Let's take a look at the mathematics behind it
An Paper sizing.
The aspect ratio is
r = w/h from where
h is the longer side.
Now you want z. A1 should be half of A0, so the aspect ratio
We have the equation
r = w/h = 0.5*h/w = 0.5/r or
r^2 = 0.5
r is simply square root of 0.5 or in other words 0.70711.
Thus, the width (shorter side) is 0.70711 times the height (longer side).
A0 paper size has an area of 1 square meter. Thus, the longer side
h*h*r = 1 m2 or
h*h = sqrt(2) m2 or
h = sqrt(sqrt(2)) = 1.18920711500272 m, The A0 paper size is therefore 1.18920711500272 m × 0.840896415253715 m.
The A1 paper size is then 0.840896415253715 m × 0.594603557501360 m.
The A2 paper size is then 0.594603557501360 m × 0.420448207626857 m.
By rounding the numbers we get for A2 595 mm x 420 mm.
By rounding the numbers we get for A1 841 mm x 595 mm.
The reason why it is 594mm and not 595mm is because the default states are:
Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving and rounding off the area of the previous paper size
However, from the Wikipedia article on ISO 216 (the standard defining paper sizes A and B):
The tolerances specified in the standard are
- ± 1.5 mm (0.06 in) for dimensions up to 150 mm (5.9 in),
- ± 2 mm for lengths in the range of 150 to 600 mm and
- ± 3 mm (0.12 in) for all dimensions above 600 mm (23.6 in).
The difference is anyway within the specified tolerance.