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%
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.