Paper Sizes
Did you know that international paper sizes (like A3, A4, etc) are based on the square root of 2?
Because the square root of 2 has this cool property:
1 × √2 × √2 = 2
Which lets us have this:
So we can have sheets that have exactly the same proportions (their ratio of side lengths are the same) and also fit in each other perfectly:
Two A4s make an A3
and have the same proportions
This makes things really efficient:
- Don't have any A3? Tape two A4's together.
- Don't have any A5? Cut an A4 in half.
And because they have the same proportions, any artwork or document can be resized to fit on any sheet:
Another benefit is that you can print something out at 70% size and fit 2 pages side-by-side on just one sheet like this:
Why 70%? Because 1/√2 = 0.7071... which is close to 70%
A similar enlargement is √2 = 1.4142... which is close to 140%
Sizes
The popular A4 size is 210 mm wide by 297 mm high:
With a width of 210 the height is: 210 × √2 ≈ 297
Here are all the sizes cut from an A0 sheet (which has an area of 1.0 m2):
Lastly here are the official sizes:
| size | mm × mm | about the size of a | area | |
|---|---|---|---|---|
| A0 | 841 × 1189 | table top | 1.0 m2 | |
| A1 | 594 × 841 | 0.5 m2 | ||
| A2 | 420 × 594 | monitor | 0.25 m2 | |
| A3 | 297 × 420 | 0.125 m2 | ||
| A4 | 210 × 297 | writing sheet | 0.0624 m2 | |
| A5 | 148 × 210 | 0.0311 m2 | ||
| A6 | 105 × 148 | 0.0155 m2 | ||
| A7 | 74 × 105 | note | 0.00777 m2 | |
| A8 | 52 × 74 | 0.003848 m2 | ||
| A9 | 37 × 52 | 0.001924 m2 | ||
| A10 | 26 × 37 | stamp | 0.000962 m2 |
Note: you can think of the "A-number" as how many folds (or cuts-in-half) away from an A0 we are. So an A3 needs 3 folds of an A0, and so is ½×½×½ = 1/8th the size.
You may also like to read about Doubling Paper.