Talk:ISO 216

B rationale

The definition, or rationale, given for the B series, is bizarre: geometric means between the A series format with a particular number and the A series format with one lower number. Perhaps that's true, but is this really the reason the B series was invented, or useful? Isn't a more useful explanation is that while the A0 was defined to have an area of 1m^2, the B0 was defined to have a (short) side of 1m? 192.114.107.4 (talk) 07:55, 7 April 2009 (UTC)

I have changed the article to reflect this Woscafrench (talk) 00:24, 21 February 2010 (UTC)

This is not the rationale that the standard itself (section 4.4) gives. Changing it back. Paul Murray (talk) 02:44, 13 October 2010 (UTC)

For those able to read German, the rationale is explained in the PDF with articles from the Discussion in the German standardization movement. This is linked to in the article ("external links"). --L.Willms (talk) 18:46, 13 May 2019 (UTC)

Root 2 rationale

I made a change to the rationale for using 1:sqrt(2) rationale for A paper as well as the inclusion of a few equations for proof. If someone can take a look at the changes and see whether or not they agree, I'd appreciate. I found the previous explanation to be badly written and confusing.Kakomu (talk) 21:15, 9 September 2008 (UTC)

Merge Silver rectangle into ISO 216?

I propose the merger for two reasons:

1. There is little that can be said about silver rectangles. Unlike golden rectangles, which are alleged to crop up everywhere and have a distinguished history, silver rectangles are of limited interest. The folding property should be described at ISO 216 anyway.
2. The name "silver rectangle" is both ambiguous and unfortunate. It is unfortunate because it is not a rectangle with the proportions of the silver ratio, as is suggested by the golden ratio/golden rectangle analogy. It is ambiguous because it is sometimes defined by root2 and sometimes by 1+root2 (the silver ratio), and there are not enough references to determine which is more common. I think the solution is to endorse neither, but to acknowledge in both ISO 216 and Silver ratio that they both have some claim to the name "silver rectangle".

Okay, I'm done. Melchoir 03:30, 21 March 2006 (UTC)

I think this is a good idea rafael.cosman

Okay, I'll get on it. Melchoir 04:18, 24 March 2006 (UTC)

Done. Rather than redirect Silver rectangle to either usage, I've made a somewhat unorthodox disambiguation page out of it. Melchoir 04:33, 24 March 2006 (UTC)

Inches

I propose that someone add inch equivalents to these measurements because Americans can't just see a measurement like 200mm and know how long that is. 71.227.254.181 23:57, 2 November 2006 (UTC)

Come on! Join the 21st century. We use millimetres and celcius now. It's beautiful. Come with us. Or get off your mental backside and learn the conversions and invest in a $1.99 pocket calculator. Write them on the back of it with a "sharpie" if you have to. A lot of us have had to learn how many metric units there are to an inch (25.41mm), foot (30.49cm), yard (91.48cm), mile (1609.3m), UK pint (568.3ml), US pint/standard lb (454.6ml/g), ounce (28.38g), UK gallon (4.546L), US gallon (3.637L) ... ETCETERA. It's not difficult. Half of those were off the top of my head. Half of them were derived with a few seconds work in Windows Calculator.

Also, if you're that bothered, why not just work 'em out yourself? Even Google will do the sums these days if you go to their online converter. (Sorry for the bile, but, god-damn... centre of the universe or what... we're working in SI units here. The measurements of science and international commerce. There'll be people in malaysia or somewhere wanting it in their old school units as well next) 193.63.174.10 (talk) 11:18, 23 October 2008 (UTC)

Why single out Americans for special treatment? This is an international English encyclopedia.

Although I'm all for making Wikipedia as accessible as possible, I must admit that I can't seem to muster any compassion for someone who doesn't know what a mm is. Shinobu 09:46, 16 November 2006 (UTC)

Let them have their inches. I can relate to the frustration, as everytime I come across an imperial measurement, I need to use google to convert it into something I can cope with. Hence, I usually add change it to SI units with imperial units in parenthesis when I come across it; no reason why we shouldn't add imperial units even when they're not present. The absence of a dual standard can make people campy about it, leading to articles that are either useless to Americans and akward for older Brits, or articles that are useless to the rest of the world. Zuiram 01:00, 16 December 2006 (UTC)

Question: should the inch equivalents be based on the A4 rounded measurements or the formula? Using the formula there is a difference (due to a rounding error) for a few of the inch values. Jw6aa 03:47, 12 February 2007 (UTC)

Answer: From a practical point of view, the inch equivalent should be based on the final measurements, not the formula. The ISO 216 is not for theoretical use but for printing and the like, where the final page size is all that matters in the end. - Tommi Kovala (unregistered user) 10:38, 21 March 2007 (GMT)

There shouldn't be any conversion to the Imperial system. The rest of the world has gotten up to time in a practical system and american isn't special or anything. -30 is 0 celsius, which is easier? Was the guy who thought of that on opium (then again, he probably was)

Psst, it's 32'F ;-) —Preceding unsigned comment added by 193.63.174.10 (talk) 11:19, 23 October 2008 (UTC)

I added inches but I guarantee this will be taken down by the wiki-overlords. There's a good reason to give inches as comparison at least in the line comparing US Paper Sizes to the international ones. That's especially true because when someone buys letter size paper it says quite plainly, 8.5" x 11", many times it does not say the metric equivalent. So inches maybe should not be all over the place, but it deserves an area in that line at least. —Preceding unsigned comment added by 74.72.44.116 (talk) 18:00, 6 September 2010 (UTC)

Everybody get your metric dicks back in your pants, jeez! I'm European myself, but every American I know of agrees they prefer the metric system as well, if they would have a choice. But they don't have the choice. for the same reason why we can't redefine the charge of the electron to be positive, Pi to it's true value of 6.28.., people in the UK to drive on the right side, all computers to agree on the same Endianness, et fucking cetera.

I'm European and I came to this article to find the measurements in both millimetres and inches, so I could describe the shape of an A7 to my european and american friends in an email. I remember that this article used to have the measurements in both units, but apparently because some dickhead felt he needed to remove those stupid inferior imperial units I have been wasting my fucking time. Thanks a lot, I'm off to Wolfram Alpha for, oh I don't know, useful reference material.

Wonderful how humans can get themselves completely deadlocked in the wrong solutions. Give me a call when you figure out a way to stop them from acting like a bunch of pack monkeys. Hint: it doesn't involve slinging more shit back and forth at eachother. As you can tell, I'm not in the business of trying to make them act more rational, or of the opinion that you can even succeed unless you fucking kill a monkey stone dead. Instead, I just try to cope. PEACE.

Why two duplicate tables

The table on the left should be deleted. The lower table is really very nice, but the drawings should be scaled consistently. jcp 05:38, 5 April 2007 (UTC)

Mistakes??

I'm pretty sure that the side parallel to the shorter side is another one of the shorter sides. I think probably perpendicular is what is meant.

Well, there's two ways to give the direction of a fold - give the direction of the crease, or of the folding motion. This, of course, makes both ways pretty useless. It should probably be phrased "by halving the preceding paper size's longer dimension," or such. Darekun 03:34, 17 July 2007 (UTC)

2007 Revision

Note that a Second Edition has been published as of 2007. I can't find information about what the revisions are, but someone should find out and update the article. —Preceding unsigned comment added by 69.46.127.11 (talk) 17:20, 10 September 2007 (UTC)

X vs. Y or Y vs. X (column major x row major or row major by column major)

For example, in the table with the various paper sizes "A4= 210 x 297". This is "x" by "y", or let's call it "length x height." Then we see "A3 = 297 x 420" or "y" by "x" or "height" by "length." This information is formatted the same way on almost any page on the Internet I could find, many of which had "pre-Wikipedia" feel to them, so I'm not questioning the accuracy at all. Is there a standard (ISO, ANSI, DIN, etc.) for the order for giving length and height measurements? (use "height" as a replaceable term for "width" if necessary). I notice that A3 has a horizontal orientation while A4 has a vertical orientation, and they give their "x" and "y" dimensions oppositely. Any significance to that? I know that putting an A4 sheet in front of a drafter in vertical orientation would earn you a weird look from him, so the orientation's aren't arbitrary.

On a side note, is there a standardization for whether "width" or "height" is the correct term for the "y" dimension?

Also, is there a standard order for quoting length and height/width in general? It seems like the natural order would be length (x) by width/height (y), being that human field of vision is significantly more horizontally oriented than vertically, so I was surprised to see A3 (and the other "fat" sizes) given with "y" dimension first. Being that drawing/drafting standards are as ambitious as they are, I can't imagine that no one has thought of this aspect B4. (my apologies for both of those awful, awful paper standardization puns). —Preceding unsigned comment added by 68.38.154.77 (talk) 00:46, 15 September 2007 (UTC)

The "orientation" of A3 isn't in any way different from A4. It's just displayed horizontally in the image to fit all the sizes neatly in to same rectangle. Ossi 14:05, 8 November 2007 (UTC)

• I have seen a lot of aspect ratios given as "longer side : shorter side". Any reason why not to do this here? TrueColour (talk) 00:59, 9 October 2008 (UTC)

Sounds sensible, given that the ISO sizes don't truly HAVE a "width" or "height" to them - you can orient the paper in landscape or portrait to suit your own needs. It just defines that one of the dimensions is "so much", and the other is a second figure. 193.63.174.10 (talk) 11:12, 23 October 2008 (UTC)

• The Concise Oxford English Dictionary uses column major by row major. E.g., A4 is 297 x 210 mm.

Considering there is no difference in mathematics or programming (different programs use either column or row major), English language as defined by Oxford, can set the rule for consistent measurements of column major. I.e.: column by row, height by width, 297 x 210 mm. Column major also happens to be logically alphabetical, allowing for an easy mnemonic. E.g., column by row is c x r. Height by width is h x w.

Now we need teachers to wave their hands to students:

for columns from top to bottom, then up slightly to the students' right, then straight down and repeat. Rather than waving their hand from left to right for columns.

for rows from students' left to right, then left and slightly down, then to the student's right and repeat. Rather than waving their hand from top to bottom for rows, which confuses the initial anchor understanding amongst students. — Preceding unsigned comment added by Eiger3970 (talk • contribs) 03:53, 31 March 2015 (UTC)

See Main Page....

there is a link to the main page on the sub-section on A4, but it's not a link.

can someone who isn't a code-noob (thats me) make this work properly!

thanks! —Preceding unsigned comment added by 128.243.253.111 (talk) 18:24, 6 February 2008 (UTC)

Formula looks broken?

I can't see the purpose of the " + 0.2 " in the formula which is described as yielding the "exact millimeter measurement" of the paper (the one with 1000/(...)) in it. Am I missing something? (I've never edited a wikipedia page before so am not about to try now :-). Neil Conway —Preceding unsigned comment added by 194.81.223.66 (talk) 13:33, 7 February 2008 (UTC)

I agree. The 0.2 bit needs a source if it should stay. Boivie (talk) 08:09, 30 March 2011 (UTC)

After a second thought; Maybe the standard is defined by rounding down values below 0.8 mm, and round up values above that. In that case you will get the right amount by adding 0.2, and put the result in a floor-function. A source would still be nice, though. Boivie (talk) 09:47, 30 March 2011 (UTC)

It was a long time ago, but it was me who added the formulae to the page, and I recall that I had to add the 0.2 as a fudge factor to make the formulae fit the known millimetre measurements. Without it, the numbers don't match, even though the formulae are otherwise logically sound. Adding 0.5 would make more sense, since in combination with the floor brackets would round to the nearest integer in each case, but this caused as many problems as it solved.

0.25 should probably be the correct fudge factor, given there are two requirements for the millimetre values: 1) Each should be an exact integer and 2) The product of consecutive values should be as close to the relevant fraction of 1m² as possible for the paper size. Note that 1m² = 1000000mm² = (1000mm)², which explains where the 1000 in the formulae comes from.

Since the product of consecutive values, per (2), involves the multiplication of two nearest integers, per (1), we'd have floor(x+.5)*floor(y+.5) somewhere along the way, and though the logic is shaky at this point two 0.5s multiply to become a 0.25.

0.2 works because it is close enough for the finite number of paper sizes available, and I left it at that because i) it made the formulae look less unwieldy (though, as pointed out, not by much) and ii) it works for all three paper classes, A, B and C, so it justifies itself somewhat. I'll have to check the numbers, but if they work with 0.25, I'll change the formula to have 1/4 instead of 0.2, as that would look more convincing. Cyrek (talk) 16:38, 11 January 2012 (UTC)

This is all bogus, according to one of the references linked to in the article. The A0 dimensions are rounded to the closest integer millimeter values from 2^(1/4) meters ~= 1.89207 meters and 2^(-1/4) meters ~= .840896 meters. That is, the long side is rounded down to 1892 millimeters and the short side up to 841 millimeters. The values for smaller paper sizes are gotten by dividing these integer values repeatedly by 2 and always rounding down. There is no need of a fudge factor, whether of .2 or .25. — Preceding unsigned comment added by 208.53.195.38 (talk) 18:40, 10 February 2012 (UTC)

I didn't make the formula but I understand why. I tried recreating the A serie table in excel and couldn't do it simply. Let say you calculate the EXACT (not rounded) A0, it gives 840.90 x 1189.21. To get the A1, you divide 1189.21 by 2, giving 594.60. If you round it, you get 595 which is no what the wikipedia table say. What I THINK happen is that they round A0 before calculating A1, and then round A1 with the round half down tie-breaking method (see the wikipedia article on rounding for details). That gives A0 1189, divided by 2 = 594.5, rounded DOWN to 594. This method works for ALL formats that are a division from a previous format (B1 to B10, C1 to C10). If you want to calculate B0, you can start with a width of 1000mm directly or do the geometric mean of the exact value of A0 (840.90 x 1189.21). For C0, I used the geometric mean of the rounded value of A0 and B0. If you have followed until now, this mean that in order to calculate A10 without fudge factor, you need to calculate A0, round it, calculate A1, round it, calculate A2, round it, etc... NOW. For the fudge value itself. If you compare the exact values from A0 to A10 with the ones from the wikipedia table, ONE TIME you would need to round up a value by an amount of 0.1, and the rest of the time you will need to round down by a value ranging from 0.11 up to 0.65. The fudge value bring those 0.65 values below the normal 0.49999 range that is properly rounded down by most software. Here's an added bonus, my formula for calculating the short and long side in excel, if the A1 cell contain the A-paper-size (0 to 10):

Short: =(1000 * SQRT(1/SQRT(2)) / (SQRT(2)^A1)) - 0.2

Long: =(1000 * SQRT(1/SQRT(2)) * SQRT(2) / (SQRT(2)^A1)) - 0.2

— Preceding unsigned comment added by 184.160.164.76 (talk) 01:09, 28 July 2012 (UTC)

It is not clear precisely how ISO 216 defines smaller paper sizes.

A0 paper is defined as having 1 m^2 area, and an aspect ratio of the square root of 2.

y * x = 1000000 mm, y / x = root(2)

y * x = 1000000 mm, y = root(2) * x

root(2) * x * x = 1000000 mm

root(2) * x ^ 2 = 1000000 mm

x^2 = ( 1000000 mm / root(2) )

x = root( 1000000 mm / root(2) ) ==============> Precise definition of A0 width

x = 840.89641525371454303112547623321 mm

---

y * x = 1000000 mm, y / x = root(2)

y * x = 1000000 mm, x = y / root(2)

y * ( y / root(2) ) = 1000000 mm

y^2 / root(2) = 1000000 mm

y^2 = 1000000 mm * root(2)

y = root( 1000000 mm * root(2) ) ==============> Precise definition of A0 height

y = 1189.2071150027210667174999705605 mm

Other A sizes are divisions of these A0 definitions.

_____________________________________________________

SO: If we start with A0 at 1 square meter by definition (1,000,000 mm^2) with an aspect ratio of 1:SquareRoot(2).

Do we find successively smaller A(n) sizes by

    dividing the base A0 area ( 1,000,000 m^2 ) by 2^n and rounding >=0.5 up & <0.5 down,

or

    dividing the larger dimension of the A(n-1) paper size by 2 and always rounding down to the nearest mm.

It seems the first method is more precise and does not require any recursion, but what does the ISO Standard actually specify?

The table of sizes indicates the bad 2nd method. If the Base A0 Area method is the correct one, we need to alter the article's table. Ace Frahm (talk) 16:30, 23 February 2013 (UTC)

Summing up regarding formulas and definitions:

• The formulas given for the actual sizes are CORRECT, but appear to be original research. This is not how the sizes are defined in the standard, according to [4]. I will change the wording to make this obvious.
• It is possible to derive a formula from the standard. This too would be WP:OR.
• It might be possible to prove that the formulas given are equivalent to the standard. This too would be WP:OR
• The text should present the actual definitions and sizes, as well as the "theoretical" relation between them. Care should be taken whenever the word "rounded" is used in the text. I will try to do this as well.

NisJørgensen (talk) 16:22, 19 December 2017 (UTC)

A00 paper?

Why not mention of A00 paper? It is in common use in draughting offices.

Sooo... how big is that? Presumably 2x the A0 size, so 1682 x 1189?

Also, the C sizes are not covered by ISO 216 and should only be referenced from these page. No detailed description necessary. 79.77.113.193 (talk) 20:22, 19 April 2008 (UTC)

Thickness

How thick/thin is A4 paper - 1mm/1μm/1nm/1pm?

Materials

Are material properties the only contraints for paper thinness?

Tools

Is there any special pen/ink to write on thinner papers?

Laws

Is there any minimum limit on thinness of paper to be accepted as evidence in a court of law?Anwar (talk) 09:15, 9 May 2008 (UTC)

What a bizarre set of questions. I'm afraid I can't give any answer for the law court thing, but for the rest, a braindump: For thinner paper I guess you'd use an oil-based ink (ie a Bic ballpoint rather than a fountain pen) and ultimately a soft pencil and a very gentle touch both to avoid the marks passing all the way through, or even tearing it. There's no defined thickness as far as I know in the ISO standards - these are simply measurements of 2D area / dimensions (width x height - thickness is far less important and easier to account for when designing a poster - or a printer - for example). How thick your paper is, and indeed even what it's made out of, pretty much depends on its intended use, and how much you're willing to pay. Thicker stuff made from better materials (e.g. with some parchment linen in the mix, less destructive bleaches, watermarks, inkjet compatible coatings) tends to cost disproportionately more. Also a paper grade tends to be measured more in terms of its density (in grammes per square metre for a single sheet) rather than its true thickness, as the latter can be fairly variable across the page (as its made up of lots of not 100% uniformly fitting fibres) and isn't that good an indicator of the ultimate quality or even the difficulty in transporting and in using the stuff (feeding it thru a printer or folding up to post in an envelope, say). General writing paper, such as in a student's A4 notepad, tends to be relatively thin, under 80gsm (50gsm or less?), and I'd estimate the thickness of a typical page around 100 microns (100um, or 0.1mm)... just enough to allow you to legibly write on both sides with a ballpoint, or a lightly applied fibretip/fountain pen. Typical printer paper is about 80 to 100gsm (for types that let you fit all of a 500-sheet ream into a laser printer bin), and premium writing or printer paper can go as high as 160gsm (typically the highest a mainstream printer allows, and sometimes you have to manually set a certain lever for it to fit - with settings for sub-100, 100-160gsm paper, and envelopes). You can test these figures for yourself better than I can thought-exercise them though... grab a set of scales and a ruler, and a known quantity of the material in question, and set-to. EG a 100 page writing pad (should measure about 1cm high with a moderate weight on top to squeeze out air from between the pages (100um x 100), and weigh about 500g --- 1 sq m for A0 = 1/16 sq m for A4, multiply by 80 and again by 100), or a 500-page ream of A3 printer paper (6.25kg for 100gsm, and maybe 6.25cm high industrially compressed into its packet). Have fun, hope this helps. 193.63.174.10 (talk) 11:01, 23 October 2008 (UTC)

Oops. Missed a bit. I don't know what you mean by the material properties being the only constraints on paper thickness, but at a guess .... yes, they are at least the main ones. Given what materials we have available to make paper & similar products from, there's a particular range of thicknesses that are useful for certain things for each type. EG parchment is very thick, but so brittle that it couldn't sensibly be much thinner, and you wouldn't dare fold it (hence, scrolls as storage). Normal mass produced paper is conversely pretty thin because of its more flexible nature, making it quite a bit more useful and versatile... in some cases it's made about as thin as it usefully can be (I've owned notepads where you could only sensibly write on one side ... with a pencil... and below that even we have tracing paper, tissue paper, etc). However it tends to be pretty absorbent, so for some uses like writing with a water-based ink pen or inkjet printing, better stuff has be used, and the addition of e.g. linen to the mix (letter writing paper) or special coatings (inkjets) makes it a bit thicker, stiffer (which can cause problems with some equipment or envelopes), and more expensive. Then there's poster card, projector transparencies (actually pieces of acetate plastic, but still using the ISO sizes), etc, which tend to be sold at the general 160gsm max for home/office machine use --- which is another definite constraint, as the mechanisms and sheer physical size of a device can only cope with a certain thickness and stiffness of substrate before they start pushing into industrial size/cost/etc territory --- or thicker for manual use only. Then onwards to actual cardboard and corrugated card, etc, which is a whole other area but still technically speaking really thick, strong paper that requires specialist printing (and cutting) techniques.

And that's about the limits of my knowledge so far as paper is concerned, from a quarter century lifetime of working and playing with the stuff to a minor-moderate extent (lots of printing, cutting, folding, and occasional administering because of schoolwork and then certain jobs). Why so interested? :D 193.63.174.10 (talk) 11:10, 23 October 2008 (UTC)

Suggest merge of Duplicate pages

This page and the Paper size page appear to have the same purpose / function and contain much of the same information. I suggest they be merged. —Preceding unsigned comment added by 88.106.221.168 (talk) 11:45, 25 August 2008 (UTC)

out of interest - A/B/C 8,9,10 sizes?

Anyone actually ever seen one of these up close? Unless they're used for defining the size of raffle tickets and the like, I can't see much call for anything under A8... Particularly not the envelopes! (I think I bought a novelty A8-ish size set of christmas cards with envelopes once - they fit ok, but were a bit fiddly to write and I wouldn't dreamt of trying to post them; A10 is almost stamp sized! Also I have an A7 notebook I bought because I spotted it going cheap in a trinket shop when on a trip and it had a nice design ... it proved to be very difficult to actually use! A6 is a lot more common (file cards, shorthand notebooks etc).

Not complaining or asking for removal, I'm just interested to hear if anyone actually uses such things in daily life or industry. 193.63.174.10 (talk) 11:23, 23 October 2008 (UTC)

I like having a stack of A7 heavy index cards around, useful for all sorts of things :) I don't really use any smaller sizes, but sometimes I cut one in half (for whatever reason), and then I know to call it A8, by definition :) Certainly I could cut it further, but at some point you've got to wonder if it's still useful to call them Ax anything, or to just quote the exact measurements in mm.

I'd also be interested to hear if anyone has stories about using the smallest sizes.

add brief explanation of DL envelope?

...or is this explained on its own page somewhere (to which we should link)?

I know what it is - wide and high enough that a piece of A4 folded into 3 along its long edge will fit neatly inside, typically for short missives with a max of about five pages... e.g. restaurant menus or other landscape type promo material, or a portrait letter / invoice / etc, typically with part of the letterhead (containing the recipient's name, mailing address and any other immediately relevant info) then being visible through a clear plastic window on the front, and the main content safely folded away on the other 2/3rds and not able to be shaken into view. But there's not even a short expo like that, and I'm not sure immediately where to or whether to include it 193.63.174.10 (talk) 11:30, 23 October 2008 (UTC)

Envelope sizes

Isn't the B-sizes generally used for envelopes? I vaguely remember using a B4-envelope to mail forms that shouldn't be folded, and B5-envelopes for "normal" folded letters written on A4-sheets. Should this be mentioned? —Preceding unsigned comment added by 92.251.150.23 (talk) 23:02, 11 April 2009 (UTC)

If you put DL into the wikipedia search box, there is an entry for "Dimension Lengthwise" which directs you back to this page. Although there is no discussion on this page, DL is mentioned as the final entry into the C series table at the top of page. As the C series is for envelopes, this seems logical. —Preceding unsigned comment added by 116.212.199.202 (talk) 00:17, 4 March 2010 (UTC)

History of Adoption?

The article mentions the publication of DIN 216 in Germany in 1922, but can anyone address the history of the adoption of these standard sizes of papers in the various countries of Europe. It would be particularly interesting to discuss when the UK went over to this metric standard. --SteveMcCluskey (talk) 22:36, 7 May 2009 (UTC)

Also, does anybody know which countries DON'T use it? The only country where I noticed that the paper is weird is the USA. 203.214.115.85 (talk) 16:14, 19 August 2009 (UTC)

I second this request. I have heard older people in the UK talking about foolscap and so on, but I'm not sure when they stopped using it. Someone reading this will know and be able to remember if there was a prolonged changeover period when you might get a stack of different-sized papers or something. A4 is ubiquitous now except for special purposes. Beorhtwulf (talk) 22:15, 28 February 2011 (UTC)

There was a gradual changeover in the UK in the mid and late 60s. This was an era before computer printers so the transition was easy. If the US had transitioned at that time then we would have a global standard now. When I was 16 and starting my A levels in 1971, all the writing pads were A4 or A5 and the old foolscap standards had almost disappeared. --Ef80 (talk) 22:19, 17 March 2016 (UTC)

In 1974 I had to re-type my dissertation at university when they changed the format for final submission from quarto to A4 after I'd already typed 20,000 of my 25,000 words. A lot of extra work in the days before word processing!! Even more annoying was that I (and the other students doing the same work) had experienced problems actually finding quarto as we all were using A4 by then! DickyP (talk) 08:35, 7 April 2020 (UTC)

Wha4 the A4?

This is a pretty good article, but like a lot of articles it forgets to give the quintessential piece of info, in this case, WHY did everyone except the US move to this system? I did a kind of O & M course a few years back, and the tutor said that the wonderful thing about this system is that you can cut a single piece of paper 1 square metre into any combination of A sizes and not waste a single square centimetre! This is kind of evident in the diagrams shown but it is not explicitly referred to. The other - even more fantastic thing - is that you can magnify (say) an A5 sheet on a Xerox, and the resulting A4 printout has EXACTLY the same proportions as the original A5 sheet! And draftsmen can purchase special sets of pens to use on these pages. The thickness of the lines the pens draw are calibrated to the different sizes of these sheets. So you can draw lines on an A4 sheet using the pen intended for that sheet size, then put that sheet on a Xerox and print a smaller version of your draft work on an A5 sheet. The picture will have exactly the same proportions as the bigger one. Then you can take a different pen (the one having a finer line and designed to work on A5 sheets ) and continue with your work. And so on for all sizes, magnifying up or reducing down. Try that with magnifying or reducing between quarto and foolscap!

I was around when Austalia converted from foolscap to A4 as the standard office size. I remember that at the beginning we all thought that the A4 sheet was absurdly short. Now, when I find some old document amongst my trivia and nostalgia items, I think, this looks like some medieval scroll. Actually, the article really needs some reference to the old imperial standards to round it out.

Btw, I am not a mathematician, but I gather that these A4 etc ratios are NOT the same thing as the golden mean, but that they are somehow connected. Is that true? Myles325a (talk) 07:28, 1 October 2009 (UTC)

Yes, if you put the sides on the same line and cut it by golden mean you get the propotion of the sides. So the propotions between the edges correspond to golden mean if im not mistaken. —Preceding unsigned comment added by 80.223.217.22 (talk) 20:22, 2 December 2009 (UTC)

That isn't true. A rectangle with the golden mean has the property that the ratio between the sum of the two sides and the long side is the same as the ratio between the long side and the short side. For A4 paper etc, the ratio between twice the short side and the long side is the same as the ratio between the long side and the short side. Woscafrench (talk) 00:24, 21 February 2010 (UTC)

C Series?

What rational was there ever for developing the C series? Surely there must have been a more pressing reason than that it is "the geometric ratio between the B series and the A series"? Woscafrench (talk) 00:24, 21 February 2010 (UTC)

I think the C series is to give sizes for envelopes. —Preceding unsigned comment added by 116.212.199.202 (talk) 00:15, 4 March 2010 (UTC)

Too many duplicates

The page content should be substantially reduced. No reason to have size tables twice, the nice size char for all three series is also presented twice. The specific property of "magic" aspect ratio is explained four times including the formal verification of ∀a≠0,b≠0: a/b = 2b/a ⇒ a/b = √2. Although I like formal verifications of statements, although Encyclopedic content must be verifiable, in my humble opinion, it is inappropriate present formal mathematic verifications of statements on pages like this one. If it is appropriate here, then someone should add formal explanation why weight of 1/16m2 80g/m2 paper is 5g also ...

And page should be renamed to reflect the ISO 269 formats are discussed here as well. Especially when you can ask Wikipedia for page related to ISO 269 and you will got one (different from this one). It's confusing.

To be short - to many duplications, too many unrelated information, too long, too hard to read.

• seconded. Paul Murray (talk) 02:24, 13 October 2010 (UTC)

193.179.199.50 (talk) 12:19, 27 July 2010 (UTC)

An+

The article doesn't explain the idea behind A0+, A1+, A2+ and A3+.--Oneiros (talk) 12:51, 18 October 2010 (UTC)

I came to the article looking for this info. Really should be added by someone who knows. Kvaks (talk) 22:18, 16 March 2022 (UTC)

Merge from Lichtenberg ratio

This Lichtenberg ratio article's content is pretty much already represented here, but in case there's any more, let's merge it before deleting; OK? Dicklyon (talk) 22:47, 15 January 2011 (UTC)

Go ahead, be bold.--Oneiros (talk) 23:07, 28 February 2011 (UTC)

More than a year later, I finally did this. Dicklyon (talk) 06:37, 17 March 2012 (UTC)

Query - Brother advert

In the current Brother adverts on TV certainly in the UK but almost certainly airing in other markets. Brother claim that A3 is 143% bigger than A4 in a sales pitch for their A3 format copiers.

Surely as A3 is twice as big as A4 then the claim should be 100%, can anyone help with this query? —Preceding unsigned comment added by 81.97.128.97 (talk) 14:38, 20 February 2011 (UTC)

(143%)² = 204% (So someone rounded up when he should have rounded down, but otherwise the number is approximately correct.) —Preceding unsigned comment added by 87.213.97.66 (talk) 12:42, 31 March 2011 (UTC)

A3 is about 30cm wide, A4 is 21cm wide. 30/21=1.43. So the width of A3 is about 143% of the width of A4 (actually 141% if you count millimeters). The area of an A3 is 200% of the area of an A4. So lengthwise the A3 is 41% bigger, and areawise 100% bigger. Boivie (talk) 14:47, 31 March 2011 (UTC)

B series

I understand why the C series is useful, and indeed many of the envelopes available in stationery shops are labelled in C sizes, but I can't understand what B is for and I don't believe I've ever seen it in use. Can anyone enlighten me? Beorhtwulf (talk) 22:16, 28 February 2011 (UTC)

Suppose that you are a bureaucrat in some public office and you should send an A4 document to someone and also include an envelope for reply. So, you will fold the A4 once and then it is A5. Then you put it into a B5 envelope and also include a C5 envelope so that the recipient can use that C5 envelope when sending back the filled document. That is how I have seen them used. ––Nikolas Ojala (talk) 23:24, 27 November 2014 (UTC)

1:√2 vs √2:1

Aspect ratio is commonly given by the longer side first, 5:3, 3:2, 4:3, 16:9 ... Anyone a reason why not doing so in this article? NuclearEnergy (talk) 20:39, 2 April 2011 (UTC)

Im not sure √2:1 would look right and anyway, aren't 1:x ratios usually written as 1:x and not x:1? Benboy00 (talk) 09:13, 30 April 2011 (UTC)

Could it be that the horizontal number usually is given first, and that papers primarily are considered in the portrait orientation? Boivie (talk) 10:40, 25 May 2011 (UTC)

Scaled Photocopying

I'm not sure quite what the "Application" section means with the stuff about scaled photocopying, but the English doesn't sound quite right or coherent. I fixed this a little, but I think either a rewrite or just a deletion may be more appropriate. Benboy00 (talk) 09:14, 30 April 2011 (UTC)

One practical thing I'm surprised is not mentioned in this article is the fact that if you, say, have a technical drawing in the scale of 1:50 (1cm measured on the drawing represents 50cm in the actual world) on a A1 sheet, you can scale that sheet in a (pretty large!) photocopier down two sizes to A3 and get the drawing to be in 1:100.

I believe this is a general quality of the system, that jumping between paper sizes always renders drawings and maps in more or less sensible scales.EDIT: well, I was wrong about that.

This fact ties into the following section about technical pens where it is mentioned that a particular line thickness scales up or down to the next size of pen in the series.

I am talking here from personal experience and half-forgotten lessons long ago, but I will try and see if I can find reliable sources for all this. Hjalti Þór (talk) 11:13, 16 September 2023 (UTC)

Duplication (again)

Why does almost everything in the article appear twice? Pdfpdf (talk) 12:13, 11 September 2011 (UTC)

Contradictory on where the standard is used

The opening says that "ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today, with the United States and Canada the only two exceptions." but the history section says that "Although they have also officially adopted the ISO 216 paper format, Colombia, Mexico, The Philippines and Chile also use mostly U.S. paper sizes in ordinary usage."

In my experience, while it might be true that Chile has adopted the standard, in practice the most commonly used format is carta (letter). The Wikipedia article on Chile concurs: [[1]]. So either the opening should say ISO 216 specifies the official paper size of most countries in the world today, or if it wishes to continue specifying the paper size used, it should also mention that Colombia, Mexico, The Philippines and Chile are exceptions.

--Siker (talk) 10:20, 23 June 2012 (UTC)

I agree with Siker, in Mexico you'd be hard pressed to find a store selling A4 paper, Letter and Legal being the norm (and what the government actually uses, despite official adoption of ISO 216). — Preceding unsigned comment added by 67.161.35.102 (talk) 10:17, 19 July 2012 (UTC)

Diagonal Sizes

I think diagonal sizes of the standarts (A4, A5, etc.) should be given in the tables.--194.27.186.205 (talk) 09:00, 21 December 2015 (UTC)

Discussion of German DIN standard

Crediting Portmann for developing the German standard in the 20th century ignores the statement that France already had the current and ISO A2, A3, B3, B4, and B5 in 1798. What did Portmann actually develop? Since this material is unsourced, I am deleting it until someone comes forward with well-sourced information about what Portmann or the DIN standard contributed.—Finell 01:53, 11 May 2016 (UTC)

Formula reduction on A4 size

The change that was undone: https://en.wikipedia.org/w/index.php?title=ISO_216&diff=next&oldid=882463098

Discarding the naming convention for short/long sides, quoting the text:

...x/y = y/x/2, which reduces to x/y = √2...

Rearranging the formula leads to:

x2 = y2/2

which reduces to

x2/y2 = 1/2}     =>     x/y = 1/√2  =>     y/x = √2

meaning that the numerator and denominator in the fraction on LHS should be swapped.

Yossik ov (talk) 19:09, 9 February 2019 (UTC)

@Yossik ov: you rearranged the formula incorrectly. It should be:

x² = y²/1/2

which reduces to

x²/y² = 2

x/y = √2

— JWilk (talk) 19:11, 11 March 2021 (UTC)

Pen widths

A good-faith editor reworded an apparent recitation of the specification (using "shall"); I tried to rewrite the paragraph using encyclopedic language ("The pen widths are specified to be..."), but hit a problem. There are three (3!) references, and all are defective. We have the absurdity of a commercial organisation charging 50 Swiss francs or so to read the wording of the specification, and are left relying on various manglings. The fact that using pen nib sizes in the root(2) sequence would match the corresponding drawing scaling is an obvious, ineluctable mathematical fact that (in a rational world at least) needs no "source". But perhaps the standard actually gives specific thicknesses for lines at different drawing sizes? If so, the wording should reflect this; but no reference tells us. The metrication.com site appears to give specified line widths for A0 and A1, then claims "just use the same for A2, A3, and A4, which is nonsense. The designingbuildings.co.uk site (can't spell "its") shows ISO pens mixed in with other pens, and just mumbles about the general principle. Markus Kuhn (can spell "its") again just gives the general principle. Does anyone have access to the standard itself? Or a statement of all the facts of the stardard written in prose that is not a copyright violation? Imaginatorium (talk) 03:59, 3 April 2019 (UTC)

"C-size" listed at Redirects for discussion

An editor has asked for a discussion to address the redirect C-size. Please participate in the redirect discussion if you wish to do so. _signed, Rosguill ^talk 23:21, 5 February 2020 (UTC)