Did you recognize that international file sizes (like A3, A4, etc) are based on the square source of 2?

Because the square source of 2 has actually this cool property:

1 × √2 × √2 = 2

Which lets us have this:


So we have the right to have sheets the have exactly the very same proportions (their proportion of next lengths room the same) and also also fit in each various other perfectly:

Two A4s make an A3and have actually the very same proportions

This makes things really efficient:

Don"t have any type of A3? Tape two A4"s together.Don"t have any kind of A5? cut an A4 in half.

And because they have the same proportions, any type of artwork or paper can it is in resized come fit on any type of sheet:


Another benefit is the you have the right to print something out at 70% size and fit 2 pages side-by-side on simply one sheet like this:


Why 70%? because 1/√2 = 0.7071... i m sorry is close come 70%

A similar enlargement is √2 = 1.4142... which is close to 140%


The renowned A4 size is 210 mm large by 297 mm high:


With a broad of 210 the height is: 210 × √2 ≈ 297

Here space all the sizes cut from one A0 sheet (which has an area the 1.0 m2):


Lastly below are the main sizes:

size mm × mmabout the dimension of aarea
A0841 × 1189table top1.0 m2
A1594 × 8410.5 m2
A2420 × 594monitor0.25 m2
A3297 × 4200.125 m2
A4210 × 297writing sheet0.0624 m2
A5148 × 2100.0311 m2
A6105 × 1480.0155 m2
A774 × 105note0.00777 m2
A852 × 740.003848 m2
A937 × 520.001924 m2
A1026 × 37stamp0.000962 m2

Note: you deserve to think of the "A-number" together how numerous folds (or cuts-in-half) away from an A0 us are. Therefore an A3 demands 3 wrinkle of one A0, and also so is ½×½×½ = 1/8th the size.