineering in America and we used the metric system
throughout with some problems in ANSI units for familiarization of the units -
ultimately, the engineer needs to adapt to the company's unit system and not
try to be a thorn.

I personally am tired of the rest of the world patronizingly explaining the
advantages of the metric system to Americans - over and over. It is not that
difficult of a concept and most technical people, engineers I know in the US
already understand the benefits of the metric system. It is mildly annoying at
best and condescending at worst. If we are in the unit system mess, there are
a lot of things that _still_ do not follow base-10 based units. For example,
font type units (points) from Switzerland. Or the way we measure time. How
come there aren't 10/100th units of a minute/hour commonly used around the
world? A second is split into 1000 milliseconds but a minute is not split into
1000 seconds. Why this inconsistency? Why 360 degrees? If we didn't have 10
fingers, the entire decimal system is worse than base 12 or duodecimal system
[3].

The problems faced by America are exactly the same type of problems if we want
to convert the entire world to duodecimal system. It is next to impossible
despite of clear advantages. Note that I am not defending the people that
arrogantly want to stick to status quo - there are certainly people like that
in the US.

[1]
[https://en.wikipedia.org/wiki/Metrication_in_the_United_Stat...](https://en.wikipedia.org/wiki/Metrication_in_the_United_States)

[2]
[https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_ba...](https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units)

[3]
[https://en.wikipedia.org/wiki/Duodecimal](https://en.wikipedia.org/wiki/Duodecimal)

~~~
msla
Another thing is that a large portion of the "metric" world isn't fully
metric, using old-fashioned units like miles and pyeong and tsubo. Really, the
whole metric vs non-metric debate comes down to _how much_ non-metric people
see in their daily lives, not any binary distinction between "always use
metric" and "never use metric" or anything of the sort.

~~~
swimfar
Almost the entire world still uses nautical miles, knots (speed), and feet for
aircraft altitude. I'm pretty sure most airplanes all use AN hydraulic
fittings, which are based on Imperial sizes (correct me if I'm wrong there).

Also, people always say that the US is the only country that uses feet,
pounds, miles, etc. But there are a lot of other countries that still use
those units, or at least understand them, even if it's not an official unit. I
even work with engineers from China who use and understand Imperial units. I
also visited a friend in Ireland who had a (pre-digital) scale that measured
weight in stones.

~~~
GuB-42
Living in France, general aviation is a bit of a mess.

\- Light aircraft use nautical units.

\- Ultralight use metric for speed and distance but feet for altitude and
vertical speed

\- Gliders use metric

\- Charts use feet for altitude. Aviation authorities define airspace using
nautical units but ground authorities use metric for things like fly over
altitudes. All converted to feet in charts but the legal text use meters.

\- AFAIK, mechanical parts for non-US built aircraft are metric. Pipe fittings
have always been in inches for some reason, but commonly converted to metric
(1/4in is written as 6.35mm).

~~~
fmajid
In France the Air Force uses feet for altitude due to NATO STANAG, and the
ALAT (Army helicopter corps) uses meters.

------
app4soft
> _ISO 216 defines the A series of paper sizes based on these simple
> principles:_

> _\- The height divided by the width of all formats is the square root of two
> (1.4142)._

> _\- Format A0 has an area of one square meter._

When we look on _A0 papers on the market_ mostly it's size is _841 mm × 1189
mm_ , that is not correspond to this standard:

\- Length Ratio: 1189/841 = 1.41379310345 (should be 1.4142)

\- Area: 0.999949 m² (should be 1.0 m²)

P.S. There are few websites which are useful for retrieving various paper
formats sizes.[0,1]

[0] [https://www.papersize.org/a-paper-
sizes.htm](https://www.papersize.org/a-paper-sizes.htm)

[1] [https://papersizes.io/a/](https://papersizes.io/a/)

~~~
function_seven
> _\- Area: 0.999949 m² (should be 1.0 m²)_

And it is! I mean, if you're not going to use an electron microscope to
measure it :)

The real measurements should be 840.9mm x 1189.2mm, but I'll forgive them for
the rounding.

~~~
occamrazor
All paper sizes are rounded to the mm and the rounding is always down, so that
is is possible to get two A(n+1) sheet by cutting one An sheet.

~~~
jwilk
It would be 840, not 841, if rounded down. Wikipedia says you should add 0.2
mm before rounding down (which gives you the expected 841), but it doesn't
explain where that number comes from.

~~~
brmgb
The answer to your question is in the comment you are replying to.

> the rounding is always down, so that is is possible to get two A(n+1) sheet
> by cutting one An sheet.

~~~
jwilk
Huh? I pointed out that the rounding is _not_ always down, and I didn't ask
any questions.

