Areas Of A Series Paper Sizes

The area of each of the A paper sizes are set by the A paper size definitions (see below). A0 is defined as having an area of 1 square metre, however the A paper size standard also specifies that each size is rounded to the nearest millimetre. Thus A0 is 841mm x 1189mm giving an area of 0.999949 square metres.

Theoretically the area of a sheet of paper of size An can be calculated as 1/2ⁿ m².

The following table gives theoretical areas compared with actual areas for each of the A paper sizes from 4A0 to A10.

Table of Theoretical and Actual Areas of A Paper Sizes

Size	Theoretical Area (sq m)	Actual Area (sq m)	Difference (sq m)	Difference (%)
4A0	4	3.999796	0.000204	0.0051%
2A0	2	1.999898	0.000102	0.0051%
A0	1	0.999949	0.000051	0.0051%
A1	0.5	0.499554	0.000446	0.0892%
A2	0.25	0.24948	0.00052	0.208%
A3	0.125	0.12474	0.00026	0.208%
A4	0.0625	0.06237	0.00013	0.208%
A5	0.03125	0.03108	0.00017	0.544%
A6	0.015625	0.01554	0.000085	0.544%
A7	0.0078125	0.00777	0.0000425	0.544%
A8	0.00390625	0.003848	0.00005825	1.4912%
A9	0.001953125	0.001924	0.000029125	1.4912%
A10	0.0009765625	0.000962	0.0000145625	1.4912%

At the smaller sizes (A8, A9 & A10) the discrepancy between the theoretical area of the sheet and the actual area is about 1.5%. Larger sizes have significantly lower differences between the theoretical area and the actual area.

A Series Paper Sizes Defined

The A series paper sizes are defined in ISO 216 by the following requirements:

The length divided by the width is 1.4142
The A0 size has an area of 1 square metre.
Each subsequent size A(n) is defined as A(n-1) cut in half parallel to its shorter sides.
The standard length and width of each size is rounded to the nearest millimetre.

Note: For reference the last item is there because the root 2 aspect ratio doesn't always give a whole number.