When you stop and think about it, there are terms and measurements that we use on a regular basis but might not have any idea about where they come from. Today I’m going to chat a bit about two paper terms that I use all of the time but only recently took the time to actually learn about. So, buckle up and get ready to learn about the weights and measures of paper!

#### Paper Sizing

Growing up in the United States, I was never really exposed to international standard paper sizes. I feel like the only two sizes of paper I ever heard about were Letter and Legal sizes. Once I entered the world of fountain pens, I learned about the paper sizes that most of the world uses, specifically the A-sized papers. Most popular notebooks and notepads are either A4 or A5-sized. You’ll also see some with other sizes like A6 or even B-sized. What do all of these numbers and letters mean?

##### A Versus B

The size that most fountain pen users are familiar with is the A size. As I mentioned, most notebooks and paper we use comes in either A4 or A5 sizes. I’m not sure if they’re just a more pleasing aspect ratio to use or a more convenient size, but whatever the reason the A sizes are more dominant than the B sizes.

Comparing the two, A and B sizes have the same proportions (width-to-height ratio), but the B sizes are bigger than their A counterparts. This is because the base sheet for the B sizes is larger than the base sheet for the A sizes. I’ll talk more about the base sheet in a bit, but as long as you know that a B5 notebook is larger than an A5 notebook, we’re doing good.

##### What Do The Numbers Mean?

When I say “A5”, we now kind of know what the A means, so what does the 5 mean? Before I get to that, let me show you a neat trick that you may or may not already know about. If you take two A5 pieces of paper and lay them side by side (long edges touching), you will now have an A4-sized “sheet” of paper. It also works with two A6-sized pieces of paper. Put them together and you now have something that is A5 sized. It also works the other way. If you cut an A4-sized piece of paper in half, you now have two A5-sized pieces of paper.

All of this great geometry(?) comes from the fact that there is a base paper size that all paper is cut from. This base size is the 0 size, so either A0 or B0. As you can probably guess, the size of a B0 sheet of paper is larger than an A0 sheet of paper. An A0 sheet has an area of exactly 1 square meter, while a B0 sheet has an area of around 1.4 square meters.So how do we arrive at the other numbers? As I showed above, if you cut a sheet in half (say an A5), you get two sheets of the next smaller size (A6). Take it back to the first sheet and it will all make sense.

If you cut an A0 sheet in half, you will have two A1 sheets. Cut one of those A1 sheets in half, you’ll have two A2 sheets. You can keep cutting them in half until you get to A5, A6, A7… The numbers equal the number of cuts that have been made! An A0 has been cut 0 times, an A1 has been cut 1 time, and so on. So that means an A5 is obtained by cutting an A0 sheet in half 5 times.

- A0 = 0 cuts
- A1 = 1 cut
- A2 = 2 cuts
- A3 = 3 cuts
- A4 = 4 cuts
- A5 = 5 cuts

While I had always known the relationship between the smaller and larger pieces of paper, I had never actually thought about how the numbers originated. Learning this was quite the revelation for me! For people who grew up with the international system of paper sizes, is this something you already knew about or is this new info for you as well?

#### Paper Weight

Another phrase that gets used a lot when we talk about paper is gsm (sometimes written as g/m^2). You probably know that gsm stands for *grams per square meter* and typically gives you an idea of how thick the paper is. Have you ever actually thought about what that means, though? It literally tells you how many grams a square meter of paper weighs.

##### Experiment Time

I wanted to try this out and see if I could come up with a the gsm for some paper. I don’t have any A0 pieces of paper laying around, but I have a lot of A5 sheets. If I can get enough A5 sheets to create my own A0 sheet, I should be able to weigh them and see how many grams a square meter of paper weighs, right?

Let’s do a little math to see how many A5 sheets we’ll need.

- A0 paper = 1 square meter of paper = 10,000 square centimeters (100cm x 100cm)

and

- A5 paper = 14.8cm x 21.0cm = 310.8 square centimeters

so

- 10,000 sq cm / 310.8 sq cm/sheet = 32.17 sheets of A5 paper

It looks like if I weigh 32 sheets of A5 paper, we’ll get pretty darn close to 1 square meter of paper. So, weighing (in grams) 32 sheets of A5 paper will show me how many grams a square meter of that paper weighs, which is the gsm of that paper!

One thing to note is that since we know the relationship between the sizes of paper, we can multiply or divide as necessary to weigh other sizes of paper. For example, what if we want to weigh A4 sheets instead? Take the number of A5 sheets and divide by 2. That’s 16 sheets of A4 paper per square meter. You can figure this out for any size (not that you’d want or need to) by taking 2 to the power of the sheet size you have (2^sheet size).

- A0 – 2^0=1 sheet
- A1 – 2^1=2 sheets
- A2 – 2^2=4 sheets
- A3 – 2^3=8 sheets
- A4 – 2^4=16 sheets
- A5 – 2^5=32 sheets
- A6 – 2^6=64 sheets

Enough with the math. Let’s actually weigh some paper! I wanted to start with paper that I actually know the gsm for, just to see how accurate my kitchen scale is. Since Clairefontaine Triomphe comes in A5 sheets and says the gsm on the notepad, that’s what I started with.

According to Clairefontaine, their Triomphe paper weighs 90gsm. I took 32 sheets from my A5 notepad and headed to the kitchen. Making sure my kitchen scale was on a level surface and started at 0 grams, I weighed the 32 sheets of paper and saw this:

How about that! A square meter of 90 gsm paper weighs 89.5 grams. It works! Is that missing 0.5 grams the accuracy of my scale or maybe rounding by Clairefontaine? Maybe that extra 0.17 sheets of paper I rounded off? I’m going to guess my scale, but I wouldn’t be surprised if Clairefontaine rounded up a bit just for a nice, round number.

Now that we know it actually works to weigh the paper, let’s try some paper that I don’t actually know the weight of. Life Bank Paper is a fairly popular paper that doesn’t have a paper weight listed anywhere on the notepad, so that sounds like a great candidate. I took a guess when I wrote the review and said it’s around 90gsm. Let’s see how close I was.

Interesting! Bank paper weighs in at exactly 80gsm. When I feel it, it feels thicker than the Clairefontaine Triomphe, which weighs more. I guess that goes to show you that simply feeling the paper isn’t always the best way to guess the gsm. Looking around online, I see some places have it listed at 84.9 gsm. That’s a significant difference. But, I just realized that Bank paper is not exactly A5-sized. It’s smaller! I guess that wasn’t a very good paper to use as an example. Looks like I need to weigh one more type of paper that I know the weight of, just to see if the Clairefontaine was a fluke. G. Lalo Verge de France weighs in at 101gsm and the listed weight is 100gsm. I call that a success!#### Conclusions

I don’t know about you, but I really enjoyed learning about these commonly-used paper phrases. It’s hard to believe that I had been using them for years without really wondering how they came to be. After learning more about the international standard paper sizes, I am impressed by what an elegant system it is. It is also impressive how nicely it ties into paper weight. Should I be surprised that they are both based on the metric system? Probably not. I hope you learned something and found this post useful. If you have anything to add or requests for future posts similar to this one, please let me know!

## Comments 7

It’s worth noting that a lot of Japanese manufacturers will use JIS paper sizing for some or all of their products, which are subtly different from the international sizes. You often see “semi-B5” for example, which is JIS B5, but it isn’t always noted which standard they’re referring to.

Author

That’s good to know, Rick. I think I’ve seen that before, but can’t think of any that I have that say that. I’l keep an eye out for those.

Math nerd note: you don’t have to weigh exactly the right number of sheets, of course. You could calculate the surface area of your sheet (e.g. the non standard Bank paper) from its dimensions. It’s still a good idea to weigh multiple sheets together unless your kitchen scale has wondrous sensitivity and accuracy.

P.s. I did not know about the 1, 2, 3 cuts… And that A0 is exactly 1 square meter. Cool!

Author

Very true, Elaine. I didn’t trust the sensitivity of my kitchen scale for just one sheet, so decided to weigh a “full” A0 sheet.

I love your experiments. I see I’m not the only one who can’t pass up a rabbit hole.

Author

Glad you enjoyed it, Bob. Who doesn’t love a good rabbit hole? 🙂