I like this paragraph from the article. Sort of first principles approach to the whole thing :)
"The basis for the whole system is the A0 format which has an area of one square meter. With an aspect ratio equal to the square root of two, a sheet of A0 paper ends up being 841 × 1189 millimeters. Figuring out the dimensions of the subsequent paper sizes does not require any real mathematical strain since each ensuing size can be created by simply folding the paper in half with the crease parallel to the shortest sides. If you do this with an A0 sheet of paper, the resulting dimensions will be 594 × 841 millimeters, or the A1 format. Take note that the height of A1 is equal to the width of A0"
This is true if the ANSI A/B/C/D/E series as well. It’s just that the successively smaller pages don’t have the same aspect ratio. The square root of two is the key point.
I do love how clever the international standard paper formats are. I also find the shape nice to use - coming from an international perspective, the Letter paper size feels to me uncomfortably short and squat, but then I hear Americans say they like the Letter paper's ratio much better than A4 - and at the end of the day, I think a lot of it is just that - familiarity.
It's the exact same thing with a lot of the US customary units vs. metric debate - so many more of the arguments actually boil down to mistaking "I'm familiar with this so it seems better" for meaning one is objectively better. It does definitely lead to some funny assertions, like people asserting that billions of people's ease of using metric units or Celsius temperatures must be false since the units are apparently not "human scale" etc.!
In moving from EU to the US, the biggest difference I noticed is the reliance on fractions over decimals. 1/4th of something as opposed to .25. That’s probably what I miss the most about using the metric system on a daily basis.
Using fractions sounds great, I think fractions have a human quality and are a more natural way to approach numbers. In writing, I think putting down 0.5 is slightly jarring compared to the better ½, at least in non-technical contexts.
I think this is also a case of just being more familiar with something, I find "1/2" or "3/8" much harder to parse than "0.5" or "0.375" (having grown up in the EU).
Totally agree.
And how does it work when you measure a thing and it is 1,35 inch do you in the US convert it to fractions? And how then do you find this fraction?
A ruler sold in the US (and Britain, on the reverse/bottom) has inch markings with fractions.
│.╷.|.╷.│.╷.|.╷.│.╷.|.╷.│.╷.|.╷.│
0⅛¼⅜½⅝¾⅞1
So the measurement, when taken, is 1⅜".
I've seen inch rulers with different fractions, e.g. one end might be eights, the other sixteenths, turn it over and there are tenths.
(I don't know how this works with digital measuring devices — I grew up in Britain so have never used inches professionally. Only in Warhammer and TV screens.)
With digital devices I assume there is a mode switch like in the digital scales I have at home in the US. I actually work in grams for things like bread making which seems easier than a combination of pounds and ounces.
I think I want my writing to reflect how I talk or think about it. So if the spoken sentence is "specification is a half millimetre" then write with ½ instead of "0.5" because the former will be read out correctly.
One classic trick to estimate a proportion is to do it as a fraction. It might be hard to tell that someone ate 44 % of a pizza, but significantly easier to judge that they ate a quarter and three quarters of the next quarter (which is 7/16 which is 44 %.)
That said, as soon as I need to do any arithmetic on the number (including compare it to other numbers) I convert it from fraction to decimal.
A foot being 12 inches makes fractions work really well in US units (as well as a mile being 8 x 10 x 11 x 6 foot). And with it working so well, many people don't seem to be able to imagine to work without them.
In metric a meter isn't as nicely divisible. Of course we get around that by subdividing 1.2m or 1.5m instead (or 0.8, kitchens and lots of furniture is designed in outer dimensions that are fractions and multiplies of 0.8 meters). But that only works well if you write them out add decimals, because saying "this cupboard is 1/2 0.8 meter wide" is just silly
The metre is not used for everything. The standard for construction and manufacturing is the millimetre. In the UK a standard kitchen unit is a 600(mm), with 300 and 900 varients. Appliances come in 500, 600 and 900 widths, that being the gap or unit they (should!) fit into. It would feel unatural to me to say 0.6 etc for a unit. These common dimensions are used like nouns, "You need 3, 600s" rather than "You need 3 units 600mm wide" tying them more closely to language and perhaps then harder to change.
I agree. I’m from Europe and being trimmed to metric through and through. My main issue with the us or imperial units is not so much the conversion factors and weird rules. It’s the simple fact that I have no feeling how hot or cold a given temperature is, how long or short a given measurement etc. Just being exposed to the system and trying to live with it helps. Sure one still converts all the time mainly to get a familiar value to compare too. But after a while that doesn’t really matter. In the end it’s mostly important if for example is 80F a warm day or not? Is 1,5miles a long walk? Etc.
Sure adding ease of use when calculating with units is a different thing. But I understood that woodworkers etc like to measure in 8th/1000th of an inch. Something I would need to be exposed for years to be able to do.
In the US I have the same issue with Celsius (plus the degrees are bigger). But I assume I could fairly easily spend some time to mentally align the scales and develop the intuition from there if I spent any time using Celsius day to day.
True. For example, as an European I'd obviously have some difficulties expressing sizes in inches and feet, but I'd have some difficulties too if I was buying a new monitor or TV and the clerk asked me the screen size in centimeters.
Well, from my own experience if you have to fit a TV set in a given space (e.g.: between two libraries) you go to the shop with the width and height of that space in centimeters and you don't care much about the diagonal in inches. You buy the largest screen that fits.
Same in Japan, though they're usually not called "inches". So my TV size is "65 series".
But "the biggest you have" is not the right answer for TV size: if your room is small and your TV is too large, it's uncomfortable to view it. The TV needs to be sized according to the viewing distance. Usually, this isn't an issue for most people: too-large TVs are usually outside their budget. But this is changing, as bigger and bigger TVs become less expensive.
What I mean by that comment is that people might come to a store and think: "Wow, this 65" TV is huge, I don't need that". But they are forgetting that when watching a movie, a lot of screen space is unused, because the aspect ratio is different (those black bars on the top and bottom).
So, if you can fit the TV somewhere, it's always a good idea to pick a larger one than you think you need.
I recently discovered something strange. If you buy a large format photo printer then a common paper size for larger prints is A3+, which is roughly 13"x19". The paper is readily available in this size in office stores and online.
If you then go to a craft store or art supply store to buy photo frames, you will find very few if any frames that match that paper size. It seems that the "fine art" world uses certain sizes that are not common sizes of photo paper! This is frustrating for me as I will sometimes want to print a photo as a gift for someone last minute and I always have to order frames from mail order and keep a few extras around. I wish i could go to the local shop and buy A3+ sized frames but even when there are some the selection is extremely limited compared to other sizes.
My understanding is that the kind of workflow used in that area is to print from a roll of paper with a bit of bleed (printing slightly larger so there’s no white edge) and then cutting down to the desired size?
It is annoying trying to get good sized frames, maybe a lot of them are custom made too? Often they’ll at least have a custom mat board cut I think.
My printer uses sheets and cannot print on rolls. It prints borderless (that is, cleanly up to the full edge of the page) so no cutting is needed.
I can order frames online (Craig Frames company). I was just surprised when I found out that this rather common large format photo printing paper size was a very uncommon frame size, and at three different local stores which sell a lot of large frames, they had little to no selection in that particular size.
My fiancée made a wonderful series of 3 watercolor paintings for me of the musical instrument I play. She’s not a pretentious paper art genius (she makes digital art for video games), so she just used the standard size she bought at the store that came as a full stack of tear-off pads for watercolor: 14”x20”, assuming that we would just be able to slap them in frames when we were done. All the local framing shops and even the chain store quoted us hundreds of dollars just to cut the border mats that would adapt them to standard frames. Online I found a solution that was tens of dollars for all 3 frames and mats and it really made me feel like a loser for going out of the way to drive around and shop local in the SF Bay Area.
So I encountered this Purgatory over the course of several years, since I began to earn professional certifications. These certificates came in standard Letter size, 8.5x11 pages, with glossy durable paper. They also issue them electronically in PDF format, Letter-size as well, so it's easy to print them and even upgrade paper quality. Last year, I finally earned graduation from college, and my certificate came in the mail: 8.5x11 as well!
So where are the Letter-size picture frames? I want to hang these credentials on my wall, or frame them and place them on a shelf! They will look very nice that way! But all picture frames on the market are for 8x10 photographs! So it's horrible; I can't use the standard-issue, original certificates at all. I can't print them as-is, and reducing their size does not yield the 8x10 aspect ratio you need.
Eventually, over the course of several years, I've managed to amass a few 8.5x11 picture frames from thrift stores. It wasn't easy, they don't match one another, and they're uncommon, but they do exist. Likewise, no big-box store or specialty framing store seems to carry such an animal.
So if these frames are so unobtanium, why are these authorities issuing certificates in this size? Don't they know we have little hope of framing them nicely? Surely there is some sort of disconnect, and surely there is a market-niche opportunity, especially for college-grads, like Josten's, or our college bookstore, to source these and sell them to us!
Yeah there’s so many different options for 8x10 and then 8.5x11 there’s often only very cheap looking thin glossy black plastic frames.
Take a look at a company called Craig Frames. That’s where I get my A3+ frames and they are lovely. Pay attention to which ones are solid wood and not just a veneer, if you have a preference. Though the veneer looks good too.
My only frustration with this situation is that I have to go online as local shops ignore that size.
Local framing is very artisanal and therefore quite expensive. These days it almost certainly makes more sense for all but the high-end case to just go online. Reminds me to add some frames or at least mattes to my to do list.
> Local framing is very artisanal and therefore quite expensive.
Local framing can be art in itself, and can definitely enhance art. As an example, I have a Vonnegut silkscreen print ("Black Heart") that I find quirky and endearing and love its origin -- but is a bit of a challenge to present in a way that doesn't dominate anything with which it shares a wall. I would have gone with a large mat and oversized frame to reduce the impact of some of the more... exotic... color choices; but the framing shop I worked with proposed a double frame with an outer black frame and an inner painted green wood frame that /exactly/ matches the color of the piece, and the result is stunning.
Maybe that’s why it was created, but I think my use is pretty far removed from that. I simply want to print the largest photos possible on my printer and that’s A3+. It prints beautiful borderless photos with no need to cut them. But despite readily available paper, frames are much less common.
I wonder how much of the Baader–Meinhof phenomenon is the result of everyone browsing the same few social media sites. The latest microtrend of one small area of a site spreads to other sites or similar areas of other sites. Once you see it in somewhere, it really does go everywhere.
Why wouldn't people use it? Simple: it was created by a German, not an American, so the US is unable to use it. The US can only adopt standards that were invented in America, with rare exception.
Anytime you see the US doing something different from the rest of the world, investigate to see who first invented and popularized it: it almost certainly came from outside the US. Whereas if there's some global standard that even the US uses, it probably got started in the US.
Which makes perfect sense. In many cases the US was probably already using their own standards/conventions when some, typically European-driven, standardization effort came along. And the US never saw a reason to go through the effort and cost to broadly switch. Aligning with Europe just isn’t a high priority.
As is widely remarked the US does use metric where it makes sense to do so. It’s just mostly not consumer-facing.
The US uses metric in some places, such as the automotive industry, but it took decades to do. For a while, in the 90s, American cars were a nasty mixture of SAE and metric fasteners, so you had to have two sets of wrenches to work on them. Meanwhile, not aligning with Europe (or anyplace else in the world) meant that American-made products were a hard sell since they were too hard to service.
In my country (Paraguay) traditional formats were U.S. Letter and "Oficio" (which I shall explain). Now we are slowly transitioning to ISO paper sizes so A4 size is becoming common and widespread. In my case (as an official translator) I have standardized all my practice to A4 sizes.
Now, a holdout is the "Oficio" size, which created a lot of problems for us. This size is usually described in printer drivers as Fanfold or Long Bond, and it is very similar to U.S. Legal size, but one inch shorter in its length (8.5 × 13 in, 216 × 330 mm). South American paper mills often call it "Oficio 2". This was, and still is in many regards, the required format for all official bureaucratic and court paperwork.
This created a lot of trouble for us because in most Spanish localizations companies (example: Microsoft in MS Office) simply translated the "Legal" paper size as "Oficio". Then every secretary and clerk here selected it believing it is "our" Oficio, only to find that text was cropped at the bottom because that "Oficio" was in fact one inch longer than our format. This led to all kinds of manual (mis)formatting.
I think this format had a German origin and came to us through old Spanish practices, but I can't be sure.
Again, thankfully this is becoming a thing of the past since A4 is slowly becoming the standard...
EDIT: That paper size is also known as "US Government Legal" and "Foolscap" and according to Wikipedia is still in use in various parts of the world.
This is the standard legal size in NY, the rest of the country uses the longer legal size. Except then some law firms in other states but based in NY still use the shorter size.
For construction plans the A0 and A1 paper sizes are standard. But those paper sizes don't come as sheets, they are printed on a roll of ca. 900mm wide and cut by the printer.
So if the drawing doesn't fit on a standard paper paper we just take the width of an A0 (841mm) and pick some arbitrary length. My personal limit is 200cm because then it becomes a bit impractical to handle. And if it really, really doesn't fit in the 841mm width, I'll take the edges of the 900mm that are usually cut off too instead of splitting the drawing awkwardly over two papers.
> Early pen plotters, e.g., the Calcomp 565 of 1959, worked by placing the paper over a roller that moved the paper back and forth for X motion, while the pen moved back and forth on a track for Y motion. The paper was supplied in roll form and had perforations along both edges that were engaged by sprockets on the rollers.
> In the 1980s, the small and lightweight HP 7470 introduced the "grit wheel" mechanism, eliminating the need for perforations along the edges, unlike the Calcomp plotters two decades earlier. The grit wheels at opposite edges of the sheet press against resilient polyurethane-coated rollers and form tiny indentations in the sheet. As the sheet is moved back and forth, the grit wheels keep the sheet in proper registration due to the grit particles falling into the earlier indentations, much like the teeth of two gears meshing. The pen is mounted on a carriage that moves back and forth in a line between the grit wheels, representing the orthogonal axis. These smaller "home-use" plotters became popular for desktop business graphics and in engineering laboratories
I think plotting on sheets was more common though.
When I studied drafting at school (age 15) in the 80s, we took paper off a roll using a guillotine slicer and the thing that held the roll had markings for the right length for A0 and A1, so you'd just pull the end of the roll to the 'A1' mark, and slice the slider across, and you had a sheet of A1 in your hand.
Sadly, this meant that the paper would have natural curl to it, but it wasn't a big deal once you'd taped it to your drafting table with masking tape.
ANSI sizes F and above define various standard “roll” sizes. I’ve never had a need for roll format, but I’ve wondered what the ISO equivalent was. Wikipedia says these were used for full-scale layouts of aircraft parts, automotive parts, wiring harnesses, etc, and in some visual art fields.
A fair few years ago I worked for a company that did a lot of business in the US. To test our software we had to get a ream of letter paper shipped out and configure a dedicated printer tray for it. Quite a lot of fuss, but when you make documents that have to be printed it’s a must.
We also had to get a cheque scanner and a book of sample cheques shipped over to integrate that in to the software, that was a fun experience!
And then you may feel inspired to acquire paper of all the different types and weights and sample how they perform with various media. Art supply stores, besides stocking premade pads and sketchbooks, often have a back area with drawers of loose paper and slightly more exotic things like acetate. However, while you can get something to a rough standard, you will never really get the same paper twice because the processes and available ingredients keep changing.
Since the paper weight being measured in grams per square metre, and:
- The A0 sheet is a square metre
- A1 is half that, A2 half again etc.
- It's simple to calculate the weight of any particular A-series sheet.
This is (nowadays only rarely) useful when determining the postage. If I have 6 A4 pages of typical 80g/m² office paper to post, the weight is 6 × (80 / 2 / 2 / 2 / 2) = 30g.
Until recently, the cheapest national postal rate was for up to 50g, so this was a relevant calculation for the once-in-five-years I sent a multipage letter.
Which matches up with large format sheet film and typically close to medium format. But is actually a significantly different aspect ratio from 35mm which became almost universal over time.
An older relative used to say "if a note is smaller than A4 it does not exist". I think it was from long experience of people losing important information when it was printed on a paper size smaller than A4. I try to keep that in mind whenever the frugal homunculus in me wants to print information in smaller formats to save on paper.
The standardisation of ISO paper sizes is nice, but it's also an annoying limitation when it comes to folding paper planes (if one wants to do it with small children that are not yet competent users of scissors), because it limits the amount of models that are viable.
63 comments
[ 2.5 ms ] story [ 127 ms ] thread"The basis for the whole system is the A0 format which has an area of one square meter. With an aspect ratio equal to the square root of two, a sheet of A0 paper ends up being 841 × 1189 millimeters. Figuring out the dimensions of the subsequent paper sizes does not require any real mathematical strain since each ensuing size can be created by simply folding the paper in half with the crease parallel to the shortest sides. If you do this with an A0 sheet of paper, the resulting dimensions will be 594 × 841 millimeters, or the A1 format. Take note that the height of A1 is equal to the width of A0"
It's the exact same thing with a lot of the US customary units vs. metric debate - so many more of the arguments actually boil down to mistaking "I'm familiar with this so it seems better" for meaning one is objectively better. It does definitely lead to some funny assertions, like people asserting that billions of people's ease of using metric units or Celsius temperatures must be false since the units are apparently not "human scale" etc.!
│.╷.|.╷.│.╷.|.╷.│.╷.|.╷.│.╷.|.╷.│
0⅛¼⅜½⅝¾⅞1
So the measurement, when taken, is 1⅜".
I've seen inch rulers with different fractions, e.g. one end might be eights, the other sixteenths, turn it over and there are tenths.
(I don't know how this works with digital measuring devices — I grew up in Britain so have never used inches professionally. Only in Warhammer and TV screens.)
To you, it’s obvious and natural that „half” is 1/2.
To me, it looks off and I have to „convert” it in my mind to 0.5, which is the way I think about it.
That said, as soon as I need to do any arithmetic on the number (including compare it to other numbers) I convert it from fraction to decimal.
In metric a meter isn't as nicely divisible. Of course we get around that by subdividing 1.2m or 1.5m instead (or 0.8, kitchens and lots of furniture is designed in outer dimensions that are fractions and multiplies of 0.8 meters). But that only works well if you write them out add decimals, because saying "this cupboard is 1/2 0.8 meter wide" is just silly
True. For example, as an European I'd obviously have some difficulties expressing sizes in inches and feet, but I'd have some difficulties too if I was buying a new monitor or TV and the clerk asked me the screen size in centimeters.
However, in the aforementioned scenario (buying a new TV), the correct answer is always: "the biggest you have".
But "the biggest you have" is not the right answer for TV size: if your room is small and your TV is too large, it's uncomfortable to view it. The TV needs to be sized according to the viewing distance. Usually, this isn't an issue for most people: too-large TVs are usually outside their budget. But this is changing, as bigger and bigger TVs become less expensive.
What I mean by that comment is that people might come to a store and think: "Wow, this 65" TV is huge, I don't need that". But they are forgetting that when watching a movie, a lot of screen space is unused, because the aspect ratio is different (those black bars on the top and bottom).
So, if you can fit the TV somewhere, it's always a good idea to pick a larger one than you think you need.
It is annoying trying to get good sized frames, maybe a lot of them are custom made too? Often they’ll at least have a custom mat board cut I think.
I can order frames online (Craig Frames company). I was just surprised when I found out that this rather common large format photo printing paper size was a very uncommon frame size, and at three different local stores which sell a lot of large frames, they had little to no selection in that particular size.
So where are the Letter-size picture frames? I want to hang these credentials on my wall, or frame them and place them on a shelf! They will look very nice that way! But all picture frames on the market are for 8x10 photographs! So it's horrible; I can't use the standard-issue, original certificates at all. I can't print them as-is, and reducing their size does not yield the 8x10 aspect ratio you need.
Eventually, over the course of several years, I've managed to amass a few 8.5x11 picture frames from thrift stores. It wasn't easy, they don't match one another, and they're uncommon, but they do exist. Likewise, no big-box store or specialty framing store seems to carry such an animal.
So if these frames are so unobtanium, why are these authorities issuing certificates in this size? Don't they know we have little hope of framing them nicely? Surely there is some sort of disconnect, and surely there is a market-niche opportunity, especially for college-grads, like Josten's, or our college bookstore, to source these and sell them to us!
Take a look at a company called Craig Frames. That’s where I get my A3+ frames and they are lovely. Pay attention to which ones are solid wood and not just a veneer, if you have a preference. Though the veneer looks good too.
My only frustration with this situation is that I have to go online as local shops ignore that size.
https://www.michaels.com/shop/frames/wall-frames/document-fr...
(and also as “diploma frames” or “certificate frames”)
Local framing can be art in itself, and can definitely enhance art. As an example, I have a Vonnegut silkscreen print ("Black Heart") that I find quirky and endearing and love its origin -- but is a bit of a challenge to present in a way that doesn't dominate anything with which it shares a wall. I would have gone with a large mat and oversized frame to reduce the impact of some of the more... exotic... color choices; but the framing shop I worked with proposed a double frame with an outer black frame and an inner painted green wood frame that /exactly/ matches the color of the piece, and the result is stunning.
Apparently someone across the pond (in Europe?) didn't know the US doesn't use the A0 paper system.
And then, other people who knew the A0 paper system didn't realize the beauty of it using √2 ratio.
Weird thread there.
Need to make a bigger version? It scales so easily.
Anytime you see the US doing something different from the rest of the world, investigate to see who first invented and popularized it: it almost certainly came from outside the US. Whereas if there's some global standard that even the US uses, it probably got started in the US.
As is widely remarked the US does use metric where it makes sense to do so. It’s just mostly not consumer-facing.
Now, a holdout is the "Oficio" size, which created a lot of problems for us. This size is usually described in printer drivers as Fanfold or Long Bond, and it is very similar to U.S. Legal size, but one inch shorter in its length (8.5 × 13 in, 216 × 330 mm). South American paper mills often call it "Oficio 2". This was, and still is in many regards, the required format for all official bureaucratic and court paperwork.
This created a lot of trouble for us because in most Spanish localizations companies (example: Microsoft in MS Office) simply translated the "Legal" paper size as "Oficio". Then every secretary and clerk here selected it believing it is "our" Oficio, only to find that text was cropped at the bottom because that "Oficio" was in fact one inch longer than our format. This led to all kinds of manual (mis)formatting.
I think this format had a German origin and came to us through old Spanish practices, but I can't be sure.
Again, thankfully this is becoming a thing of the past since A4 is slowly becoming the standard...
EDIT: That paper size is also known as "US Government Legal" and "Foolscap" and according to Wikipedia is still in use in various parts of the world.
> F4 is a paper size 210 mm × 330 mm (8.27 in × 13.0 in).
Which is different than what GP states (216 mm x 330 mm).
Also, if you cut Tabloid in half you get letter, so it's not complete arbitrary.
Things I learned working on printers at HP
So if the drawing doesn't fit on a standard paper paper we just take the width of an A0 (841mm) and pick some arbitrary length. My personal limit is 200cm because then it becomes a bit impractical to handle. And if it really, really doesn't fit in the 841mm width, I'll take the edges of the 900mm that are usually cut off too instead of splitting the drawing awkwardly over two papers.
I saw both methods being taught at school when I was a child, though only with A2 or A3 size paper.
> Early pen plotters, e.g., the Calcomp 565 of 1959, worked by placing the paper over a roller that moved the paper back and forth for X motion, while the pen moved back and forth on a track for Y motion. The paper was supplied in roll form and had perforations along both edges that were engaged by sprockets on the rollers.
> In the 1980s, the small and lightweight HP 7470 introduced the "grit wheel" mechanism, eliminating the need for perforations along the edges, unlike the Calcomp plotters two decades earlier. The grit wheels at opposite edges of the sheet press against resilient polyurethane-coated rollers and form tiny indentations in the sheet. As the sheet is moved back and forth, the grit wheels keep the sheet in proper registration due to the grit particles falling into the earlier indentations, much like the teeth of two gears meshing. The pen is mounted on a carriage that moves back and forth in a line between the grit wheels, representing the orthogonal axis. These smaller "home-use" plotters became popular for desktop business graphics and in engineering laboratories
I think plotting on sheets was more common though.
Sadly, this meant that the paper would have natural curl to it, but it wasn't a big deal once you'd taped it to your drafting table with masking tape.
We also had to get a cheque scanner and a book of sample cheques shipped over to integrate that in to the software, that was a fun experience!
https://en.m.wikipedia.org/wiki/Sizing
And paper weight:
https://www.strathmoreartist.com/faq-full/paper-weight-what-...
And then you may feel inspired to acquire paper of all the different types and weights and sample how they perform with various media. Art supply stores, besides stocking premade pads and sketchbooks, often have a back area with drawers of loose paper and slightly more exotic things like acetate. However, while you can get something to a rough standard, you will never really get the same paper twice because the processes and available ingredients keep changing.
- The A0 sheet is a square metre
- A1 is half that, A2 half again etc.
- It's simple to calculate the weight of any particular A-series sheet.
This is (nowadays only rarely) useful when determining the postage. If I have 6 A4 pages of typical 80g/m² office paper to post, the weight is 6 × (80 / 2 / 2 / 2 / 2) = 30g.
Until recently, the cheapest national postal rate was for up to 50g, so this was a relevant calculation for the once-in-five-years I sent a multipage letter.
https://en.wikipedia.org/wiki/Photo_print_sizes
An older relative used to say "if a note is smaller than A4 it does not exist". I think it was from long experience of people losing important information when it was printed on a paper size smaller than A4. I try to keep that in mind whenever the frugal homunculus in me wants to print information in smaller formats to save on paper.
The standardisation of ISO paper sizes is nice, but it's also an annoying limitation when it comes to folding paper planes (if one wants to do it with small children that are not yet competent users of scissors), because it limits the amount of models that are viable.