# Reason for A paper size width/height ratio **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [November 21, 2009, 7:27pm UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436 "2009-11-21T19:27:01Z")\ **Posts on this page:** 8\ **Page:** 2
**Author:** ![jasonh300](https://avatars.discourse-cdn.com/v4/letter/j/46a35a/32.png) [@jasonh300](https://boards.straightdope.com/u/jasonh300)\ **Post date:** [November 23, 2009, 8:09am UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/21 "2009-11-23T08:09:44Z")
> [@Exapno\_Mapcase](#): > > I can’t understand what you mean by this. Of course you have to refigure the number of words on a given line. In the days of setting lead type, you couldn’t scale it down that way. Neither typography nor readability works that way. The type size for a trade paperback is not half that of a large hardback. It likely is the same. You can’t use the same margins or leading for a book page twice as large or half as large either. Everything needs to be redone from scratch. The problem I run into on a daily basis: People bring artwork in to me, laid out at 8 1/2" x 11", to print flyers. Then they decide that they want posters, printed on 11" x 17". But the proportion is different. You end up with a few inches of white space at the top and bottom. Nobody can understand this. They try to tell me that 8 1/2 x 11 is half of 11x17, so you just have to enlarge it. They can’t understand why I can’t enlarge it without changing the proportions. Then they decide they want a smaller flyer…5 1/2" x 8 1/2". Once again, white space at the top and bottom. And then tiny little postcards…5 1/2" x 4 1/4". Each of these is cut in half, but the proportions are all messed up. The only time the ratios line up is if you go from 11" x 17" to 5 1/2" x 8 1/2". Also 8 1/2" x 11" down to 4 1/4" x 5 1/2" (but then they want the postcard at a more standard 4" x 6", which doesn’t work proportionally with anything.) The International Standard paper sizes would work well for me…I’d never be able to remember the dimensions, but it’d save me a lot of trouble. ---
**Author:** ![Dave.B](https://avatars.discourse-cdn.com/v4/letter/d/9f8e36/32.png) [@Dave.B](https://boards.straightdope.com/u/Dave.B)\ **Post date:** [November 23, 2009, 12:47pm UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/22 "2009-11-23T12:47:50Z")
Also maybe worth noting, in terms of the scale issue at least, is that if you have an A1 CAD drawing at 1:100 scale, it will print out very nicely and conveniently on A3 at 1:200. ---
**Author:** ![Alex\_Dubinsky](https://avatars.discourse-cdn.com/v4/letter/a/dbc845/32.png) [@Alex\_Dubinsky](https://boards.straightdope.com/u/Alex_Dubinsky)\ **Post date:** [November 24, 2009, 4:16am UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/23 "2009-11-24T04:16:45Z")
Ftg convinced me. The sqrt(2) standard was nowhere as rational as it seems. Too bad there’s so many thick people not understanding ftg (or maybe the understanding ones aren’t posting–always a sad phenomenon in threads). It’s found it advantages today, though. Makes a lot of sense with computers. > [@Dave.B](#): > > Also maybe worth noting, in terms of the scale issue at least, is that if you have an A1 CAD drawing at 1:100 scale, it will print out very nicely and conveniently on A3 at 1:200. :smack: Two scale-downs will give you back exactly half the original page no matter what its ratio was. ---
**Author:** ![dropzone](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dropzone/32/7515_2.png) [@dropzone](https://boards.straightdope.com/u/dropzone)\ **Post date:** [November 24, 2009, 5:17am UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/24 "2009-11-24T05:17:32Z")
Since so much of my, for now, former profession was structured around the standard ANSI and Architectural (US) paper sizes, and considering the several, given a plotter using a roll of a specific width but indeterminate length and that I plotted all copies rather than sending them out to a print shop, paper sizes I invented for my own use, this thread has me misty-eyed. ---
**Author:** ![Tenebras](https://avatars.discourse-cdn.com/v4/letter/t/977dab/32.png) [@Tenebras](https://boards.straightdope.com/u/Tenebras)\ **Post date:** [November 24, 2009, 6:58am UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/25 "2009-11-24T06:58:37Z")
> [@ftg](#): > > Just to make it 100% absolutely clear. I am fully aware of the special property of sqrt(2) insofar as preserving the ratio. > > Got that? Anyone not able to understand this? > > In particular, **Tenebras** , just FYI. I have PhD in Computer Science. I can do basic Math. I am aware that 5x4 and 8x5 are not the same proportions. **In fact that was the whole point of the example!** (I would really like an explanation as to why you would suspect I wasn’t aware of this.) > > That in no way explains why paper makers _have_ to choose that ratio. It seems to me to not be so much sensible as compulsive. (Remember the OP?) There is one, and only one, reason why paper makers should choose the ratio 1:sqrt(2). The reason is that cutting such a piece of paper in half results in two pieces of paper which are similar (in the sense of geometry) to the original sheet. That’s it. That’s the reason. If this is a property which you would like your paper to have, then there is one and only one ratio to choose. A system of standard paper sizes based around this proportion is nice because any sheet of A_n_ paper can be cut or folded to be the next smaller size and _the proportions remain the same_. That’s the reason and it’s the reason that your Z paper is not as convenient. Any sheet of _A_ paper is the same shape as any other sheet of _A_ paper. I never thought that you did not know that 8:5 and 5:4 were different ratios, I was simply posting to make clear that the “Z” scale paper does not have the shape preserving aspect. If you wanted to extend the notation you could say that a sheet of A_x_ paper is a sheet whose sides are in the ratio 1:sqrt(2) and whose area is 2[sup]-x[/sup]. Then B0 paper would be approximately A(sqrt(2)) and C0 would be approximately A(fourth root of 2). Does this kind of thing display an obsessive attention to detail? That depends on what you consider obsessive. Is the metric system obsessive because one kilometer is 1000 meters? There’s no physical reason why most of the world doesn’t use feet and miles, just convention. Just for completeness’ sake, the ANSI sizes (A, B=letter, C, D, E) are defined retroactively in terms of letter paper and doubling, but have the unfortunate side-effect of being different shapes. ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [November 24, 2009, 7:28pm UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/26 "2009-11-24T19:28:24Z")
> [@ianzin](#): > > I’m sorry they don’t have [Wikipedia](http://en.wikipedia.org/wiki/Foolscap_folio) where you live. They do. It’s just down the street. I can’t interupt my train of thought every time to look _everything_ up. Unfortunately, if I spent all my time looking up all the stuff I wondered about, I’d spend every waking hour on the internet, and never get anything done… Oh wait… ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [November 24, 2009, 8:27pm UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/27 "2009-11-24T20:27:34Z")
**Alex Dubinsky** : Please do not refer to other posters as “thick.” A ream of paper is thick, not other posters. Personal insults are not permitted in this forum. ---
**Author:** ![Powers](https://avatars.discourse-cdn.com/v4/letter/p/edb3f5/32.png) [@Powers](https://boards.straightdope.com/u/Powers)\ **Post date:** [December 2, 2009, 4:01pm UTC](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436/28 "2009-12-02T16:01:29Z")
> [@Alex\_Dubinsky](#): > > The sqrt(2) standard was nowhere as rational as it seems. I don’t see how the square root of two could ever be rational. =) Powers &8^] [Previous page](https://boards.straightdope.com/t/reason-for-a-paper-size-width-height-ratio/518436.md?page=1)